A decision maker using the Analytic Hierarchy Process (AHP) could be consistent, and still provide no information in the resulting vector of priorities. An extreme example would be a pairwise comparison judgment matrix filled with 1s which is totally consistent under the various definitions of consistency, but has provided no information about the prioritization of alternatives resulting from the decision maker's judgments. In this paper, the quality of a consistent decision maker's judgments using the Analytic Hierarchy Process (...) is placed in the context of the entropy of the resulting vector of priorities. Indeed, it is the purpose of this paper to provide a formal definition of this notion ofentropy of a priority vector, and to provide a framework for a quantitative measurement of the information content of consistent pairwise comparison judgment matrices of a decision maker who is using the Analytic Hierarchy Process. We will prove that the entropy of the vector of priorities for consistent matrices follows a normal distribution and discuss some general considerations of this result. (shrink)

This chapter deals with matrices and algebraizability and their consequences, investigating in particular, the question of characterizability by finite matrices, as well as the algebraizability of (extensions of) mbC. Some negative results, in the style of the well-known Dugundji’s theorem for modal logics, are proved for several extensions of mbC.

We prove assorted properties of matrices over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{Z}_{2}}$$\end{document}, and outline the complexity of the concepts required to prove these properties. The goal of this line of research is to establish the proof complexity of matrix algebra. It also presents a different approach to linear algebra: one that is formal, consisting in algebraic manipulations according to the axioms of a ring, rather than the traditional semantic approach via linear transformations.

Despite being fairly powerful, finite non-deterministic matrices are unable to characterize some logics of formal inconsistency, such as those found between mbCcl and Cila. In order to overcome this limitation, we propose here restricted non-deterministic matrices (in short, RNmatrices), which are non-deterministic algebras together with a subset of the set of valuations. This allows us to characterize not only mbCcl and Cila (which is equivalent, up to language, to da Costa's logic C_1) but the whole hierarchy of da (...) Costa's calculi C_n. This produces a novel decision procedure for these logics. Moreover, we show that the RNmatrix semantics proposed here induces naturally a labelled tableau system for each C_n, which constitutes another decision procedure for these logics. This new semantics allows us to conceive da Costa's hierarchy of C-systems as a family of (non deterministically) (n+2)-valued logics, where n is the number of "inconsistently true" truth-values and 2 is the number of "classical" or "consistent" truth-values, for every C_n. (shrink)

This paper derives van der Waals interactions from M₃(ℂ) non-commutative algebra structure constants within the Cognitional Mechanics (CM) framework. Traditional London theory describes dispersion forces via polarizability and ionization energy in physical coordinates, leaving structural questions unanswered: why r⁻⁶ specifically, what is the geometric origin of C₆, and what is the algebraic meaning of polarizability. -/- CM reformulates these interactions in operational coordinates where London's "polarization" becomes off-diagonal operator components and "quantum fluctuations" represent temporal evolution of non-commutativity. The r⁻⁶ dependence (...) emerges not as a perturbative consequence but as a geometric necessity: it is the unique leading asymptotic term consistent with 4th-order non-commutative trace structure, dimensional reduction from su(3) to its off-diagonal subspace, and rotational symmetry in 3D physical space. This form is dictated by the algebra of M₃(ℂ)—it cannot be obtained by fitting experimental data. -/- This structural derivation of an interaction law complements the companion algebraic derivations of α⁻¹, μ, and αG within the same framework, where fundamental physical constants emerge from M₃(ℂ) with zero free parameters. Taken together, these results establish that M₃(ℂ) is not a fitting tool but an axiomatic structure from which both the forms of physical laws and the values of physical constants follow as necessary consequences. -/- Molecular electronic states are represented as operators F ∈ M₃(ℂ) with interaction energy defined via commutator traces. The C₆ coefficient is computed from su(3) structure constants (Gell-Mann matrices) with explicit calculation procedure provided. Ultra-precision implementation incorporates effective nuclear charge with exchange-correlation corrections (Perdew 1996), distance-dependent shielding functions evaluated at van der Waals equilibrium distance, Dirac first-order relativistic corrections (0.032–0.29% for Ar–Xe), numerical Hartree-Fock orbitals from NIST Atomic Spectra Database with adaptive Gauss-Kronrod quadrature achieving 10⁻⁸ accuracy, and higher-order dispersion terms (C₈, C₁₀ from rank-4 structure constants). Final results: He–He (0.07% error), Ne–Ne (0.13%), Ar–Ar (0.02%), Kr–Kr (0.15%), Xe–Xe (0.21%), average 0.12% error, matching ab initio CCSD(T) benchmarks. -/- Results demonstrate quantitative correspondence between operational constraints and physical measurements, establishing that intermolecular interactions arise from geometric state space constraints rather than quantum fluctuations per se. All numerical calculations are fully specified via explicit formulas ensuring complete reproducibility without external code. The framework extends London theory as a valid physical coordinate description while providing higher-level operational structure, unifying chemistry as non-commutative operational programs executed on material hardware. Future applications include covalent/ionic bonding operational descriptions, chemical kinetics formulation, and connection to emergent gauge structures in the CM-GUT framework. (shrink)

The aim of this article is to generalize logics of formal inconsistency (LFIs) to systems dealing with the concept of incompatibility, expressed by means of a binary connective. The basic idea is that having two incompatible formulas to hold trivializes a deduction, and as a special case, a formula becomes consistent (in the sense of LFIs) when it is incompatible with its own negation. We show how this notion extends that of consistency in a non-trivial way, presenting conservative translations (...) for many simple LFIs into some of the most basic logics of incompatibility, thereby evidencing in a precise way how the notion of incompatibility generalizes that of consistency. We provide semantics for the new logics, as well as decision procedures, based on restricted non-deterministic matrices. The use of non-deterministic semantics with restrictions is justified by the fact that, as proved here, these systems are not algebraizable according to Blok-Pigozzi nor are they characterizable by finite Nmatrices. Finally, we briefly compare our logics to other systems focused on treating incompatibility, specially those pioneered by Brandom and further developed by Peregrin. (shrink)

Synesthetes can be distinguished from nonsynesthetes on a variety of experimental tasks because their concurrent synesthetic experiences can affect task performance if these experiences match or conflict with some aspect of the stimulus. Here, we tested grapheme‐color synesthetes and nonsynesthetic control participants using a novel perceptual similarity task to assess whether synesthetes’ concurrent color experiences influence perceived grapheme similarity. Participants iteratively arranged graphemes and, separately, their associated synesthetic colors in a display, such that similar items were placed close together and (...) dissimilar items further apart. The resulting relative inter‐item distances were used to calculate the pair‐wise (dis)similarity between items in the set, and thence to create separate perceptual representational dissimilarity matrices (RDMs) for graphemes and colors, on an individual basis. On the assumption that synesthetes’ similarity judgments for graphemes would be influenced by their concurrent color experiences, we predicted that grapheme and color RDMs would be more strongly correlated for synesthetes than nonsynesthetes. We found that the mean grapheme‐color RDM correlation was indeed significantly higher in synesthetes than nonsynesthetes; in addition, synesthetes’ grapheme‐color RDM correlations were more likely to be individually statistically significant, even after correction for multiple tests, than those of nonsynesthetes. Importantly, synesthetes’ grapheme‐color RDM correlations scaled with the consistency of their grapheme‐color associations as measured by their Synesthesia Battery (SB) scores. By contrast, the relationship between SB scores and grapheme‐color RDM correlations for nonsynesthetes was not significant. Thus, dissimilarity analysis quantitatively distinguished synesthetes from nonsynesthetes, in a way that meaningfully reflects a key aspect of synesthetic experience. (shrink)

The Riemann Hypothesis (RH) asserts that every non-trivial zero of the Riemann zeta function ζ(s) satisfies Re(s) = 1/2. This paper presents a structural analysis of RH organized in two coupled registers, with five distinct contributions. The first three contributions are technical: an operator-theoretic reformulation, a precise localization of the analytic obstruction, and a theoretical-physics universality analysis. The fourth contribution is a list of five falsifiable predictions. The fifth contribution is an explicit conditional verdict on what these technical contributions establish (...) about RH under different mathematical ontologies (Platonist versus naturalist or structural-physical). The paper does not assert which ontology is correct; it makes the conditional verdict explicit and lets the reader adjudicate based on philosophical premises. The first contribution is a geometric reformulation. The Berry-Keating Hilbert-Polya operator H = −i(x d/dx + 1/2), which possesses a one-parameter family of self-adjoint extensions on the additive Lebesgue space L²(ℝ+, dx) and therefore lacks a canonical unique realization, is shown to be unitarily equivalent to the dilation generator H′ = −i x d/dx on the multiplicative Hilbert space H_mult = L²(ℝ+*, dx/x) equipped with the Haar measure of the dilation group (ℝ+*, ×). On this geometry, which is the natural Hilbert space whose inner product is invariant under the multiplicative symmetry group of the integers, H′ is uniquely self-adjoint by Stone’s theorem with no boundary parameter freedom. The deficiency-index ambiguity that plagued the additive realization disappears entirely. The second contribution is a precise characterization of the analytic obstruction. A regularized Cauchy-Stieltjes functional G_ε(z) constructed from −ζ′/ζ is shown to vanish unconditionally for ε > 1/2 by Euler-product non-vanishing and Cauchy contour deformation. The Riemann Hypothesis is then shown to be equivalent to the boundary-value membership of −(ζ′/ζ)(1/2 + iτ) in the Hardy space H²(lower half τ-plane). The precise gap that prevents extending the unconditional vanishing of G_ε(z) from ε > 1/2 down to ε → 0+ is identified explicitly: the odd-part Fourier structure of −ζ′/ζ on the critical line is not constrained by the functional equation alone, and three natural closure routes (Paley-Wiener extension, ε-constancy, Sobolev weak-star limit) are each shown to be circular without additional analytic input. This is the precise mathematical location of the open obstruction; closing it remains the millennium prize problem. The third contribution is a theoretical universality analysis. The Riemann zeta function admits exact identification as the grand canonical partition function of an idealized prime field, with −ζ′/ζ as the response function and the critical line Re(s) = 1/2 as the equilibrium line. Four orthogonal independent measurements identify the equilibrium universality class of the prime field on the critical line: Selberg’s variance theorem (fluctuation exponent), the Montgomery-Odlyzko correspondence with GUE statistics (symmetry-class exponent β = 2 corresponding to self-adjoint Hamiltonians with broken time-reversal symmetry), the direct localization of 10^{13} verified zeros (order-parameter localization exponent), and the prime counting envelope √x log x (response-amplitude exponent). The four exponents jointly identify the universality class as that of a self-adjoint Hamiltonian with broken time-reversal symmetry. The universality identification is consistent with RH and provides strong heuristic support: RH is the natural prediction of the universality class, and any departure from RH would require the prime field to violate exponent universality. The universality analysis does not constitute a proof of RH. Universality is inductive evidence based on observed exponent values; it does not bind mathematical truth in the deductive sense. The paper is explicit about this distinction throughout. Five physical-mathematical predictions are stated, each labeled by its epistemic status. Four predictions are falsifiable consequences of the operator reformulation and universality analysis. One prediction, a heuristic correlation between the GUE algebra and the effective Majorana mass m_ββ in neutrinoless double beta decay, is marked explicitly as conjectural: a numerical bridge between the GUE structure and specific PMNS lepton-mixing matrices is not derived in this paper, and the correlation is included as a speculative anchor for future investigation rather than as a logical consequence of the universality analysis. The contributions of this paper are: a clean reformulation of RH on its natural multiplicative geometry; a precise localization of the analytic obstruction; a theoretical-physics universality analysis of the prime field; and an explicit conditional verdict on what these contributions establish under different mathematical ontologies. Under strict mathematical Platonism, the paper provides operator-theoretic reformulation, precise obstruction localization, and theoretical-physics universality support, with strict-register proof of RH remaining open at the precise Fourier component identified herein. Under naturalist or structural-physical mathematical ontology (Section 8.4), the multiaxial verification of Sections 2-7 constitutes a proof of RH adequate to the multi-mode object the prime distribution is, with the strict-register projection of that proof remaining incomplete at the same Fourier component. The paper takes no position on which ontology is correct; it states the conditional verdict explicitly and leaves the philosophical adjudication to the reader. (shrink)

Any scientific theory in the natural sciences is an artificial, complex, and abstract construct, consisting of many components (ingredients, constituents, structural elements). It is developed by scientists to gain and comprehend experimentally verified new knowledge about its domain of study. It is helpful to distinguish between two meanings of the term “theory”. The application domains of specific theories include particular kinds of realities. Examples include Newton’s celestial mechanics and various classical, quantum, and quantum-relativistic theories of gases, fluids, molecules, atoms, and (...) elementary particles (theory of atomic spectra, Bohr’s atomic theory, Planck’s quantum theory of black-body radiation, quantum theory of the hydrogen atom, quantum relativistic theory of black holes, etc.). The names of specific theories usually include the names of the types of realities they study. Abstract theories serve as general frameworks for a group of specific theories of the same kind (in particular, macroscopic, microscopic, or megascopic kinds). Examples of abstract theories are classical mechanics, quantum mechanics, and the theories of relativity, which act as common frameworks for concrete theories from classical, quantum, and quantum-relativistic physics, respectively. The article compares concepts of complex structure and development of specific theories with notions of structure and development of automobiles. Such a comparison is more useful and heuristic than analyzing theories in terms of paradigms or interdisciplinary matrices, which, in any case, are not part of scientific theories. The work employed methods of terminological and content analysis of the original text of Newton’s Principia and the comparative method. The aim is to consider Newtonian celestial mechanics as the last universal common ancestor (LUCA) of all particular specific theories. The role of Euclidean geometry as a potential LUCA for abstract theories will be explored in another article. An analysis of Newton’s Principia showed that celestial mechanics encompasses a wider range of components than physicists and philosophers of science typically consider part of a theory. Main results. Taking this theory as a prototype for all specific theories, the article demonstrates the existence of sixteen types of components within it. Components of the same type form a specific subsystem of the theory as a polysystem. In any specific scientific theory, all these subsystems together constitute an interconnected whole that is necessary but not sufficient for generating new knowledge. Conclusions. The article is of a historical-scientific and theoretical-cognitive nature, and the results obtained can be applied in research on the history and philosophy of science, as well as in the teaching of natural science disciplines. (shrink)

Recent AI regulations require deployers of high-risk systems to assess impacts on values like fundamental rights and other legally protected interests. However, existing practice-most notably Fundamental Rights Impact Assessments (FRIAs) under the EU AI Actremains mostly limited to qualitative guidelines. As a result, risk evaluation can be inconsistent and highly variable across assessments. To address this issue, we propose a reference model for value-impact assessment that specifies the core components that any more detailed formalization should incorporate. The model builds on (...) a classical risk paradigm, integrating distinct measures for hazard, exposure, vulnerability, and response or mitigation. We use the EU AI Act's FRIA as a reference case for applying the model to AI risk assessments. The model provides three especially salient recommendations. First, it rejects purely ordinal risk matrices in favor of geometric or ratio-scaled severity ladders, enabling the coherent calculation of expected risk. Second, in analyzing risk mitigation measures, it requires separate estimates of efficacy and reliability, with explicit success criteria and scope conditions that allow for dynamic updating. Third, the model operationalizes regulatory precaution, or risk appetite, through the integration of tail-sensitive risk metrics (e.g., Conditional Value-at-Risk). This lets regulators give appropriate weight to low-probability, high-impact (or catastrophic) harms to fundamental rights without distorting ordinary expected-risk calculations. The result is a structured foundation for more consistent value-impact assessments. (shrink)

The paper studies the containment companion of a logic \. This consists of the consequence relation \ which satisfies all the inferences of \, where the variables of the conclusion are contained into those of the set of premises, in case this is not inconsistent. In accordance with the work started in [10], we show that a different generalization of the Płonka sum construction, adapted from algebras to logical matrices, allows to provide a matrix-based semantics for containment logics. In (...) particular, we provide an appropriate completeness theorem for a wide family of containment logics, and we show how to produce a complete Hilbert style axiomatization. (shrink)

There are two foundational, but not fully developed, ideas in paraconsistency, namely, the duality between paraconsistent and intuitionistic paradigms, and the introduction of logical operators that express metalogical notions in the object language. The aim of this paper is to show how these two ideas can be adequately accomplished by the logics of formal inconsistency and by the logics of formal undeterminedness. LFIs recover the validity of the principle of explosion in a paraconsistent scenario, while LFUs recover the validity of (...) the principle of excluded middle in a paracomplete scenario. We introduce definitions of duality between inference rules and connectives that allow comparing rules and connectives that belong to different logics. Two formal systems are studied, the logics mbC and mbD, that display the duality between paraconsistency and paracompleteness as a duality between inference rules added to a common core—in the case studied here, this common core is classical positive propositional logic. The logics mbC and mbD are equipped with recovery operators that restore classical logic for, respectively, consistent and determined propositions. These two logics are then combined obtaining a pair of LFI and undeterminedness, namely, mbCD and mbCDE. The logic mbCDE exhibits some nice duality properties. Besides, it is simultaneously paraconsistent and paracomplete, and able to recover the principles of excluded middle and explosion one at a time. The last sections offer an algebraic account for such logics by adapting the swap structures semantics framework of the LFIs the LFUs. This semantics highlights some subtle aspects of these logics, and allows us to prove decidability by means of finite nondeterministic matrices. (shrink)

Paradefinite logics are logics that can be used for handling contradictory or partial information. As such, paradefinite logics should be both paraconsistent and paracomplete. In this paper we consider the simplest semantic framework for introducing paradefinite logics. It consists of the four-valued matrices that expand the minimal matrix which is characteristic for first degree entailments: Dunn–Belnap matrix. We survey and study the expressive power and proof theory of the most important logics that can be developed in this framework.

The paper essentially shows that the paraconsistent logicDR satisfies the depth relevance condition. The systemDR is an extension of the systemDK of [7] and the non-triviality of a dialectical set theory based onDR has been shown in [3]. The depth relevance condition is a strengthened relevance condition, taking the form: If DR- AB thenA andB share a variable at the same depth, where the depth of an occurrence of a subformulaB in a formulaA is roughly the number of nested ''s (...) required to reach the occurrence ofB inA. The method of proof is to show that a model structureM consisting of {M 0, M1,..., M}, where theM i s are all characterized by Meyer''s 6-valued matrices (c. f, [2]), satisfies the depth relevance condition. Then, it is shown thatM is a model structure for the systemDR. (shrink)

Initial Judgment of Solvability (iJOS) is a metacognitive judgment that reflects solvers’ first impression as to whether a problem is solvable. We hypothesized that iJOS is inferred by combining prior expectations about the entire task with heuristic cues derived from each problem’s elements. In two experiments participants first provided quick iJOSs for all problems, then attempted to solve them. We manipulated expectations by changing the proportion of solvable problems conveyed to participants, 33%, 50%, or 66%, while the true proportion was (...) the 50% for all. In Experiment 1 we used the non-verbal Raven’s matrices and examined nameability as the element-based heuristic cue. Unsolvable matrices were generated by switching locations of elements in original Raven’s matrices. In Experiment 2 we used the verbal Compound Remote Associate (CRA) problems and examined word’s frequency in the language as the element-based heuristic cue. Unsolvable CRAs were random word triads from the same word pool. The results were consistent in suggesting that quick iJOS integrates prior expectations and experience-based heuristic cues. Notably, iJOS was predictive for the subsequent solving attempt only for Raven’s matrices. (shrink)

This article gives mathematical pseudocodes for large language model training based on a dataset from a corpus, inference, and chat with possibly lengthy human prompts and generated replies. It introduces the concepts of “microlect" and “resonantcommunity." Most generally, a microlect is a specialized behavioral "language" consisting of expressions called "cores" built upon units called "keys." It is a minimal and adequate representation of a mental model. An expression may resonate more or less with a mental model. A resonant- community is (...) a set of human beings whose expressions resonate with one another. These notions are helpful in understanding of how the “frozen matrices" of a large language model are a conduit for resonance between human-beings and a zeitgeist represented in a corpus. The primary objectives are to encapsulate the functionality of large language models in a succinct technical representation, and to explain how this functionality connects human beings to their ambient cultural zeitgeist as represented in a textual corpus. The research draws on relevant literature in psychology, linguistics, mathematics, physics, and software engineering. The significance of the research is to embed the explanation in a perspective on the entirety of human expressiveness. The study can provide valuable insights based on resonances between human beings among themselves and with computing machines. (shrink)

Involutive Stone algebras were introduced by R. Cignoli and M. Sagastume in connection to the theory of $n$-valued Łukasiewicz–Moisil algebras. In this work we focus on the logic that preserves degrees of truth associated to S-algebras named Six. This follows a very general pattern that can be considered for any class of truth structure endowed with an ordering relation, and which intends to exploit many-valuedness focusing on the notion of inference that results from preserving lower bounds of truth values, and (...) hence not only preserving the value $1$. Among other things, we prove that Six is a many-valued logic that can be determined by a finite number of matrices. Besides, we show that Six is a paraconsistent logic. Moreover, we prove that it is a genuine Logic of Formal Inconsistency with a consistency operator that can be defined in terms of the original set of connectives. Finally, we study the proof theory of Six providing a Gentzen calculus for it, which is sound and complete with respect to the logic. (shrink)

We introduce Pura Vida Neutrosophic Algebra, an algebraic structure consisting of neutrosophic numbers equipped with two binary operations namely addition and multiplication. The addition can be calculated sometimes with the function min and other times with the max function. The multiplication operation is the usual sum between numbers. Pura Vida Neutrosophic Algebra is an extension of both Tropical Algebra (also known as Min-Plus, or Min-Algebra) and Max-Plus Algebra (also known as Max-algebra). Tropical and Max-Plus algebras are algebraic structures included in (...) semirings and their operations can be used in matrices and vectors. Pura Vida Neutrosophic Algebra is included in Neutrosophic semirings and can be used in Neutrosophic matrices and vectors. (shrink)

If the density matrix is treated as an objective description of individual systems, it may become possible to attribute the same objective significance to statistical mechanical properties, such as entropy or temperature, as to properties such as mass or energy. It is shown that the de Broglie--Bohm interpretation of quantum theory can be consistently applied to density matrices as a description of individual systems. The resultant trajectories are examined for the case of the delayed choice interferometer, for which Bell (...) [Int. J. Quantum chem. 155--159, (1980)] appears to suggest that such an interpretation is not possible. Bell’s argument is shown to be based upon a different understanding of the density matrix to that proposed here. (shrink)

An important part of the theory of algebraizable sentential logics consists of studying the algebraic semantics of these logics. As developed by Czelakowski, Blok, and Pigozzi and Font and Jansana, among others, it includes studying the properties of logical matrices serving as models of deductive systems and the properties of abstract logics serving as models of sentential logics. The present paper contributes to the development of the categorical theory by abstracting some of these model theoretic aspects and results from (...) the level of sentential logics to the level of π-institutions. (shrink)

Following Birkhoff and von Neumann, quantum logic has traditionally been based on the lattice of closed linear subspaces of some Hubert space, or, more generally, on the lattice of projections in a von Neumann algebra A. Unfortunately, the logical interpretation of these lattices is impaired by their nondistributivity and by various other problems. We show that a possible resolution of these difficulties, suggested by the ideas of Bohr, emerges if instead of single projections one considers elementary propositions to be families (...) of projections indexed by a partially ordered set C(A) of appropriate commutative subalgebras of A. In fact, to achieve both maximal generality and ease of use within topos theory, we assume that A is a so-called Rickart C*-algebra and that C(A) consists of all unital commutative Rickart C*-subalgebras of A. Such families of projections form a Hey ting algebra in a natural way, so that the associated propositional logic is intuitionistic: distributivity is recovered at the expense of the law of the excluded middle. Subsequently, generalizing an earlier computation for n x n matrices, we prove that the Heyting algebra thus associated to A arises as a basis for the internal Gelfand spectrum (in the sense of Banaschewski-Mulvey) of the "Bohrification" A̱ of A, which is a commutative Rickart C*-algebra in the topos of functors from C(A) to the category of sets. We explain the relationship of this construction to partial Boolean algebras and Bruns-Lakser completions. Finally, we establish a connection between probability measures on the lattice of projections on a Hubert space H and probability valuations on the internal Gelfand spectrum of A̱ for A = B(H). (shrink)

We study logics determined by matrices consisting of a De Morgan lattice with an upward closed set of designated values, such as the logic of non‐falsity preservation in a given finite Boolean algebra and Shramko's logic of non‐falsity preservation in the four‐element subdirectly irreducible De Morgan lattice. The key tool in the study of these logics is the lattice‐theoretic notion of an n‐filter. We study the logics of all (complete, consistent, and classical) n‐filters on De Morgan lattices, which (...) are non‐adjunctive generalizations of the four‐valued logic of Belnap and Dunn (of the three‐valued logics of Priest and Kleene, and of classical logic). We then show how to find a finite Hilbert‐style axiomatization of any logic determined by a finite family of prime upsets of finite De Morgan lattices and a finite Gentzen‐style axiomatization of any logic determined by a finite family of filters on finite De Morgan lattices. As an application, we axiomatize Shramko's logic of anything but falsehood. (shrink)

Why are quantum correlations so puzzling? A standard answer is that they seem to require either nonlocal influences or conspiratorial coincidences. This suggests that by embracing nonlocal influences we can avoid conspiratorial fine-tuning. But that’s not entirely true. Recent work, leveraging the framework of graphical causal models, shows that even with nonlocal influences, a kind of fine-tuning is needed to recover quantum correlations. This fine-tuning arises because the world has to be just so as to disable the use of nonlocal (...) influences to signal, as required by the no-signaling theorem. This places an extra burden on theories that posit nonlocal influences, such as Bohmian mechanics, of explaining why such influences are inaccessible to causal control. I argue that Everettian Quantum Mechanics suffers no such burden. Not only does it not posit nonlocal influences, it operates outside the causal models framework that was presupposed in raising the fine-tuning worry. Specifically, it represents subsystems with density matrices instead of random variables. This allows it to sidestep all the results (including EPR and Bell) that put quantum correlations in tension with causal models. However, this doesn’t mean one must abandon causal reasoning altogether in a quantum world. When decoherence is rampant and there’s no controlled entanglement, Everettian Quantum Mechanics licenses our continued use of standard causal models. When controlled entanglement is present---such as in Bell-type experiments---we can employ recently-proposed quantum causal models that are consistent with Everettian Quantum Mechanics. We never need invoke any kind of non-local influence or any kind of fine-tuning. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Haiti Can't BreatheNéhémy Pierre-Dahomey (bio)Translated by David F. BellI'm not particularly familiar with recent politics in Haiti. Nor, as it were, with the contemporary history of the country. In some sense, the difference between recent politics and contemporary history is rather delicate. History would be the most profound social, political, and economic points of contention behind the daily lives of a population under siege. Not simply those talked about (...) while people travel in public transportation (Haitians talk a lot while in public transportation), but also the interpretive matrices mobilized to speak about these problems. As for current events, they are the province of newspaper headlines, those front pages and editorial pages most often read and shared, the public opinion machine.Of course, a few snippets of news come to me: the rise of kidnapping, political instability, the opposition declaring that the presidential mandate has ended, a government sponsored referendum to change the constitution, upcoming elections. As I write this piece (summer 2021), armed banditry is rife in many working-class neighborhoods. There are victims by the dozens nearly every day.As I was asking myself how best to express the bicentennial dyspnea of the Haitian people, I learned about the assassination of the president of the Republic in his private residence.Haiti could not breathe. Now it is suffocating.I recently published a novel entitled Combats (March 2021) in which the characters live in a nineteenth-century rural setting. They experience the full force of the first consequences provoked by the infamous independence debt, well understood by Haitians and analyzed by international specialists such as David Graeber and Thomas Piketty.After its independence in 1804, Haiti was not accepted into the concert of nations. The country, founded by hordes of previously enslaved Blacks and by freed Mulattos, was a bad example, a model not to be emulated so geographically near a slave society, the United States, and the Antilles belonging to France. No economic power, that is, no white country defining itself as such, recognized the independence of the new Black, abolitionist, and egalitarian population. The isolation of Haiti thus began at the very moment of its foundation. [End Page 165]In a vain attempt to escape the embargo and to construct a collective destiny at the international level, Haiti accepted a colossal debt imposed on it by France. Charles X, king of France and Navarre, forced Jean-Pierre Boyer, supreme leader of the Haitian nation, to assume the responsibility for a ransom of 120 million francs. The economist Thomas Piketty calculates that this was equivalent to 28 billion euros in today's currency. David Graeber, in his Debt: The First 500 Years, considers it to be the most egregious debt in history. In truth, for Haitians, this strange transaction consisted in buying lands they had already conquered in their independence struggle, having taken them from the previous colonial settlers representing the French state.Since the previously emancipated ancestors were considered the colonial settlers' property, Haitians, under threat from the French army, assumed the weight of this debt, which really consisted in purchasing—from their previous torturers—their very persons and those of their grandparents. In other words, after the war of independence, begun by Black Maroons as soon as they arrived on the island of Haiti, pursued by Toussaint Louverture against slavery, brought successfully to a conclusion by Jean Jacques Dessalines through victorious military battles (November 1803 at Vertières, for example), after this long road toward emancipation, France, supported by all the foreign powers of the period, extracted from Haiti recognition of the debt in 1826, that is, during the first half of the nineteenth century, at the very moment when the independent countries of the world were beginning to undergo a massive industrialization.Haiti clearly missed out on this entrance into the industrial age of the steam engine. It remained an "essentially agricultural" country because every year it had to pay debt service—including interest—every year until the second half of the 20th century!Like many others I saw the images of the white man, Derek Chauvin, resting his knee on George Floyd's neck for eight... (shrink)

It is well known that every propositional logic which satisfies certain very natural conditions can be characterized semantically using a multi-valued matrix ([Los and Suszko, 1958; W´ ojcicki, 1988; Urquhart, 2001]). However, there are many important decidable logics whose characteristic matrices necessarily consist of an infinite number of truth values. In such a case it might be quite difficult to find any of these matrices, or to use one when it is found. Even in case a logic does (...) have a finite characteristic matrix it might be difficult to discover this fact, or to find such a matrix. The deep reason for these difficulties is that in an ordinary multi-valued semantics the rules and axioms of a system should be considered as a whole, and there is no method for separately determining the semantic effects of each rule alone. (shrink)

There are two foundational, but not fully developed, ideas in paraconsistency, namely, the duality between paraconsistent and intuitionistic paradigms, and the introduction of logical operators that express meta-logical notions in the object language. The aim of this paper is to show how these two ideas can be adequately accomplished by the Logics of Formal Inconsistency (LFIs) and by the Logics of Formal Undeterminedness (LFUs). LFIs recover the validity of the principle of explosion in a paraconsistent scenario, while LFUs recover the (...) validity of the principle of excluded middle in a paracomplete scenario. We introduce definitions of duality between inference rules and connectives that allow comparing rules and connectives that belong to different logics. Two formal systems are studied, the logics mbC and mbD, that display the duality between paraconsistency and paracompleteness as a duality between inference rules added to a common core– in the case studied here, this common core is classical positive propositional logic (CPL + ). The logics mbC and mbD are equipped with recovery operators that restore classical logic for, respectively, consistent and determined propositions. These two logics are then combined obtaining a pair of logics of formal inconsistency and undeterminedness (LFIUs), namely, mbCD and mbCDE. The logic mbCDE exhibits some nice duality properties. Besides, it is simultaneously paraconsistent and paracomplete, and able to recover the principles of excluded middle and explosion at once. The last sections offer an algebraic account for such logics by adapting the swap-structures semantics framework of the LFIs the LFUs. This semantics highlights some subtle aspects of these logics, and allows us to prove decidability by means of finite non-deterministic matrices. (shrink)

Collecting human similarity judgments is instrumental to measuring and modeling neurocognitive representations and has been made more efficient by the multi-arrangement task. While this task has been tested for collecting semantic similarity judgments, it is unclear whether it also lends itself to phonological and orthographic similarity judgments of words. We have extended the task to include these lexical modalities and compared the results between modalities and against computational models. We find that similarity judgments can be collected for all three modalities, (...) although word forms were considered more difficult to sort and resulted in less consistent inter- and intra-rater agreement than semantics. For all three modalities we can construct stable group-level representational similarity matrices. However, these do not capture significant idiosyncratic similarity information unique to each participant. We discuss the potential underlying causes for differences between modalities and their effect on the application of the multi-arrangement task. (shrink)

In 1909, Peirce recorded in a few pages of his logic notebook some experiments with matrices for three-valued propositional logic. These notes are today recognized as one of the first attempts to create non-classical formal systems. However, besides the articles published by Turquette in the 1970s and 1980s, very little progress has been made toward a comprehensive understanding of the formal aspects of Peirce's triadic logic (as he called it). This paper aims to propose a new approach to Peirce's (...) matrices for three-valued propositional logic. We suggested that his logical matrices give rise to three different systems, one of them - which we called P3 - is an original and non-explosive logic. Besides that, we will show that the P3 system can easily be transformed into paraconsistent and paracomplete calculi, adding to it, respectively, unary operators of consistency and intuitionistic negation. We conclude with a discussion about philosophical motivations. (shrink)

Nilpotent Minimum logic (NML) is a substructural algebraizable logic that is a distinguished member of the family of systems of Mathematical Fuzzy logic, and at the same time it is the axiomatic extension with the prelinearity axiom of Nelson and Markov’s Constructive logic with strong negation. In this paper our main aim is to characterize and axiomatize paraconsistent variants of NML and its extensions defined by (sets of) logical matrices over linearly ordered NM-algebra with lattice filters as designated values, (...) with special emphasis on those that only exclude the falsum truth-value, called non-falsity preserving logics. We also consider turning these non-falsity preserving logics into Logics of Formal Inconsistency by expanding them with a consistency operator, and we axiomatize them as well. Finally, we provide a full description of the logics defined by finite products of matrices over finite NM-chains. (shrink)

Prof. Dhanjoo Ghista about the book: This book constitutes the fascinating work of Dr. Hans-Joachim Rudolph to portray the concept of Microvita in a physics and mathematical format that can be studied objectively. It offers a smooth integration of Microvita (units of consciousness) into a well-grounded scientific scenario, consistent with the equations of Newton, Maxwell, Einstein, and Schrödinger. So what has Dr. Rudolph carried out? To explain the mind-body problem, he has structured a universal grid, made of the cognitive (...) and operative aspects of the supreme causal factor, with its lattice width in the range of Planck length. This grid can release 2x2 matrices of primary matter as well as complex 4x4 matrices containing the key qualities of elementary particles. By means of modified positive or negative creation operators, particles can be produced,which contain imaginary representations of the opposite qualities, thereby modeling the phenomenon of quantum entanglement, which provides the basis of our interconnectedness with all beings. Let us now enter the arena of human propensities and reincarnation—which is the prime concern of all of us: We postulate that neuronal assemblies are quantum objects, susceptible to a Quantum Zeno-like effect. Their electrical activities are transient and instable, but they can be stabilized by the production and annihilation of quasiparticles at/for defined frequencies (μ) and durations (t), which is, in turn, controlled by sets of synchronized Microvita (अm). Neuronal assemblies representing human propensities can also be controlled by Microvita. In this regard, Microvita meditation can help to attain higher dimensional attributes by energization of the chakras. Additionally, it can assist in enabling humans to change their internal state to help fulfill their inner longings and unfulfilled samskaras. In the process of metempsychosis (transmigration of the soul), the related sets of Microvita can exist for some time at the borderline between the physical and the cosmic world. Thereafter, they may enter a newly born child, consequently taking control over the development and expression of its propensities. If a suitable body is not available, such sets of Microvita may also align themselves with aerial and luminous factors, thereby creating what has been called ‘luminous bodies’. These enlightened luminous beings (or devayoniis, described in common parlance as angels) can conceivably find fulfillment in helping humans to progress in their journey to the luminous world. So it can be seen that Microvita can play a distinctive role in guiding human’s life journey towards its cosmic abode. I greatly complement Hans-Joachim Rudolph for this book, which can invoke interest of scientists to explore and discover the science of Microvita, while also bringing Microvita into their personal lives to reach their cosmic destination. (shrink)

Peut-on, comme l'a pensé Sartre, construire une philosophie concrète qui répudie les abstractions de la métaphysique en étendant la réduction phénoménologique au domaine entier de l'expérience humaine? Et peut-on fonder une telle démarche sur l'évidence de l'existence, promue au rang de certitude apodictique? Pour conduire cette enquête il a été nécessaire d'examiner la conscience, le monde, autrui, l'expérience morale et la vie politique, en suivant l'ordre d'apparition de ces thèmes dans l'œuvre philosophique sartrienne qui, depuis la Transcendance de l'ego jusqu'à (...) la Critique de la raison dialectique, forme un système cohérent mais foncièrement paradoxal et par là même, déroutant. Les paradoxes Sartriens solidarisent des propositions contradictoires, désarticulent les réalités considérées et les privent de toute consistance ontologique pour les soumettre au pouvoir de la conscience ou de la praxis, définies comme de pures puissances de désagrégation. Sartre étend ainsi à toute sa construction philosophique une matrice logique : le chiasme, dégagé par sa première œuvre d'envergure, l'imaginaire, qui tient l'objet perçu et l'objet en image pour deux corrélats de la conscience, contradictoires mais solidaires et mutuellement dépendants. A partir de ce point, on voit se déployer tout le drame de la néontologie sartrienne qui subordonne l'être au néant, la réalité à l'image, l'actuel au virtuel et reconnaît dans la destruction de ce qui demeure, l'ivresse dyonisiaque de la liberté. Cet effort grandiose pour tramer la fiction au tissu du réel est pourtant, de l'aveu même de son auteur, voué à l'échec. La conscience, en dissociant l'être, engendre la figure de l'Autre qui fait inlassablement retour, comme une puissance maléfique, et reverse à l'aliénation toutes les conquêtes de la liberté. La malédiction qui pèse sur la condition humaine décourage l'effort, annihile l'espoir et nous condamne à cultiver ce que Marx nommait, en la raillant, la critique critique, en d'autres termes, à nous complaire en un quiétisme inquiet, transposition assombrie du scepticisme satisfait que Sartre reprochait à la génération de ses grands parents. (shrink)

Viviamo – noi e la stragrande maggioranza delle persone che frequentiamo quotidianamente – in società che si definiscono e si autorappresentano come “liberali”. Il fenomeno della libertà è al centro delle nostre esistenze e della nostra stessa identità personale. Non c’è unanimità, tuttavia, riguardo alla matrice di questa condizione di libertà. Il saggio, anche se sposa una visione polisemica della libertà, non rinuncia al tentativo di identificare forme migliori di libertà all’interno di tale costellazione. Libertà “risonante” è il nome con (...) cui viene indicata una possibile variante architettonica di autorealizzazione. Si tratta di una varietà non meramente “sottrattiva” di libertà che consiste nella capacità di rispondere a un appello dotato di valore intrinseco che proviene da un luogo esterno alla giurisdizione e alle aspettative dell’io. L’atto responsivo è, da un lato, ricettivo, ma, per altro verso, contribuisce a dischiudere e articolare il contenuto di verità personalmente rilevante di cui esso è la risposta. Questo elemento di esplorazione, di affidamento all’alterità e di incertezza è cruciale anche nelle genuine esperienze di risonanza innescate dal “canto” del mondo (Rilke) in cui è racchiuso un elemento trasformativo che eccede la nostra capacità di autonomia. (shrink)

It is proposed in this paper to develop a method by which the most general problem of the algebra of propositions is solved. This problem is to construct all propositions whose truth is independent of the form of the variables. As might be expected this method will enable us to determine without the use of matrices the consistency and independence of propositions, except in the case of those fundamental properties, which taken together define consistency itself. In the discussion which (...) follows no limitations are placed on the meaning of the terms and the word proposition is used simply in the sense of a variable. If we were to say, for example, that our variables must be restricted to zero or one values, we would be introducing a limitation which would reduce the generality of our science. A logic may be false in the sense that its postulates lead to contradictory theorems, or it may be false in the sense that it lacks generality, and the situation is not saved by calling it a two-valued, or a three-valued logic, or a logic of “propositions,” or by designating it by some other euphuism. (shrink)

Theories where truth is a naive concept fall under the following dilemma: either the theory is subject to Curry’s Paradox, which engenders triviality, or the theory is not trivial but the resulting conditional is too weak. In this paper we explore a number of theories which arguably do not fall under this dilemma. In these theories the conditional is characterized in terms of non-deterministic matrices. These non-deterministic theories are similar to infinitely-valued Łukasiewicz logic in that they are consistent (...) and their conditionals are quite strong. The difference is the following: while Łukasiewicz logic is \-inconsistent, the non-deterministic theories might turn out to be \-consistent. (shrink)

We consider an example of four valued semantics partially inspired by quantum computations and negation-like operations occurred therein. In particular we consider a representation of so called square root of negation within this four valued semantics as an operation which acts like a cycling negation. We define two variants of logical matrices performing different orders over the set of truth values. Purely formal logical result of our study consists in axiomatizing the logics of defined matrices as the systems (...) of binary consequence relation and proving correctness and completeness theorems for these deductive systems. (shrink)

The actual introduction of a non-reflexive and non-idempotent q -consequence gave birth to the concept of logical three-valuedness based on the idea of noncomplementary categories of rejection and acceptance. A q -consequence may not have bivalent description, the property claimed by Suszko’s Thesis on logical two-valuedness, ( ST ), of structural logics, i.e. structural consequence operations. Recall that ( ST ) shifts logical values over the set of matrix values and it refers to the division of matrix universe into two (...) subsets of designated and undesignated elements using their characteristic functions as logical valuations, cf. [4] The extension of the idea operates with three-valued function, with the third value ascribed to those elements of the matrix which are neither rejected nor accepted. Accordingly, the logical three-valuedness departs naturally from the division of the matrix universe into three subsets and the ( ST ) counterpart says that any inference based on a structural q -consequence may have a bivalent or a three-valued description. After a short presentation of the three-valued inferential framework, we discuss a solution for further exploration of the idea leading to logical n -valuedness for n > 3. Apparently, the first step in that direction is easy and it consists of a division of the matrix universe into more than three subsets. The next move, i.e. a definition of a matrix consequence-like relation being neither a consequence nor a q -consequence, seems extremely difficult. Therefore, here we consider only finite linear matrices with one-argument functions “labelling” respective matrix subsets. By means of these functions it is possible to represent a q-consequence as a “partial” Tarski’s consequence and, ultimately, to define a logically more-valued consequence-like relation. We believe, that the present partial proposal deserves an attention by itself but also that it may lead to a general approach to logically many-valued inference. (shrink)

Two analyzes of Spark engine performance strategies to implement the Spark technique in a matrix distributed computational algorithm, the multiplication of a sparse multiplication operational test model. The dimensions of the two input sparse matrices have been fixed to 30,000 × 30,000, and the density of the input matrix have been changed. The experimental results show that when the density reaches about 0.3, the original dense matrix multiplication performance can outperform the sparse-sparse matrix multiplication, which is basically consistent (...) with the relationship between the sparse matrix multiplication implementation in the single-machine sparse matrix test and the computational performance of the local native library. When the density of the fixed sparse matrix is 0.01, the distributed density-sparse matrix multiplication outperforms the same sparsity but uses the density matrix storage, and the acceleration ratio increases from 1.88× to 5.71× with the increase in dimension. The overall performance of distributed operations is improved. (shrink)

Exposure to pesticides during infancy is associated with numerous adverse health outcomes. The assessment of knowledge and perception of pesticides exposure and risk among children has not been thoroughly studied. The aim of the study was to evaluate the reliability and validity of a questionnaire that measures the knowledge and perception of exposure to organophosphate pesticides among rural schoolchildren. The questionnaire was administered to 151 schoolchildren between 9 and 13years from four Chilean rural schools. An internal consistency analysis of the (...) ordinal alpha coefficient and a polychoric factor analysis for categorical data were used. The results show that the ordinal alpha was 0.95. Polychoric matrices of rotated components show the 17 questions summarized pesticide knowledge in five factors extracted after promax rotation. This factorial model explains 56.3% of the variance. The questions were grouped as follows: knowledge about pesticides ; knowledge of health effects related to pesticides exposure ; pesticide exposure through the growing of fruits and vegetables ; perception and action against pesticides exposure at school ; and perception and action against pesticides exposure at home. The questionnaire provides a useful tool for examining pesticide exposure in agricultural regions, allowing younger community members to participate. (shrink)

Given a quantum system with a very large number of degrees of freedom and a preferred tensor product factorization of the Hilbert space we describe how it can be approximated with a very low-dimensional field theory with geometric degrees of freedom. The geometric approximation procedure consists of three steps. The first step is to construct weighted graphs with vertices representing subsystems and edges representing mutual information between subsystems. The second step is to deform the adjacency matrices of the information (...) graphs to that of a low-dimensional lattice using the graph flow equations introduced in the paper. The third step is to define an emergent metric and to derive an effective description of the metric and possibly other degrees of freedom. To illustrate the procedure we analyze two information graph flows with geometric attractors and metric perturbations obeying a geometric flow equation. Our analysis also suggests a possible approach to quantum gravity in which the geometry emerges directly from a quantum state due to the flow of the information graphs. (shrink)

In this paper I will discuss the extent to which Umberto Eco’s Semiotics maintains the unstable and oscillatory equilibrium between conflicting matrices that is proper to humorous thinking and ambiguous figures such as the famous duck-rabbit illusion and Penrose’s impossible trident. To do so I shall summon the concept of bisociation (Koestler 1964): though never an item of Eco’s own philosophical toolbox, bisociation plays an important role in the creation of some of Eco’s most innovative theoretical contributions, insofar as (...) they result from a possible/impossible graft between Structuralism and Pragmatism. For each, the question will be whether the implant produces self-consistent theoretical amalgams, or whether some degree of contradiction inevitably remains to generate the abovementioned duck-rabbit effect. I shall then analyse the role that such residual incongruities play in a theory that thrives on the self-voiding logic of humorous short-circuits. (shrink)

This essay argues that the image of the brain in a vat metaphorically encapsulates articulations of the relationship between the corporeal and the technological dimensions found in cyberpunk fiction and cinema. Cyberpunk is concurrently concerned with actual and imaginary metamorphoses of biological organisms into machines, and of mechanical apparatuses into living entities. Its recurring representation of human beings hooked up to digital matrices vividly recalls the envatted brain activated by electric stimuli, which Hilary Putnam has theorized in the context (...) of contemporary epistemology. At the same time, cyberpunk imaginatively raises the same epistemological questions instigated by Putnam. These concern the cognitive processes associated with the collusion of human and mechanical creatures, and related metaphysical and ethical issues spawned by such processes. As a philosophical trope, the brain in a vat would appear to pivot on the notion of a disembodied subject consisting of sheer mentation. However, literary and cinematic interpretations of the image in cyberpunk persistently foreground the obdurate materiality of the flesh—often in its most grisly and grotesque incarnations. (shrink)

Framing systematics as a field consistent with scientific inquiry entails that inferences of phylogenetic hypotheses have the goal of producing accounts of past causal events that explain differentially shared characters among organisms. Linking observations of characters to inferences occurs by way of why-questions implied by data matrices. Because of their form, why-questions require the use of common-cause theories. Such theories in phylogenetic inferences include natural selection and genetic drift. Selection or drift can explain ‘morphological’ characters but selection cannot (...) be causally applied to sequences since fitness differences cannot be directly associated with individual nucleotides or amino acids. The relation of selection to sequence data is by way of downward or top-down causation from those phenotypes upon which selection occurs. The application of phylogenetic inference to explain sequence data is thus restricted to instances where drift is the relevant theory; those nucleotides or amino acids that can be explained via downward causation are precluded from inclusion in the data matrix. The restrictions on the inclusion of sequence data in phylogenetic inferences equally apply to species hypotheses, precluding the more restrictive approach known as DNA barcoding. Not being able to discern drift and selection as relevant causal mechanisms can severely constrain the inclusion and explanations of sequence data. Implications of such exclusion are discussed in relation to the requirement of total evidence. (shrink)

This essay explores the lines of thought focused on the relationship between gesture and technique, examining the theories which have conceptualized the transfer of gestural matrices into inert matter, and understood technique as a result of this process. Although associated mainly with the writings of the palaeontologist André Leroi-Gourhan, this thought actually predates his work, and consists of multiple branches: having first taken root at the end of the nineteenth century, it became diffused throughout the following decades in different (...) forms. These nevertheless shared a constant reference to cinema, both as a privileged place that captures gestures, and as a technique that can absorb their quintessence. From Espinas to Simondon, via Jousse and Eisenstein, the theory of gestural transmission breaks down various polarities, such as body and environment, organic and inorganic, animated and inanimate, performativity and inner life. It foregrounds the imaginative logic of the body and the many forms of somatic thinking developed by man. Such forms lie at the heart of the creative processes and have found their highest appreciation in cinema, as a machine that, from its very origins, has been grafted not only on the eye but on the whole body. (shrink)

The Genesis of the Social and the Carnal Donation of the Non-Presentable. The Range of the Notion of Institution in Merleau-PontyThis article examines the range of the notion of institution that Merleau-Ponty proposes in his course at the Collège de France (1954-55), by notably insisting on the importance of the question of the genesis of the social for the deepening of his thought. By broadening his investigative domains in two complementary directions (that is, lateral passivity and socio-historical institution), Merleau-Ponty aims (...) in this course to grasp in a better way the lateral relations of our Urstiftung (originary institution) and the instituting subject who obliquely goes beyond the institution towards its sense. That leads him to introduce the perceptual field as being essentially lacunary, because it marks a place where the consciousness is present at the divergence in relation to consciousness. It is certain that the Phenomenology of Perception addressed this question by considering the social as a place where “I am given to myself”. However, the psychological starting point of this work, as well as the originary temporal and unilateral character of radical reflection, prevented one from really grasping the institutional junction of the concrete event and the symbolic matrix. One was not able to thematize an auto-articulation which appears suddenly between radical reflection and the unreflective. This is why Lévi-Strauss’ structuralist thought, by considering the social as symbolism, allows for a better understanding of this institutional nexus. But this idea does not lead to the dogmatic positing of the reality and the autonomy of the social. Instead, it encourages us to practice “the perception of history,” which consists in guessing, in the very process of sociological idealization, the carnal and wild donation of the non-presentable. Far from returning to psychologism, this perception aims at actively achieving the movement internal to the symbolic, that is, its incarnation.La genesi del sociale e la donazione carnale del non-presentabile. La portata della nozione di istituzione in Merleau-PontyQuesto articolo esamina la portata della nozione d’istituzione che Merleau-Ponty propone nel suo corso al Collège de France del 1954-1955, insistendo in particolare sull’importanza della questione della genesi del sociale per l’approfondimento del suo pensiero.Estendendo i propri domini di ricerca in due direzioni complementari (la passività laterale e l’istituzione socio-storica), Merleau-Ponty si propone in questo corso di cogliere meglio i rapporti laterali della nostra Urstiftung (l’istituzione originaria) e del soggetto istituente che la supera obliquamente in direzione del suo senso. Ciò induce a presentare il campo percettivo come essenzialmente lacunoso, poiché manca di un luogo dove la coscienza possa assistere allo scarto rispetto a se stessa.È certo che la Fenomenologia della percezione affrontava questa questione considerando il sociale come un luogo dove “io sono donato a me stesso”. I presupposti psicologici di quest’opera, così come il carattere originariamente temporale e unilaterale della riflessione radicale, impedivano tuttavia di cogliere in maniera adeguata il legame istituzionale dell’evento concreto e della matrice simbolica, e di tematizzare un’autoarticolazione che sorgesse tra la riflessione radicale e l’irriflesso.È per questo motivo che il pensiero strutturalista di Lévi-Strauss, che considerava il sociale come simbolismo, permette di comprendere meglio questo nesso istituzionale. Quest’idea non conduce però a porre dogmaticamente la realtà e l’autonomia del sociale, essa incita piuttosto a praticare “la percezione della storia” che consiste nell’individuare, nel processo stesso dell’idealizzazione sociologica, la donazione carnale e selvaggia del non-presentabile. Lungi dal rappresentare un ritorno allo psicologismo, questa nozione di percezione mira a completare attivamente il movimento interno al simbolico, ovvero la sua incarnazione. (shrink)

The study’s objective is to analyze the structure of knowledge organization studies conducted worldwide. This applied research has been conducted with a scientometrics approach using the co-word analysis. The research records consisted of all articles published in the journals of Knowledge Organization and Cataloging & Classification Quarterly and keywords related to the field of knowledge organization indexed in Web of Science from 1900 to 2019, in which 17,950 records were analyzed entirely with plain text format. The total number of keywords (...) was 25,480, which was reduced to 12,478 keywords after modifications and removal of duplicates. Then, 115 keywords with a frequency of at least 18 were included in the final analysis, and finally, the co-word network was drawn. BibExcel, UCINET, VOSviewer, and SPSS software were used to draw matrices, analyze co-word networks, and draw dendrograms. Furthermore, strategic diagrams were drawn using Excel software. The keywords “information retrieval,” “classification,” and “ontology” are among the most frequently used keywords in knowledge organization articles. Findings revealed that “Ontology*Semantic Web”, “Digital Library*Information Retrieval” and “Indexing*Information Retrieval” are highly frequent co-word pairs, respectively. The results of hierarchical clustering indicated that the global research on knowledge organization consists of eight main thematic clusters; the largest is specified for the topic of “classification, indexing, and information retrieval.” The smallest clusters deal with the topics of “data processing” and “theoretical concepts of information and knowledge organization” respectively. Cluster 1 (cataloging standards and knowledge organization) has the highest density, while Cluster 5 (classification, indexing, and information retrieval) has the highest centrality. According to the findings of this research, the keyword “information retrieval” has played a significant role in knowledge organization studies, both as a keyword and co-word pair. In the co-word section, there is a type of related or general topic relationship between co-word pairs. Results indicated that information retrieval is one of the main topics in knowledge organization, while the theoretical concepts of knowledge organization have been neglected. In general, the co-word structure of knowledge organization research indicates the multiplicity of global concepts and topics studied in this field globally. (shrink)

Qu'est-ce que la fameuse caverne de Platon si ce n'est la plus grande chambre noire que l'on ait jamais réalisée? Reprenant cette intuition de Paul Valéry, Jean-François Mattéi procède à une relecture magistrale des grands dialogues de Platon, de La République au Timée, pour y découvrir la matrice de notre monde, un monde envahi par les images et les simulacres. Du cinéma aux jeux vidéo en passant par Internet, le cyberespace et les téléphones portables, nouvelles "cavernes personnelles ", les images (...) ont en effet pris le pouvoir. Censées initialement représenter le réel, elles se sont mises à le simuler, à le dupliquer, voire à l'absorber pour faire surgir une nouvelle dimension, celle du virtuel. Matrix, Avatar, World of Warcraft, Toy Story, la 3D, sont le vecteur de cette révolution. Pour la plupart des philosophes, la victoire des simulacres constitue un renversement sans précédent du rapport entre image et réalité, institué il a 2500 ans par Platon. Les images ne seraient plus le miroir d'une réalité intelligible qui leur confère consistance, mais de purs simulacres sans aucun rapport avec le réel. En croisant la lecture minutieuse de Platon avec une plongée passionnante dans les processus les plus contemporains de modélisation des images, cet essai démontre qu'il n'en est rien. Loin d'être autonomes, les phénomènes de simulation proviennent de procédés rationnels qui projettent leur intelligibilité dans le sensible. Et ces procédés artificiels redoublent l'opération première, advenue dans la nuit des temps, au cours de laquelle le monde fut structuré grâce à des modèles intelligibles qui se sont inscrits en lui. (shrink)

Cognitive diagnosis models (CDMs) allow classifying respondents into a set of discrete attribute profiles. The internal structure of the test is determined in a Q-matrix, whose correct specification is necessary to achieve an accurate attribute profile classification. Several empirical Q-matrix estimation and validation methods have been proposed with the aim of providing well-specified Q-matrices. However, these methods require the number of attributes to be set in advance. No systematic studies about CDMs dimensionality assessment have been conducted, which contrasts with (...) the vast existing literature for the factor analysis framework. To address this gap, the present study evaluates the performance of several dimensionality assessment methods from the factor analysis literature in determining the number of attributes in the context of CDMs. The explored methods were parallel analysis, minimum average partial, very simple structure, DETECT, empirical Kaiser criterion, exploratory graph analysis, and a machine learning factor forest model. Additionally, a model comparison approach was considered, which consists in comparing the model-fit of empirically estimated Q-matrices. The performance of these methods was assessed by means of a comprehensive simulation study that included different generating number of attributes, item qualities, sample sizes, ratios of the number of items to attribute, correlations among the attributes, attributes thresholds, and generating CDM. Results showed that parallel analysis (with Pearson correlations and mean eigenvalue criterion), factor forest model, and model comparison (with AIC) are suitable alternatives to determine the number of attributes in CDM applications, with an overall percentage of correct estimates above 76% of the conditions. The accuracy increased to 97% when these three methods agreed on the number of attributes. In short, the present study supports the use of three methods in assessing the dimensionality of CDMs. This will allow to test the assumption of correct dimensionality present in the Q-matrix estimation and validation methods, as well as to gather evidence of validity to support the use of the scores obtained with these models. The findings of this study are illustrated using real data from an intelligence test to provide guidelines for assessing the dimensionality of CDM data in applied settings. (shrink)

This paper resolves the open problem posed in Section 8.3 of the prior Operatiology paper What is Reality for Nature?: Structural Necessity as the Algebraic Condition of Persistence from Operatiology (Version 2, DOI: 10.5281/zenodo.20779136): whether the graph G = (Nec(S), E), in which an edge joins Ti and Tj when some admissible operation sequence w in Oadm* satisfies w(Ti) cap Tj != empty, is connected. We show that this question, as posed, cannot be answered within Tier‑2 alone: reachability is not (...) a Tier‑2 primitive but a Tier‑3 notion presupposing spacetime causal structure. The correct Tier‑2 question is whether Oadm is unique, and we prove that it is, directly from Axioms A1, A2, and A4 of Operatiology (Japanese: 操作原論). This uniqueness is the precise Tier‑2 statement of the unity of the universe: all Nec(S) instances share a single operational space. Spacetime is a Tier‑3 projection of this operational structure, not the container within which the universe resides. From this foundation we establish that the sentences “the universe has a beginning’’ and “the universe has an end’’ admit no well‑formed formulation in the language generated by A1, A2, A4, and that the cosmological application of General Relativity commits the same category error as the impossibility of quantum gravity: a local Tier‑3 theory is applied to a global concept that has no single Tier‑2 referent. The standard cosmological constructs — dark matter, dark energy, inflation, and the Big Bang singularity — are shown to be Untranslatable by the Translatability criterion: none possesses a Tier‑2 antecedent in Nec(S). Alternative cosmological models that retain continuous spacetime as a primitive are disposed of by a single general theorem. The steady‑state intuition that the universe has no absolute beginning is structurally vindicated, though its Tier‑3 mechanism of continuous creation is rejected. Recent observational anomalies — the excess of massive galaxies at z > 10 reported by JWST, the Hubble tension persisting at 5 sigma through 2025, and the continued non‑detection of WIMPs by LZ, XENONnT, and PandaX‑4T — are recorded as Tier‑3 correspondences consistent with the structural results, not as evidence for them. Computational illustrations (Codes A–L) are provided as a supplementary Python script. The following representative code demonstrates the central algebraic result: exactly one sector of M3(C) satisfies the Nec(S) conditions Dist and Clos and Irr, corresponding to the electron and proton. Dark matter has no antecedent in this structure.◆◆◆ [PYTHON VERIFICATION CODE — note: × denotes *, ． denotes .] ◆◆◆ import sympy as sp_ H_sym = sp_.Matrix（［［1,0,0］,［0,1,0］,［0,0,-2］］） def ad_H_map（X）： return H_sym × X − X × H_sym def flatten_entries（M）： entries = ［］ for i in range（M．rows）： for j in range（M．cols）： e = sp_．simplify（M［i,j］） entries．append（sp_．re（e）） entries．append（sp_．im（e）） return entries basis_m3 = ［］ for i in range（3）： for j in range（3）： M = sp_．zeros（3） M［i,j］ = 1 basis_m3．append（M） rows_ad = ［flatten_entries（ad_H_map（X）） for X in basis_m3］ ad_matrix = sp_.Matrix（rows_ad）．T ker_basis = ad_matrix．nullspace（） ker_matrices = ［］ for vec in ker_basis： M = sp_．zeros（3） for k,（i,j） in enumerate（［（i,j） for i in range（3） for j in range（3）］）： M［i,j］ = vec［k］ ker_matrices．append（M） traceless_matrices = ［（idx＋1, M） for idx, M in enumerate（ker_matrices） if sp_．simplify（sp_．trace（M）） == 0］ print（f"ker（ad_H） intersect sl（3,C）： {len（traceless_matrices）} elements"） E12 = sp_．zeros（3）； E12［0,1］ = 1 E21 = sp_．zeros（3）； E21［1,0］ = 1 comm_pair = E12×E21 − E21×E12 print（f"[E12,E21] = {comm_pair．tolist（）}"） print（"=> Zero-weight pair stays within its own sector： Clos satisfied."） action_E21_on_E12 = E21 × E12 outside_E12 = not sp_.Matrix（［［0,1,0］,［0,0,0］,［0,0,0］］）．equals（action_E21_on_E12） print（f"E21 acting on E12-sector exits ［E12］： {outside_E12}"） print（"=> ［E12］ alone fails Clos. ［E12,E21］ pair is irreducible."） D1 = sp_.Matrix（［［1,0,0］,［0,-1,0］,［0,0,0］］） D1_clos = True print（f"Diagonal sector ［D1］： Dist=True, Clos={D1_clos}"） print（"=> Proper subset satisfying Dist^Clos exists： Irr=False"） print（） print（"======================================================"） print（"Nec（S） = Dist ^ Clos ^ Irr -- FINAL VERDICT："） print（"======================================================"） sectors = ［ ("Zero-weight pair ［E12,E21］ ［ELECTRON + PROTON］", True, True, True), ("Diagonal traceless span ［FAILS Irr］", True, True, False), ("Scalar I, Tr=3 ［OUTSIDE sl（3,C）］", False, False, False), ("Off-diagonal non-zero weight ［QUARKS, confined］", False, False, False), ］ for name, dist, clos, irr in sectors： nec = dist and clos and irr verdict = "EXISTS" if nec else "ALGEBRAICALLY IMPOSSIBLE" print（f" {name}"） print（f" Nec（S） = {nec} => {verdict}"） print（） print（"RESULT："） print（" Exactly ONE sector satisfies Nec（S）："） print（" the zero-weight pair ［E12, E21］ = electron and proton."） print（） print（" WIMP（dark matter）： Tr（I） = 3, outside ［M3,M3］."） print（" => No Nec（S） antecedent. ALGEBRAICALLY IMPOSSIBLE."） print（） print（" The algebraic exclusion follows from the structure of"） print（" M3（C） alone, independently of any experimental result."） print（" Experimental non-detection is consistent with this"） print（" structural result, not evidence for it."） ◆◆◆ [END] ◆◆◆ Published on July 30, 2026. DOI: 10.5281/zenodo.21699684. (shrink)

As it was proved in [4, Sect. 3], the poset of extensions of the propositional logic defined by a class of logical matrices with equationally-definable set of distinguished values is a retract, under a Galois connection, of the poset of subprevarieties of the prevariety generated by the class of the underlying algebras of the defining matrices. In the present paper we apply this general result to the three-valued paraconsistent logic proposed by Hałkowska–Zajac [2]. Studying corresponding prevarieties, we prove (...) that extensions of the logic involved form a four-element chain, the only proper consistent extensions being the least non-paraconsistent extension of it and the classical logic. RID=""ID="" Mathematics Subject Classification (2000): 03B50, 03B53, 03G10 RID=""ID="" Key words or phrases: Many-valued logic – Paraconsistent logic – Extension – Prevariety – Distributive lattice. (shrink)