Quantum Logic

The article presents the chess composition as a logical art, with concrete examples. It began with Arabic mansuba, and later evolved to new-strategy designed by Italian Alberto Mari. The redefinition of mate (e.g. mate with a free field) or a theme to quasi-pseudo theme, opens the new space for combinations, and enables to connect it with other fields like computer science. The article was exhibited in Holland Park, W8 6LU, The Ice House between 18. Oct - 3. Nov. 2013.

Classical physics and quantum physics suggest two meta-physical types of reality: the classical notion of a objectively definite reality with properties "all the way down," and the quantum notion of an objectively indefinite type of reality. The problem of interpreting quantum mechanics (QM) is essentially the problem of making sense out of an objectively indefinite reality. These two types of reality can be respectively associated with the two mathematical concepts of subsets and quotient sets (or partitions) which are category-theoretically dual (...) to one another and which are developed in two mathematical logics, the usual Boolean logic of subsets and the more recent logic of partitions. Our sense-making strategy is "follow the math" by showing how the logic and mathematics of set partitions can be transported in a natural way to Hilbert spaces where it yields the mathematical machinery of QM--which shows that the mathematical framework of QM is a type of logical system over ℂ. And then we show how the machinery of QM can be transported the other way down to the set-like vector spaces over ℤ₂ showing how the classical logical finite probability calculus (in a "non-commutative" version) is a type of "quantum mechanics" over ℤ₂, i.e., over sets. In this way, we try to make sense out of objective indefiniteness and thus to interpret quantum mechanics. (shrink)

Recent developments in pure mathematics and in mathematical logic have uncovered a fundamental duality between "existence" and "information." In logic, the duality is between the Boolean logic of subsets and the logic of quotient sets, equivalence relations, or partitions. The analogue to an element of a subset is the notion of a distinction of a partition, and that leads to a whole stream of dualities or analogies--including the development of new logical foundations for information theory parallel to Boole's development of (...) logical finite probability theory. After outlining these dual concepts in mathematical terms, we turn to a more metaphysical speculation about two dual notions of reality, a fully definite notion using Boolean logic and appropriate for classical physics, and the other objectively indefinite notion using partition logic which turns out to be appropriate for quantum mechanics. The existence-information duality is used to intuitively illustrate these two dual notions of reality. The elucidation of the objectively indefinite notion of reality leads to the "killer application" of the existence-information duality, namely the interpretation of quantum mechanics. (shrink)

The notion of a partition on a set is mathematically dual to the notion of a subset of a set, so there is a logic of partitions dual to Boole's logic of subsets (Boolean logic is usually mis-specified as "propositional" logic). The notion of an element of a subset has as its dual the notion of a distinction of a partition (a pair of elements in different blocks). Boole developed finite logical probability as the normalized counting measure on elements of (...) subsets so there is a dual concept of logical entropy which is the normalized counting measure on distinctions of partitions. Thus the logical notion of information is a measure of distinctions. Classical logical entropy naturally extends to the notion of quantum logical entropy which provides a more natural and informative alternative to the usual Von Neumann entropy in quantum information theory. The quantum logical entropy of a post-measurement density matrix has the simple interpretation as the probability that two independent measurements of the same state using the same observable will have different results. The main result of the paper is that the increase in quantum logical entropy due to a projective measurement of a pure state is the sum of the absolute squares of the off-diagonal entries ("coherences") of the pure state density matrix that are zeroed ("decohered") by the measurement, i.e., the measure of the distinctions ("decoherences") created by the measurement. (shrink)

In the paper we will employ set theory to study the formal aspects of quantum mechanics without explicitly making use of space-time. It is demonstrated that von Neuman and Zermelo numeral sets, previously efectively used in the explanation of Hardy’s paradox, follow a Heisenberg quantum form. Here monadic union plays the role of time derivative. The logical counterpart of monadic union plays the part of the Hamiltonian in the commutator. The use of numerals and monadic union in the classical probability (...) resolution of Hardy’s paradox [1] is supported with the present derivation of a commutator for sets. (shrink)

In recent work, we introduced a new semantics for conditionals, covering a large class of what we call preconditionals. In this paper, we undertake an axiomatic study of preconditionals and subclasses of preconditionals. We then prove that any bounded lattice equipped with a preconditional can be represented by a relational structure, suitably topologized, yielding a single relational semantics for conditional logics normally treated by different semantics, as well as generalizing beyond those semantics.

Challenges to classical logic have emerged from several sources. According to recent work, the behavior of epistemic modals in natural language motivates weakening classical logic to orthologic, a logic originally discovered by Birkhoff and von Neumann in the study of quantum mechanics. In this paper, we consider a different tradition of thinking that the behavior of vague predicates in natural language motivates weakening classical logic to intuitionistic logic or even giving up some intuitionistic principles. We focus in particular on Fine's (...) recent approach to vagueness. Our main question is: what is a natural non-classical base logic to which to retreat in light of both the non-classicality emerging from epistemic modals and the non-classicality emerging from vagueness? We first consider whether orthologic itself might be the answer. We then discuss whether accommodating the non-classicality emerging from epistemic modals and vagueness might point in the direction of a weaker system of fundamental logic. (shrink)

Dieser Text befasst sich mit den streng logischen Grundlagen der Quantenphysik. Streng - bedeutet, dass er hauptsächlich nach dem Buch von Walther Brüning mit dem Titel Grundlagen der Strengen Logik folgt und damit Paradoxien und Antinomien ausgeschlossen sein sollen. Das Buch bildet die Grundlage und daher ergibt es sich, dass dieser Text lediglich eine umfassendere Darstellung der Theorie ist, die bei einer konsequenten Weiterführung in den Grundlagen der Quantenphysik mündet. Die Axiome der Quantenphysik fallen in drei Begriffe: Eine physikalische Welt, (...) deren mathematisch beschreibbare Zeitentwicklung in eine neue physikalische Welt übergeht. Hier soll es zunächst nur um drei Sachverhalte handeln. Es wird sich ergeben, dass 61 Elementarteilchen eine Beschreibung der Realität zulassen. Diese Beschreibung ist aber nicht die letzte Wahrheit, sondern soll nur einen Beitrag leisten, sich mit den Grundlagen auseinanderzusetzen, um sich in Zukunft von einem festen Ausgangspunkt weiterentwickeln zu können. (shrink)

Der Autor dieses Textes hat in seinem Text "Grundlagen der Quantenphysik 2" gezeigt, dass auf triadisch verlängerter tetradischer Stufe neue Informationen im Wert von 2 323 Ganzformeln hinzukommen. Dies ist ein relativer Wert, der nur zu verstehen ist, wenn man eine Ganzformel als Ausgangsbasis heranzieht. -/- Weiters ist in der Statistik das geometrische Mittel für relative (bzw. normalisierte) Werte ein Maß für Wachstumsprozesse (bzw. Schrumpfungs-/Zerfallsprozesse). -/- Das geometrische Mittel von 2 323 ist nun ungefähr 48, 2. -/- Könnte es also (...) sein, dass die Quantenphysik etwas missverstanden wurde? Nämlich nicht als Wachstumsprozess, sondern eher als klassisch mechanische Wechselwirkungen? -/- Dafür spricht auch, dass bei einer Interpretation der Realität durch mehr Sachverhalte, klassische Begriffe, wie "Elementarteilchen" verschwinden und an Stelle derer neue, unbekannte Begriffe, wie "Quanteninteraktionen", metaphysisch resultieren. -/- Walther Brüning zeigt in seinem Buch Grundlagen der Strengen Logik die Möglichkeit für Kettenschlüsse der (vollständigen) Strengen Syllogistik auf. Dieser Text ist die Analyse solcher Kettenschlüsse. -/- Es wird sich ergeben, dass die Interaktionen von 48 Materieteilchen kongruent zu den Kettenschlüssen der vollständigen Strengen Syllogistik ist. -/- Als Grundlage für diesen Text wird der Text "Logische Grundlagen der Quantenphysik" vorausgesetzt. Das Buch Grundlagen der Strengen Logik von Walther Brüning wiederum bildet für den letztgenannten Text die Grundlage. (shrink)

Die Strenge Logik bietet einen einfachen Weg zur Erforschung a priorischer Fakten. Das heißt sie bildet die analytische Metaphysik aller Dinge, die teilhaben am Sein und damit an der Realität. Alle Dinge, die der Realität zugeordnet werden, werden hier auch als streng logisch aufgefasst, d. h. sie unterliegen dem Prinzip der Identiät und dem Prinzip der Limitation. Als Grundlage für diesen Text wird der Text Logische Grundlagen der Quantenphysik vorausgesetzt. Das Buch Grundlagen der Strengen Logik von Walther Brüning wiederum bildet (...) für den letztgenannten Text die Grundlage. (shrink)

This article argues that the world available to perception is not reality in its final or immediate form, but a manifestation of a deeper unmanifest domain through observation, neural mediation, and selective stabilization. The unmanifest is understood not as nothingness, but as a prephenomenal field in which objects, spatial boundaries, temporal order, and determinate histories have not yet fully emerged. The argument proceeds along three lines: structural affinities between neural networks and the cosmic web; the relation between quantum indeterminacy and (...) statistical regularity; and participatory approaches to observation associated with John Wheeler. On this basis, I propose Quantum-Inspired Poly-Logic (QPL) as a formal framework for modeling manifestation. QPL describes how competing logical possibilities may coexist prior to stabilization and how a determinate phenomenal order may emerge through their resolution. Space, time, form, and history are thus interpreted not as absolutely primitive features of being, but as emergent products of manifestation. (shrink)

Human thinking does not proceed within a single logic. It stabilizes meaning at the intersection of multiple, partially incompatible logics while tolerating indeterminacy. This paper develops quantum-inspired polylogical systems - formal framework in which this cognitive fact becomes a principle of inference. Building on Resolution Matrix Semantics, indeterminate truth values are interpreted as semantic superpositions, and logical systems themselves form a space of interacting constraints. Inference is reconceived not as derivation within a fixed logic, but as the emergence of stable (...) semantic configurations through interference and suppression. Unlike conventional quantum AI, which accelerates classical reasoning, the proposed model alters the semantics of inference itself. Poly-Logic Quantum AI thus offers a structural model of human reasoning—one that explains coherence without certainty, context sensitivity without logic switching, and the emergence of new ideas without randomness. The result is a theory of artificial reasoning closer to human thinking than to calculation. (shrink)

This paper introduces and defends Neo-Superdeterminism, a refined interpretation of quantum mechanics that challenges the necessity of free experimental choice. Building on the philosophical underpinnings of classical determinism and the logical consequences of Bell’s theorem, Neo-Superdeterminism proposes a causally closed universe in which all events—including the choices of experimenters—are part of the same deterministic fabric. Contrary to common objections, this view does not imply conspiracy or fatalism, but rather a consistent ontology that rejects the metaphysical separation between observer and system. (...) By questioning the privileged role of human agency in physical theory, this approach addresses the anthropocentric biases embedded in many interpretations of quantum mechanics. It offers a path toward reconciling realism, locality, and causality without recourse to metaphysical indeterminism or observer-centric collapse. The paper argues that embracing this framework not only preserves scientific integrity but may also provide a more coherent foundation for future developments in physics. Ultimately, Neo-Superdeterminism invites us to reconsider our place within the system we study—not as detached arbiters of truth, but as lawful expressions of the universe itself. (shrink)

The number of independent messages a physical system can carry is limited by the number of its adjustable properties. In particular, systems that have only one adjustable property cannot carry more than a single message at a time. We demonstrate this is the case for the single photons in the double-slit experiment, and the root of the fundamental limit on measuring the complementary aspect of the photons. Next, we analyze the other ‘quantal’ behavior of the systems with a single adjustable (...) property, such as noncommutativity and no-cloning. Finally, we formulate a mathematical theory to describe the dynamics of such systems and derive the standard Hilbert-space formalism of quantum mechanics. Our derivation demonstrates the physical foundation of the quantum theory. (shrink)

Quantum mechanics exhibits inherent probabilistic behavior, violations of classical probability, and a formalism seemingly disconnected from spacetime. We show that these features naturally emerge in single-variable systems, which can encode only a single independent unit of information at a time and therefore behave probabilistically. Imposing reversibility and conservation of total probability on the generalized probability formalism leads uniquely to a quadratic probability theory, with linear unitary transformations and probabilities given by squared moduli. From this, the Hilbert-space structure, Born’s rule, and (...) unitary evolution follow directly. This first-principles derivation of quantum theory is consistent with the experimental fact that observing quantum effects requires coherence. (shrink)

The mathematical formalism of quantum theory has been established for nearly a century, yet its physical foundations remain elusive. In recent decades, connections between quantum theory and information theory have garnered increasing attention. This study presents a physical derivation of the mathematical formalism quantum theory based on information-theoretic considerations in physical systems. We postulate that quantum systems are characterized by single independent adjustable variables. Utilizing this physical postulate along with the conservation of total probability, we derive the standard Hilbert space (...) formalism of quantum theory, including the Born probability rule. This comprehensive derivation of quantum theory offers a clear and concise physical foundation for the mathematical formalism of quantum mechanics. (shrink)

Since the pioneering work of Birkhoff and von Neumann, quantum logic has been interpreted as the logic of (closed) subspaces of a Hilbert space. There is a progression from the usual Boolean logic of subsets to the "quantum logic" of subspaces of a general vector space--which is then specialized to the closed subspaces of a Hilbert space. But there is a "dual" progression. The notion of a partition (or quotient set or equivalence relation) is dual (in a category-theoretic sense) to (...) the notion of a subset. Hence the Boolean logic of subsets has a dual logic of partitions. Then the dual progression is from that logic of partitions to the quantum logic of direct-sum decompositions (i.e., the vector space version of a set partition) of a general vector space--which can then be specialized to the direct-sum decompositions of a Hilbert space. This allows the logic to express measurement by any self-adjoint operators rather than just the projection operators associated with subspaces. In this introductory paper, the focus is on the quantum logic of direct-sum decompositions of a finite-dimensional vector space (including such a Hilbert space). The primary special case examined is finite vector spaces over ℤ₂ where the pedagogical model of quantum mechanics over sets (QM/Sets) is formulated. In the Appendix, the combinatorics of direct-sum decompositions of finite vector spaces over GF(q) is analyzed with computations for the case of QM/Sets where q=2. (shrink)

Logical monism is the view that there is ‘One True Logic’. This is the default position, against which pluralists react. If there were not ‘One True Logic’, it is hard to see how there could be one true theory of anything. A theory is closed under a logic! But what is logical monism? In this article, I consider semantic, logical, modal, scientific, and metaphysical proposals. I argue that, on no ‘factualist’ analysis (according to which ‘there is One True Logic’ expresses (...) a factual claim, rather than an attitude like approval), does the doctrine have both metaphysical and methodological import. Metaphysically, logics abound. Methodologically, what to infer from what is not settled by the facts, even the normative ones. I conclude that the only interesting sense in which there could be -- or could fail to be -- One True Logic is noncognitive. The same may be true of the monism-pluralism debate about normative areas, like moral, epistemic, and prudential ones, generally. (shrink)

This chapter gives some elements of the history of trivalent logics and presents the key technical notions. We stress that Boole and Frege were aware of reasons to go beyond bivalence, in ways that influenced Łukasiewicz in particular. Then we put particular emphasis on the 1930s as a pivotal moment in the application of trivalence to a range of interconnected phenomena, such as probability and hypothetical reasoning, quantum indeterminacy, computability theory, and the semantic paradoxes. The chapter goes on to present (...) basic elements regarding the connection of trivalent logics to other logics, including intuitionistic logic, modal logics, fuzzy and many-valued logics, and finally to classical and non-classical logics more broadly. Along the way, we present basic systems of mixed consequence, and provide glimpses into the theory of ternary computation. (shrink)

We give a theory of epistemic modals in the framework of possibility semantics and axiomatize the corresponding logic, arguing that it aptly characterizes the ways in which reasoning with epistemic modals does, and does not, diverge from classical modal logic.

Modal Interpretations of quantum mechanics distinguish between the realm of possibility, where the dynamical state determines what may be the case, and the realm of actuality, where the value state represents what actually is the case. In particular, the Modal-Hamiltonian Interpretation proposes an ontology in which there are no individual objects: quantum systems are characterized as non-individual bundles of properties. The aim of the present paper is to propose some rst steps towards the development of a new modal logic adapted (...) to describe a possibilist modality in an ontology of properties. The main idea consists in conceiving possibility as fundamental and introducing actuality as an operator acting on possible facts. On this basis, propositions referring to possible facts and propositions referring to actual facts are distinguished, and some relations between the realm of possibility and the realm of actuality are introduced. (shrink)

Standard quantum logics are typically defined over the orthomodular lattice associated with Hilbert space, yet there is no consensus on how this structure should be interpreted logically or ontologically. This paper offers a unified perspective on these issues by combining an epistemological three-layer model for scientific theories with quantum set theory. We argue that quasi-set theory is best understood not as an alternative semantics for quantum logics, but as an ontological framework operating at a different epistemological level: the ontological one. (...) From this standpoint, the distinctive non-classical features of quantum logic are explained by representational assumptions about identity and individuality, rather than by positing any direct revisions of the logical principles themselves. (shrink)

El análisis de los vínculos que pueden ser establecidos entre la lógica cuántica, las semánticas no deterministas de Nmatrices y las teorías de cuasiconjuntos es el núcleo central de este trabajo. La necesidad de tal análisis ha surgido de forma natural luego de que la relación entre Nmatrices y lógica cuántica quedó explicitada en un trabajo previo: los estados cuánticos, entendidos como medida de probabilidad, pueden ser interpretados como valuaciones de una cierta Nmatriz para el retículo cuántico de proyectores. El (...) Teorema de Kochen-Specker priva a la lógica cuántica de veritativo funcionalidad, pero no de admitir una semántica no determinista Nmatricial. Esto es, la semántica de Nmatrices es compatible con los requerimientos semánticos y algebraicos del retículo de proyectores cuánticos. Si tenemos en cuenta que las teorías de cuasiconjuntos (Quasi-sets y Quasets) han surgido motivadas por la ontología cuántica, que las teorías de conjuntos están fuertemente vinculadas con la lógica y que originalmente uno de los objetivos de la teoría de quasets QST era brindar una semántica para los entes cuánticos, entonces el puente establecido entre la lógica cuántica y las semánticas no deterministas puede ser visto como el detonador que inicia la búsqueda de vínculos entre estas teorías. Por un lado, la lógica cuántica de Birkhoff y von Neumann está comprometida con la representación de espacios de Hilbert de la Mecánica cuántica. Por otro lado, esta representación (como quedará claro más adelante) está comprometida con una ontología de individuos. Por lo tanto, la lógica cuántica y la ontología están vinculadas a través del formalismo de espacios de Hilbert. Como dijimos, las teorías de cuasiconjuntos han surgido motivadas por la ontología de los entes del micromundo. Esto implica que los cuasiconjuntos y la lógica cuántica mantendrían de forma indirecta cierta relación. (shrink)

Intuition is often treated as an essentially non-formal faculty that resists logical modeling and algorithmic explanation. This paper challenges that view by introducing a quantum-inspired poly-logical framework in which intuition emerges as a formally definable inferential phenomenon. Indeterminacy is reinterpreted not as incomplete information but as logical superposition, and reasoning agents are modeled as operating in superpositions of incompatible logics. In this setting, inference is not confined to any single logic: emergent inference occurs when a conclusion is accepted at the (...) superposed level even though it is derivable in none of the component logics. Such conclusions are defined as instances of artificial intuition, arising through logical interference and collapse. The framework provides a constructive account of insight, offers a non-monological perspective on Gödelian limitations, and suggests applications to artificial intelligence, normative reasoning, and models of rational agency. (shrink)

In this commentary on Suárez’s recently published work (2025), I aim to retrieve an original argument hitherto unpublished – which I refer to as Suárez’s Paradox (Suárez, 1992) – together with the response he himself proposes. Drawing on both the paradox and the epistemological model proposed to resolve it, I argue that we are presented with a theoretical framework capable of enabling a philosophically significant approach to current debates on the interpretation of quantum logics. I conclude by assessing the value (...) of this proposal not only in terms of its internal content but also considering its capacity to bridge two philosophical domains that, over recent decades, have largely evolved in isolation: the philosophy of logic and the philosophy of science. (shrink)

This paper gives a formulation of quantum logic in the abstract algebraic setting laid out by Dunn and Hardegree (2001). On this basis, it provides a comparative analysis of viable quantum logical bivalent semantics and their classical counterparts, thereby showing that the truth-functional status of classical and quantum connectives is not as different as usually thought. Then it points out that bivalent semantics for quantum logic – compatible with realism about quantum mechanics – can be maintained, albeit at the price (...) of truth-functionality. Finally, the paper critically addresses Geoffrey Hellman’s argument (1980) that this lack of truth-functionality entails a change of meaning between classical and quantum connectives. (shrink)

This research attempts to understand the profound relationship between the soul and consciousness through a new concept based on the fabrics of normal and inverted spacetime. The concept of normal and inverted spacetime is based on my other theories, the Theory of Everything and the Law of the Universe. In this research, I propose the idea that the soul Is not consciousness, but rather that the soul Is a normal spacetime fabric that moves from the future to the past and (...) from a state of entropy to a state of order within cells. Therefore, living cells have less entropy. The scientist Schrödinger, one of the founders of quantum mechanics, confirmed this statement. Consciousness, on the other hand, is an inverted spacetime fabric that moves from the past to the future or from a state of order to a state of entropy. When these two fusions combine, they form the present moment. The present of man Is different from the present of the planet .and the present of the universe, but man's present is balanced with both Consciousness here is not a fixed thing, and the soul, which gives life, is not a fixed thing either. Therefore, man's present is volatile. Consciousness, which is an inverted spacetime fabric, moves toward entropy, generating a wave. Probabilities overlap to form different ideas, such as electron probabilities. When exerting great effort, such as exercising, the entropy in the body increases, which also increases awareness. The person feels that time slows down. However, there is also the normal spacetime fabric that tends toward order, represented by the soul, which attempts to reduce entropy. The critical point is a finite difference between the two spacetime fabrics. This permissible dividing line between the two fabrics within the body maintains the balance between life and death. When the energy is completely and significantly disrupted, the soul .separates from the body and death occurs This concept is linked to the law of the universe derived from my other theory, :"The Theory of Everything." The law states E_t = m ×(Δx)² / t² This law states that energy in time equals the product of mass times the square of the difference between the two spacetime fabrics divided by the square of time. The energies that the environment provides to humans work to increase the inverted spacetime fabric, i.e., Increase entropy, i.e., Increase consciousness, .i.e., increase thought This law represents the general framework for understanding the universe and the strange properties of quantum mechanics, as I mentioned in my other theory, an amendment to relativity, and how the universe speaks through consciousness, and how consciousness becomes a link between the soul and matter, and between humans and the universe -/- . (shrink)

Resolution Matrix Semantics (RMS) introduces the alternative truth-value-based framework for modal logic, providing a substantive alternative to Kripke’s relational semantics of possible worlds. Drawing inspiration from Y. Ivlev’s substantive semantics, RMS utilizes a 4-valued structure—necessary truth (tn), contingent truth (tc), contingent false (fc), and necessary false (fn)—augmented by indeterminate values (t, f, t/f) to define modal systems Km, KDm, KTm, S4m, and S5m, analogous to Kripke’s K, KD, T, S4, and S5. By directly assigning determined and indeterminate truth values via (...) an interpretation function, RMS validates formulas without relying on accessibility relations, as demonstrated through soundness and completeness proofs and a tailored tableau method. The framework’s versatility extends to applications in deontic logic, artificial intelligence, and quantum computing, enabling context-dependent reasoning with computational efficiency. RMS thus bridges philosophical logic and practical domains, offering a truth-centric perspective on modal reasoning’s complexities. (shrink)

This book concerns the metasemantics of quantum mechanics (QM). Roughly, it pursues an investigation at an intersection of the philosophy of physics and the philosophy of language, and it offers a critical analysis of rival explanations of the semantic facts of standard QM. Two problems for such explanations are discussed: categoricity and permanence. New results include 1) a reconstruction of Einstein's incompleteness argument, which concludes that a local, separable, and categorical QM cannot exist, 2) a reinterpretation of Bohr's principle of (...) correspondence, grounded in the principle of permanence, 3) a meaning-variance argument for quantum logic, which follows a line of critical reflections initiated by Weyl, and 4) an argument for semantic indeterminacy leveled against inferentialism about QM, inspired by Carnap's work in the philosophy of classical logic. (shrink)

Most believe that there are no empirical grounds that make the adoption of quantum logic necessary. Ian Rumfitt has further argued that this adoption is not possible either, for the proof that distribution fails in quantum mechanics is rule-circular or unsound. I respond to Rumfitt, by showing that neither is the case: rule-circularity disappears when an appropriate semantics is considered, and soundness is restored by slightly modifying standard quantum mechanics. Thus, although this is indeed not necessary, it is however possible (...) to rationally adjudicate against classical logic. (shrink)

One cannot fully understand a theory—any theory—without knowing how its meaning is determined, without figuring out the purported relationship between the language of the theory and its semantic attributes. Explaining this relationship is the main task of metasemantics. This chapter introduces this task, in general terms, and then presents representationalism and non-representationalism as rival metasemantic views about quantum mechanics (QM). The analysis of the overall hypothesis of the book, that metasemantics contributes to an adequate philosophical understanding of QM, will focus (...) on two problems for these views: categoricity and permanence. (shrink)

Autonomous Intentional Masking (AIM) is the SUPRA-CONSCIOUS PROCESSOR (the super-chip) that explains (and controls) everything in Nature (the relationship between mind and matter) (nuclear energy).What it achieves: Frameless frame of reference. Extended superposition of I/O and memory. Infinite number of transistors, sensors, gates. XYX is XY is XX is X, reproducing the fundamental algorithm in Nature, if zero, then, one, completely integrated with, if one, then, zero. Contact to license.

Zero and One (modern) is Yin and Yang (ancient). What's next in AI? Advanced Autonomous Intelligence. This article introduces The Circular Theory (Autonomous Intentional Masking) as the New Thought Dynamic required for Advanced Autonomous Intelligence. It explains the Constant Variable (a Unified Unitized Field) which self-actualizes via Fifteen Sustainable Society Projects organized into a Health, Stealth, Wealth configuration. This self-actualizes into a Wealth-not-War Mentality automatically supported by the required Circular-Linear Financial Co-Dependence Between Liabilities and Assets which is not possible without (...) an Automatically-Conserved-Unified-Unitized-Circular-Linear Field (The Constant-Variable) (One Circumference and One Diameter). Focus is on Service-Based-Sustainability and the (US) Dollar Value of an Hour (the Physical Representation (Universal Tokenization) of Mind). (shrink)

Zero and One (modern) is Yin and Yang (ancient). What's next in AI? Advanced Autonomous Intelligence. This article introduces The Circular Theory (Autonomous Intentional Masking) as the New Thought Dynamic required for Advanced Autonomous Intelligence. It is supported by the Constant Variable (A Unified Unitized Field) which self-actualizes via Fifteen Sustainable Society Projects organized into a Health, Stealth, Wealth configuration. This self-actualizes into a Wealth-not-War Mentality (supported by the required Circular-Linear Financial Co-Dependence Between Liabilities and Assets which is not possible (...) without an Automatically-Conserved-Unified-Unitized-Circular-Linear Field) (The Constant-Variable) (One Circumference and One Diameter). Focus is on Service-Based-Sustainability and the (US) Dollar Value of an Hour (the Physical Representation (Universal Tokenization) of Mind). (shrink)

This paper provides an overview of Janusz Czelakowski’s contributions to the theory of partial Boolean (σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document}-)algebras, and, more in general, to the foundation of Quantum Mechanics. Particular attention is paid to the logic of partial Boolean σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document}-algebras, to characterizations of PBAs embeddable into Boolean (σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document}-)algebras, and their representation as self-adjoint idempotent (...) elements of partial commutative algebras with involution. Also, applications to the theory of orthomodular posets as well as Czelakowski’s theory of partial Boolean algebras in a broader sense will be discussed. Finally, further representation theorems and their importance for quantum logic will be outlined. (shrink)

Non-classical generalizations of classical modal logic have been developed in the contexts of constructive mathematics and natural language semantics. In this paper, we discuss a general approach to the semantics of non-classical modal logics via algebraic representation theorems. We begin with complete lattices L equipped with an antitone operation ¬ sending 1 to 0, a completely multiplicative operation ◻, and a completely additive operation ◊. Such lattice expansions can be represented by means of a set X together with binary relations (...) ⊲, R, and Q, satisfying some first-order conditions, used to represent (L,¬), ◻, and ◊, respectively. Indeed, any lattice L equipped with such a ¬, a multiplicative ◻, and an additive ◊ embeds into the lattice of propositions of a frame (X,⊲,R,Q). Building on our recent study of "fundamental logic", we focus on the case where ¬ is dually self-adjoint (a≤¬b implies b≤¬a) and ◊¬a≤¬◻a. In this case, the representations can be constrained so that R=Q, i.e., we need only add a single relation to (X,⊲) to represent both ◻ and ◊. Using these results, we prove that a system of fundamental modal logic is sound and complete with respect to an elementary class of bi-relational structures (X,⊲,R). (shrink)

Epistemic modals have peculiar logical features that are challenging to account for in a broadly classical framework. For instance, while a sentence of the form $$p\wedge \Diamond \lnot p$$ (‘p, but it might be that not p’) appears to be a contradiction, $$\Diamond \lnot p$$ does not entail $$\lnot p$$, which would follow in classical logic. Likewise, the classical laws of distributivity and disjunctive syllogism fail for epistemic modals. Existing attempts to account for these facts generally either under- or over-correct. (...) Some theories predict that $$ p\wedge \Diamond \lnot p$$, a so-called epistemic contradiction, is a contradiction only in an etiolated sense, under a notion of entailment that does not always allow us to replace $$p\wedge \Diamond \lnot p$$ with a contradiction; these theories underpredict the infelicity of embedded epistemic contradictions. Other theories savage classical logic, eliminating not just rules that intuitively fail, like distributivity and disjunctive syllogism, but also rules like non-contradiction, excluded middle, De Morgan’s laws, and disjunction introduction, which intuitively remain valid for epistemic modals. In this paper, we aim for a middle ground, developing a semantics and logic for epistemic modals that makes epistemic contradictions genuine contradictions and that invalidates distributivity and disjunctive syllogism but that otherwise preserves classical laws that intuitively remain valid. We start with an algebraic semantics, based on ortholattices instead of Boolean algebras, and then propose a possibility semantics, based on partial possibilities related by compatibility. Both semantics yield the same consequence relation, which we axiomatize. We then show how to lift an arbitrary possible worlds model for a non-modal language to a possibility model for a language with epistemic modals. The goal throughout is to retain what is desirable about classical logic while accounting for the non-classicality of epistemic vocabulary. (shrink)

Timothy Williamson has recently argued that the applicability of classical mathematics in the natural and social sciences raises a problem for the endorsement, in non-mathematical domains, of a wide range of non-classical logics. We first reconstruct his argument and present its restriction to the case of quantum logic (QL). Then we show that there is no problematic tension between the applicability of classical mathematical models to quantum phenomena and the endorsement of QL in the reasoning about the latter. Once we (...) identify the premise in Williamson’s argument that turns out to be false when restricted to QL, we argue that the same premise fails for a wider variety of non-classical logics. In the end, we use our discussion to draw some general lessons concerning the relationship between applied logic and applied mathematics. (shrink)

The rapid advancements in healthcare technologies have resulted in an enormous increase in biomedical data, creating the need for innovative approaches to harness this information for early disease detection. Big Data Analytics (BDA) combined with Artificial Intelligence (AI) offers unprecedented opportunities to analyze complex biomedical signal patterns and predict the onset of diseases at an early stage. The application of AI techniques like machine learning and deep learning in conjunction with BDA allows for the detection of subtle patterns in large (...) datasets that might be missed by conventional diagnostic methods. This paper explores the integration of Big Data Analytics and AI for early disease detection through the analysis of biomedical signal patterns, such as electrocardiograms (ECG), electroencephalograms (EEG), and wearable sensor data. AI algorithms, trained on vast datasets, can recognize early warning signals of various diseases such as cardiovascular disorders, neurodegenerative diseases, and respiratory conditions. The ability to analyze these signals in real time enables early intervention, potentially improving patient outcomes and reducing healthcare costs. A comprehensive literature review highlights the use of BDA and AI in biomedical applications and the challenges associated with data volume, quality, and heterogeneity. We propose a system methodology that combines AI models with real-time Big Data Analytics to process biomedical signals efficiently and accurately. The proposed system leverages AI for feature extraction and classification while utilizing Big Data tools to handle the massive influx of data from biomedical devices and sensors. This approach not only enhances diagnostic precision but also paves the way for personalized healthcare solutions. (shrink)

Modern Thought Dynamics: The Circular Theory Autonomous Intentional Masking (AIM) Monetization, Tokenization, Digitization Templates See: Back to Basics: The Ontology of Information, The Constant Variable: A Unified Field Theory, The Importance of Unitization, Advanced Autonomous Intelligence (all articles on Medium and PhilPapers) Also, AIM on Amazon and Medium.

There are fundamentally two mathematical logics. One the Boolean logic of subsets, usually presented today in the special case of propositional logic, which has many sublogics and extensions, the most important being the intuitionistic logic usually modeled by the open subsets of a topological space. The other co-fundamental mathematical logic is the topic of this book, the logic of partitions. We are using ”logic” in a mathematical sense as being about basic mathematical objects, subsets of a universe set or partitions (...) on a universe set.1 Logic, in this mathematical sense, is not about propositions, although, as with any mathematical theory, it involves propositions about the basic objects, e.g., that an element is in a subset or that a distinction is made by a partition. Moreover, by taking the universe set to be the one element set 1, with two subsets ∅ and 1, there is a special case of subset logic, namely propositional logic, that can be interpreted as being about propositions with ∅ representing falsehood and 1 representing truth. (shrink)

We introduce a sequent system which is Gentzen algebraisable with orthomodular lattices as equivalent algebraic semantics, and therefore can be viewed as a calculus for orthomodular quantum logic. Its sequents are pairs of non-associative structures, formed via a structural connective whose algebraic interpretation is the Sasaki product on the left-hand side and its De Morgan dual on the right-hand side. It is a substructural calculus, because some of the standard structural sequent rules are restricted—by lifting all such restrictions, one recovers (...) a calculus for classical logic. (shrink)

El presente trabajo pretende explicitar que los operadores modales, como construcciones lógicas, insertos en las interpretaciones modales (MI) de la mecánica cuántica son usados de manera informal sin una semántica modal adecuada. Primero se estudiarán en detalle los motivos por los que ninguna lógica cuántica puede ofrecer una base apropiada para formalizar estos operadores en contextos mecánico-cuánticos. A continuación, se presentará el enfoque de las historias cuánticas como una nueva lógica cuántica (NQL) intrínsecamente booleana como posible herramienta para formalizar operadores (...) modales en el contexto de las MI. Tras comentar brevemente las principales MI, se propondrá abordar un estudio de las modalidades presentes en ellas desde esta NQL prestando siempre especial atención al problema de la medida como hilo conductor. Finalmente, se pretende señalar cuáles han de ser los primeros pasos necesarios para ofrecer una exposición lógicamente consistente de las modalidades en contextos cuánticos relevantes con NQL como herramienta, así como señalar las ventajas que esta perspectiva podría llegar a ofrecer. (shrink)

Este artículo presenta una aproximación lógico-filosófica al problema de las medidas sin interacción (ifm, por sus siglas en inglés) presentes en ciertos experimentos físicos mecánico-cuánticos. Se explicitarán tanto las posibles vías para abordar el estudio de las IFM desde una perspectiva formal, como algunos de los principales retos a la hora de llevar a cabo dicha aproximación.

We give a proof-theoretic as well as a semantic characterization of a logic in the signature with conjunction, disjunction, negation, and the universal and existential quantifiers that we suggest has a certain fundamental status. We present a Fitch-style natural deduction system for the logic that contains only the introduction and elimination rules for the logical constants. From this starting point, if one adds the rule that Fitch called Reiteration, one obtains a proof system for intuitionistic logic in the given signature; (...) if instead of adding Reiteration, one adds the rule of Reductio ad Absurdum, one obtains a proof system for orthologic; by adding both Reiteration and Reductio, one obtains a proof system for classical logic. Arguably neither Reiteration nor Reductio is as intimately related to the meaning of the connectives as the introduction and elimination rules are, so the base logic we identify serves as a more fundamental starting point and common ground between proponents of intuitionistic logic, orthologic, and classical logic. The algebraic semantics for the logic we motivate proof-theoretically is based on bounded lattices equipped with what has been called a weak pseudocomplementation. We show that such lattice expansions are representable using a set together with a reflexive binary relation satisfying a simple first-order condition, which yields an elegant relational semantics for the logic. This builds on our previous study of representations of lattices with negations, which we extend and specialize for several types of negation in addition to weak pseudocomplementation; in an appendix, we further extend this representation to lattices with implications. Finally, we discuss adding to our logic a conditional obeying only introduction and elimination rules, interpreted as a modality using a family of accessibility relations. (shrink)

Hardy and Unruh constructed a family of non-maximally entangled states of pairs of particles giving rise to correlations that cannot be accounted for with a local hidden-variable theory. Rather than pointing to violations of some Bell inequality, however, they pointed to apparent clashes with the basic rules of logic. Specifically, they constructed these states and the associated measurement settings in such a way that the outcomes satisfy some conditionals but not an additional one entailed by them. Quantum mechanics avoids the (...) broken ‘if …then …’ arrows in such Hardy–Unruh chains, as we call them, because it cannot simultaneously assign truth values to all conditionals involved. Measurements to determine the truth value of some preclude measurements to determine the truth value of others. Hardy–Unruh chains thus nicely illustrate quantum contextuality: which variables do and do not obtain definite values depends on what measurements we decide to perform. Using a framework inspired by Bub and Pitowsky and developed in our book Understanding Quantum Raffles (co-authored with Michael E. Cuffaro), we construct and analyze Hardy–Unruh chains in terms of fictitious bananas mimicking the behavior of spin-1/2 particles. (shrink)

Dynamic quantum logic (DQL) is studied to represent the proposition of dynamism in quantum information theory as traditional quantum logic cannot deal with it. Although DQL includes many important notions for quantum physics and quantum information theory, there are still missing elements. Some concepts of measuring a specific physical quantity cannot be represented in the exiting DQL. In this study, we add a new concept of measurement to DQL, and discuss the property of this new logic.