The Yijing/Binary System Episode involved Leibniz' discovery of a de facto representation of the binary number system in the sixty-four-hexagram Fu Xi "Yijing." Scholars have left the match unexplained, since they have found no evidence of a forgotten binary number system in ancient China. The interesting similarities and differences are discussed between the thought of Leibniz and that of Shao Yong, both of whom, it is argued, understood and recognized the importance of the double (...) geometric progression in the diagram. (shrink)

Gottfried Wilhelm Leibniz is the self-proclaimed inventor of the binary system and is considered as such by most historians of mathematics and/or mathematicians. Really though, we owe the groundwork of today’s computing not to Leibniz but to the Englishman Thomas Harriot and the Spaniard Juan Caramuel de Lobkowitz, whom Leibniz plagiarized. This plagiarism has been identified on the basis of several facts: Caramuel’s work on the binary system is earlier than Leibniz’s, Leibniz was acquainted—both directly and (...) indirectly—with Caramuel’s work and Leibniz had a natural tendency to plagiarize scientific works. (shrink)

Scholars writing on theories of punishment generally try to answer two main questions: what human behaviour should be punished and why? Only cursorily do they concern themselves with the question as to how confident in the occurrence of criminal behaviour we must be prior to punishing—i.e., the question of the criminal standard of proof. Theories of punishment are ultimately theories about choices of action—in particular, about how to treat individuals. If this is correct, it seems that they should not overlook (...) one of the fundamental variables governing human decision-making: the uncertainty about the facts relevant to our acting. Now, the question as to whether existing theories of punishment require a standard of proof as high as ‘proof beyond a reasonable doubt’ is gaining increasing attention in the scholarship. However, scholars working on theories of punishment give little attention to a particular way in which human decision-making handles the problem of uncertainty. In our everyday lives, we often decide in a many-valued, rather than a binary, fashion. Instead of having a single evidential threshold, the satisfaction of which determines whether we act or stay put, we tend to adjust our actions to our degree of confidence in certain states of affairs. In other words, we decide based on a ladder of evidential thresholds: the features of our actions vary according to the evidential threshold that we have satisfied. Notably, criminal trials do not follow this structure and theorists generally take this departure for granted. Why shouldn’t trials work as ‘ex post facto bets,’ whereby the response that the state is willing to ‘wager’ correlates with the fact finder’s confidence in the defendant’s guilt? The paper explores this question; in particular, it assesses whether the main theories of punishment necessarily deliver a binary system of verdicts. The work is part of a long-term research project on the comparison between the binary and the many-valued models of the system of criminal verdicts. (shrink)

The thesis of this paper is that a new kind of epistemology evolves from the use of artificial intelligence. The path it takes changes our understanding of the world, of human values and also of science and will be irreversible. The question that arises is whether this form of intelligence also influences our knowledge structure. By this I mean the area that we outline philosophically as the epistemological area. So the question is, under these circumstances, is the way we gain (...) knowledge today still comparable to the definitions that philosophy has provided us with for centuries? The answer is: No! The paper sketches in broad outlines what the cornerstones of change will be and what consequences this will have for our way of understanding. (shrink)

We introduce the appropriate iterated version of the system of ordinal notations from [G1] whose order type is the familiar Howard ordinal. As in [G1], our ordinal notations are partly inspired by the ideas from [P] where certain crucial properties of the traditional Munich' ordinal notations are isolated and used in the cut-elimination proofs. As compared to the corresponding “impredicative” Munich' ordinal notations (see e.g. [B1, B2, J, Sch1, Sch2, BSch]), our ordinal notations arearbitrary terms in the appropriate simple (...) term algebra based on the notion of collapsing functions (which we would rather identify as projective functions). In Sect. 1 below we define the systems of ordinal notationsPRJ( ), for any primitive recursive limit wellordering . In Sect. 2 we prove the crucial well-foundness property by using the appropriate well-quasi-ordering property of the corresponding binary labeled trees [G3]. In Sect. 3 we interprete inPRJ( ) the familiar Veblen-Bachmann hierarchy of ordinal functions, and in Sect. 4 we show that the corresponding Buchholz's system of ordinal notationsOT( ) is a proper subsystem ofPRJ( ), although it has the same order type according to [G3] together with the interpretation from Sect. 2 in the terms of labeled trees. In Sect. 5 we use Friedman's approach in order to obtain an appropriate purely combinatorial statement which is not provable in the theory of iterated inductive definitions ID< λ, for arbitrarily large limit ordinalλ. Formal theories, axioms, etc. used below are familiar in the proof theory of subsystems of analysis (see [BFPS, T, BSch]). (shrink)

The first collection of Leibniz's key writings on the binary system, newly translated, with many previously unpublished in any language. -/- The polymath Gottfried Wilhelm Leibniz (1646–1716) is known for his independent invention of the calculus in 1675. Another major—although less studied—mathematical contribution by Leibniz is his invention of binary arithmetic, the representational basis for today's digital computing. This book offers the first collection of Leibniz's most important writings on the binary system, all newly translated (...) by the authors with many previously unpublished in any language. Taken together, these thirty-two texts tell the story of binary as Leibniz conceived it, from his first youthful writings on the subject to the mature development and publication of the binary system. -/- As befits a scholarly edition, Strickland and Lewis have not only returned to Leibniz's original manuscripts in preparing their translations, but also provided full critical apparatus. In addition to extensive annotations, each text is accompanied by a detailed introductory “headnote” that explains the context and content. Additional mathematical commentaries offer readers deep dives into Leibniz's mathematical thinking. The texts are prefaced by a lengthy and detailed introductory essay, in which Strickland and Lewis trace Leibniz's development of binary, place it in its historical context, and chart its posthumous influence, most notably on shaping our own computer age. (shrink)

We investigate the formal theory of binary quantifiers, that is, quantifiers that take seriously the surface structure of natural language quantifier phrases. We show how to develop a natural deduction system for logics of this sort and demonstrate soundness and completeness results.

Black-white, male-female — these and other markers, applied maliciously or not, enable the social dominance of one group.

Let ( * X, * T) be the nonstandard extension of a Hausdorff space (X, T). After Wattenberg [6], the monad m(x) of a near-standard point x in * X is defined as m(x) = μ T (st(x)). Consider the relation $R_{\mathrm{ns}} = \{\langle x, y \rangle \mid x, y \in \mathrm{ns} (^\ast X) \text{and} y \in m(x)\}.$ Frank Wattenberg in [6] and [7] investigated the possibilities of extending the domain of R ns to the whole of * X. Wattenberg's (...) extensions of R ns were required to be equivalence relations, among other things. Because the nontrivial ways of constructing such extensions usually produce monadic relations, the said condition practically limits (to completely regular spaces) the class of spaces for which such extensions are possible. Since symmetry and transitivity are not, after all, characteristics of the kind of nearness that is obtained in a general topological space, it may be expected that if these two requirements are relaxed, then a monadic extension of R ns to * X should be possible in any topological space. A study of such extensions of R ns is the purpose of the present paper. We call a binary relation $W \subseteq ^\ast X \times ^\ast X$ an infinitesimal on * X if it is monadic and reflexive on * X. We prove, among other things, that the existence of an infinitesimal on * X that extends R ns is equivalent to the condition that the space (X, T) be regular. (shrink)

While we completely understood that a binary dwarf companion of the Sun has not been accepted by majority of astronomers, allow us to present some new arguments, along with our own serendipitous encounter with such a binary companion of the Sun. We hope that the present note will be found useful for further investigations, in relation to Planet Nine and such a dwarf star companion of the Sun (sometimes dubbed as Nemesis). Nonetheless, this article is not an exhaustive (...) review of such dwarf companion star theories. (shrink)

This paper presents a way of formalising definite descriptions with a binary quantifier ι, where ιx[F, G] is read as ‘The F is G’. Introduction and elimination rules for ι in a system of intuitionist negative free logic are formulated. Procedures for removing maximal formulas of the form ιx[F, G] are given, and it is shown that deductions in the system can be brought into normal form.

The study considers the development of methods for detecting anomalous network connections based on hybridization of computational intelligence methods. An analysis of approaches to detecting anomalies and abuses in computer networks. In the framework of this analysis, a classification of methods for detecting network attacks is proposed. The main results are reduced to the construction of multi-class models that increase the efficiency of the attack detection system, and can be used to build systems for classifying network parameters during the (...) attack. A model of an artificial immune system based on an evolutionary approach, an algorithm for genetic-competitive learning of the Kohonen network and a method of hierarchical hybridization of binary classifiers with the addition to the detection of anomalous network connections have been developed. The architecture of the network distributed attack detection system has been developed. The architecture of the attack detection system is two-tier: the first level provides the primary analysis of individual packets and network connections using signature analysis, the second level processes the processing of aggregate network data streams using adaptive classifiers. A signature analysis was performed to study network performance based on the Aho-Korasik and Boyer-Moore algorithms and their improved analogues were implemented using OpenMP and CUDA technologies. The architecture is presented and the main points of operation of the network attack generator are shown. A system for generating network attacks has been developed. This system consists of two components: an asynchronous transparent proxy server for TCP sessions and a frontend interface for a network attack generator. The results of the experiments confirmed that the functional and non-functional requirements, as well as the requirements for computing intelligent systems, are met for the developed attack detection system. (shrink)

This paper presents rules in sequent calculus for a binary quantifier I to formalise definite descriptions: Ix[F, G] means ‘The F is G’. The rules are suitable to be added to a system of positive free logic. The paper extends the proof of a cut elimination theorem for this system by Indrzejczak by proving the cases for the rules of I. There are also brief comparisons of the present approach to the more common one that formalises definite (...) descriptions with a term forming operator. In the final section rules for I for negative free and classical logic are also mentioned. (shrink)

This chapter shows how Luce Irigaray reaches back to alternative sources of philosophy as she looks for the conditions for the emergence of the female subject. It also shows the grip of rigidity on Western philosophy since its inception and points out its consequences with regard to subjectivity and power. Philosophy has operated with a rigid binary system of logic ever since its inception in ancient Greece. Everyone agrees that Parmenides had an enormous influence on the development of (...) logic. However, there is disagreement on how this influence should be evaluated. It is the awareness of the use of power and efforts to mastery which accompany the construction of dichotomies that lie at the heart of feminist critiques of binary logic. The Pythagorean table of opposites, which was developed in the sixth century BCE, is an early articulation of a binary system. (shrink)

ArgumentThe Jesuit Joachim Bouvet established an analogy between the binary arithmetic developed by Leibniz and the diagram Fuxi liushisi gua fangwei (or FX64), attributed to Shao Yong, which organizes the sixty-four hexagrams according to the Fuxi/Xiantian order. Consequently, this diagram could be considered as binary. Some scholars argue that the diagram is not binary because of the different construction of the two systems and the “wrong” reading direction used by Bouvet and Leibniz—opposite to the one used in (...) China. Nevertheless, by a superimposition of Leibniz’s binary table and of the derivation table used to construct the diagram, this article shows that the diagram is binary, since it is constituted of two elements and the binary system can use other symbols than 0 and 1. The reverse methodology used in constructing the two systems because of their different purpose—division for the FX64 diagram and multiplication for Leibniz’s dyad—allows their reading from either one direction or the reverse. This does not affect the fact that they are both binary, since it leads to the same form and structure. (shrink)

While addressing the decolonial critique of Eurocentric modernity and the call for alternative cosmo-visions, this article retraces Juri Lotman’s culturological exploration towards the concept of ternarity [тернарность]: the scrutiny of the so-called binarism is what connects – without overlapping – the two perspectives. This long-distance dialogue will be built starting with the key notion of binary opposition, which will be analysed as a decolonial problem (Part I) and as a culturological problem (Part II). The analysis will focus on two (...) central issues that stem from the either-or logic: the “othering mindset”, and the culture–nature dualism. (shrink)

Everyday thinking and scientific theorizing about human action control are equally driven by the apparently obvious contrast between will and habit or, in their more modern disguise: intentional and automatic processes, and model-based and model-free action planning. And yet, no comprehensive category system to systematically tell truly willed from merely habitual actions is available. As I argue, this is because the contrast is ill-conceived, because almost every single action is both willed and habitual, intentional and automatic, and model-based and (...) model-free, simply because will and habit (and their successors) do not refer to alternative modes or pathways of action control but rather to different phases of action planning. I further discuss three basic misconceptions about action control that binary theorizing relies on: the assumption that intentional processes compete with automatic processes (rather than the former setting the stage for the latter), the assumption that action control is targeting processes (rather than representations of action outcomes), and the assumption that people follow only one goal at a time (rather than multiple goals). I conclude that (at least the present style of) binary theorizing fails to account for action control and should thus be replaced by a more integrative view. (shrink)

ArgumentThis essay seeks to identify the cultural significance of Goethe's scientific writings. He reformulates, in the light of his own concrete experience, “crucial turning-points” in the history of science – key ideas, the historical understanding of which is vital to present understanding – thus situating his own scientific work at the bi-polar center of the Western scientific tradition, conceived as the dramatic interplay over centuries of two opposing modes of thought. For in his experimentation he recaptures the glimpse of living (...) form gained in aesthetic perception, from which such inherited theoretical positions are ultimately derived. At each stage of this process, imagination, in its aesthetic modality, is essential, for it alone reveals the world as it truly is. The literary quality of his writings on nature, as on culture, reveals Goethe's stylistic achievement in devising a medium in which the insights gained in contemplation may be so transmitted as to make a similar, imaginative, appeal to his reader – re-enacting the abstract-concrete equilibrium characterizing all aesthetic experience. Matching his style to the subtle, delicate, connectedness of Nature, Goethe recreates the delights of participating in natural creativity. His Janus-faced, scientific-literary, style illustrates “binary synthesis,” the principle that unites Goethe's science with his art.Beauty is the normal state.There can be no such thing as an eclectic philosophy, but there can be eclectic philosophers. But an eclectic is anyone who, from whatever exists and is happening round about, appropriates the things he or she finds congenial to her or his nature; and this context validly includes all that can be called culture and progress in a theoretical and practical sense. It follows that two eclectic philosophers could turn into the greatest opponents if they are antagonistic to one another, each picking out whatever suits him or her in every traditional system of philosophy. (shrink)

In this paper, we explore the relation between an agent’s doxastic attitude and her arguments in support of a given claim. Our main contribution is the design of a logical setting that allows us reason about binary arguments which are either in favour or against a certain claim. This is a setting in which arguments and propositions are the basic building blocks so that the concept of argument-based belief emerges in a straightforward way. We work against the background of (...) Dung’s abstract argumentation framework, extending it to a new setting in which we can study the formal properties of binary arguments as well as the larger structures they establish. This paper introduces a formal ‘two-dimensional’ language to talk about propositions and arguments, for which a sound and complete axiom system is provided. (shrink)

This paper deals with two sorts of binary Kripke-style semantics, i.e., algebraic and non-algebraic semantics, for three-valued logic. We first introduce three systems, their corresponding algebraic structures, and associated algebraic completeness results. We next introduce various types of algebraic and non-algebraic binary relational Kripke-style semantics. © 2016 Elsevier B.V., All rights reserved.

The question of whether reality is fundamentally digital or analog has captivated physicists, philosophers, and computer scientists for decades. Traditional approaches have forced this inquiry into a binary framework, seeking to classify reality as either discrete (digital) or continuous (analog). This paper presents a revolutionary paradigm shift through the introduction of the Triadic Information-Reality Framework (TIRF), which proposes that reality exists in three fundamental modes: Digital, Analog, and Liminal. Drawing upon recent experimental evidence from quantum mechanics, Wheeler's information-theoretic foundations, (...) the holographic principle, and dialectical philosophical analysis, we demonstrate that the digital-analog dichotomy represents a false binary that has constrained our understanding of reality's true nature. -/- Our framework resolves longstanding paradoxes in quantum mechanics, unifies disparate theoretical perspectives, and makes testable predictions about the behavior of physical systems across different scales. The Liminal mode, representing states that are "neither continuous nor discrete," provides a theoretical foundation for understanding quantum superposition, measurement transitions, and the emergence of spacetime at the Planck scale. Through mathematical formalization using mode state vectors and transition operators, we show how reality's character depends on observation parameters, scale, and temporal context. -/- The implications of TIRF extend beyond theoretical physics to quantum computing, artificial intelligence, and our fundamental understanding of information processing in the universe. We present four key experimental predictions that can distinguish our framework from existing theories, including mode transition signatures during quantum measurement, modified information bounds for each mode, triadic entanglement patterns, and novel computational complexity classes. This work represents the first comprehensive attempt to transcend the binary thinking that has dominated discussions of reality's nature, offering a more nuanced and empirically grounded understanding of existence itself. (shrink)

The feature selection (FS) process has an essential effect in solving many problems such as prediction, regression, and classification to get the optimal solution. For solving classification problems, selecting the most relevant features of a dataset leads to better classification accuracy with low training time. In this work, a hybrid binary crow search algorithm (BCSA) based quasi-oppositional (QO) method is proposed as an FS method based on wrapper mode to solve a classification problem. The QO method was employed in (...) tuning the value of flight length in the BCSA which is controlling the ability of the crows to find the optimal solution. To evaluate the performance of the proposed method, four benchmark datasets have been used which are human intestinal absorption, HDAC8 inhibitory activity (IC50), P-glycoproteins, and antimicrobial. Accordingly, the experimental results are discussed and compared against other standard algorithms based on the accuracy rate, the average number of selected features, and running time. The results have proven the robustness of the proposed method relied on the high obtained value of accuracy (84.93–95.92%), G-mean (0.853–0.971%), and average selected features (4.36–11.8) with a relatively low computational time. Moreover, to investigate the effectiveness of the proposed method, Friedman test was used which declared that the performance supremacy of the proposed BCSA-QO with four datasets was very evident against BCSA and CSA by selecting the minimum relevant features and producing the highest accuracy classification rate. The obtained results verify the usefulness of the proposed method (BCSA-QO) in the FS with classification in terms of high classification accuracy, a small number of selected features, and low computational time. (shrink)

In previous work [4] we introduced and examined the class of betweenness algebras. In the current article we study a larger class of algebras with binary operators of possibility and sufficiency, the weak mixed algebras. Furthermore, we develop a system of logic with two binary modalities, sound and complete with respect to the class of frames closely related to the aforementioned algebras, and we prove an embedding theorem which solves an open problem from [4].

We present a proof for a conjecture previously formulated by Dzhafarov et al.. The conjecture specifies a measure for the degree of contextuality and a criterion for contextuality in a broad class of quantum systems. This class includes Leggett–Garg, EPR/Bell, and Klyachko–Can–Binicioglu–Shumovsky type systems as special cases. In a system of this class certain physical properties \ are measured in pairs \ \); every property enters in precisely two such pairs; and each measurement outcome is a binary random (...) variable. Denoting the measurement outcomes for a property \ in the two pairs it enters by \ and \, the pair of measurement outcomes for \ \) is \ \). Contextuality is defined as follows: one computes the minimal possible value \ for the sum of \ ) that is allowed by the individual distributions of \ and \; one computes the minimal possible value \ for the sum of \ across all possible couplings of the entire set of random variables \ in the system; and the system is considered contextual if \ ). This definition has its justification in the general approach dubbed Contextuality-by-Default, and it allows for measurement errors and signaling among the measured properties. The conjecture proved in this paper specifies the value of \ in terms of the distributions of the measurement outcomes \ \). (shrink)

Rhythmic stress is assigned automatically in everyday speech. Usually, it is produced without conscious planning of which syllables have to be stressed. However, the ‘grammaticalisation’ of rhythmic patterns is the result of language processing. It is the outcome of a selective process which is proposed to lead to a preference or dispreference for specific rhythmic structures. In the languages of the world, judging by the typological data available, some rhythmic patterns seem to be completely avoided – even if this means (...) an increase of complexity within a stress system. Focussing on asymmetries in binary stress systems, it is suggested in this paper that processing limitations in speech production motivate stress patterns. It is also demonstrated that the domain of the prosodic word is insufficient for a motivation of these asymmetries. Since one-word sentences are not the rule, but the exception, asymmetries find their motivation on the level of the sentence. (shrink)

Saul Kripke’s work on the semantics of modal logics is well known, unlike his work on Anderson and Belnap’s system E of Entailment (a modal relevance logic), which included his proof of the decidability of its implicational fragment E_>, and also a counterexample to the conjecture of Belnap that E_> is the intersection of the implicational fragments of the relevance logic R and the modal logic S4. This led to Storrs McCall’s suggesting that the “mingle” axiom might be added (...) to E_>, and that this system might be used instead of S4_>. We give a counterexample to this conjecture. We also disprove the conjecture Anderson and Belnap attribute to McCall, in which “restricted mingle” is added to E_>. We use a modal extension of the lattice M_0 and follow ideas of Meyer. In the 1970s, Dunn showed that RM (R with the mingle axiom) can be modeled using a binary accessibility relation, like the accessibility relation in Kripke’s semantics for normal modal logics and his semantics for intuitionistic logic. Dunn also gave a variant interpretation for EM (E with the mingle axiom). We explore some other variations of these binary relational semantics. (shrink)

Philosophical and ethical discussions of warfare are often tied to emerging technologies and techniques. Today we are presented with what many believe is a radical shift in the nature of war-the realization of conflict in the cyber-realm, the so-called.

We prove an exponential lower bound on the size of proofs in the proof system operating with ordered binary decision diagrams introduced by Atserias, Kolaitis and Vardi [2]. In fact, the lower bound applies to semantic derivations operating with sets defined by OBDDs. We do not assume any particular format of proofs or ordering of variables, the hard formulas are in CNF. We utilize (somewhat indirectly) feasible interpolation. We define a proof system combining resolution and the OBDD (...) proof system. (shrink)

This pilot study examines how individuals of diverse sexual orientations and gender identities and expressions (SOGIE), specifically fa’afafine, fa’atama, and lesbian/bisexual women, navigate and contribute to Samoa’s fisheries value chains. Drawing on a culturally grounded Pacific Research Paradigm and employing talanoa driven focus group discussions, in-depth interviews, and vendor surveys conducted between October and December 2021, we document the informal yet essential roles these communities play across reef gleaning, nearshore fishing, post-harvest processing, and fish vending. Grounded theory analysis reveals that, (...) while SOGIE individuals possess extensive ecological knowledge and adaptive livelihood strategies, their participation remains largely invisible to formal fisheries programs due to binary driven policies, systemic stigma, and restrictive village governance. Fa’afafine are encouraged and accepted in taking on “feminine” tasks (e.g. processing and retail), and similarly, fa’atama performing “masculine” fishing methods and roles are also accepted, though without formal recognition. Lesbian/bisexual women sustain critical gleaning niches that underpin household food security. Economic resilience often relies on kinship networks and livelihood diversification, yet access to training, credit, and decision-making forums is constrained. By centring relational values, this study not only broadens gender analysis in fisheries beyond men and women but also offers practical recommendations: policy frameworks must explicitly include SOGIE individuals in training, microfinance, and governance; and fisheries extension services should co-design interventions with local SOGIE organizations. Our findings underscore the transformative potential of queering fisheries policies in Pacific contexts and chart pathways for more equitable and inclusive marine resource management. (shrink)

I show that the logic $\textsf {TJK}^{d+}$, one of the strongest logics currently known to support the naive theory of truth, is obtained from the Kripke semantics for constant domain intuitionistic logic by dropping the requirement that the accessibility relation is reflexive and only allowing reflexive worlds to serve as counterexamples to logical consequence. In addition, I provide a simplified natural deduction system for $\textsf {TJK}^{d+}$, in which a restricted form of conditional proof is used to establish conditionals.

In this article, we explore the extraction of recursive nested structure in the processing of binary sequences. Our aim was to determine whether humans learn the higher-order regularities of a highly simplified input where only sequential-order information marks the hierarchical structure. To this end, we implemented a sequence generated by the Fibonacci grammar in a serial reaction time task. This deterministic grammar generates aperiodic but self-similar sequences. The combination of these two properties allowed us to evaluate hierarchical learning while (...) controlling for the use of low-level strategies like detecting recurring patterns. The deterministic aspect of the grammar allowed us to predict precisely which points in the sequence should be subject to anticipation. Results showed that participants’ pattern of anticipation could not be accounted for by “flat” statistical learning processes and was consistent with them anticipating upcoming points based on hierarchical assumptions. We also found that participants were sensitive to the structure constituency, suggesting that they organized the signal into embedded constituents. We hypothesized that the participants built this structure by merging recursively deterministic transitions. (shrink)

Male infertility contributes to nearly half of the global infertility, yet nursing scholarship continues to marginalize men's experiences, reflecting entrenched assumptions that equate reproduction with femininity. This article reframes male infertility as a relational, socially embedded phenomenon and a site of disciplinary transformation. Drawing on intersectionality, masculinity theory, performativity, and stigma, this article shows how race, class, sexuality, disability, and cultural context intersect to produce compounded stigma, invisibility, and restricted access to care. For example, queer and trans men remain largely (...) invisible in heteronormative reproductive discourse, while men from low‐resource settings face systemic barriers to psychosocial support. To address these silences, this paper proposes an intersectional nursing proposition grounded in reflexivity, cultural humility, couple‐centeredness, and structural awareness. Visual scaffolding (one table and two figures) clarifies the pathway from entrenched binaries to intersectional praxis. The manuscript presents male infertility as both a clinical and theoretical challenge, urging nursing to reconceptualize care, vulnerability, and reproductive justice to serve diverse masculinities and reduce structural inequities. (shrink)

Consider chemical elements as a system, we create an undirected chemical network with 99 elements and 1916 edges from Chemspider, a website that provide search engines to collect compounds. Using this network and the network that we used in our previous work with 97 elements and 2198 edges, we found that RootedPageRank, a link prediction tool in complex network, can be used to predict potential binary compounds, because the changing trend of PageRank probability of each element in these (...) networks all follow the periodic law, despite of the difference of scale of these networks. The accuracy test indicates that at least 7 among top 10 predicted compoundss in one network can be verified using the compoundss in the other network or in other chemical database, proving that this method can be used to provide guidance in finding potential binary compounds, suggesting that we can study chemical properties from the view of complex network. (shrink)

In 1941, Tarski published an abstract, finitely axiomatized version of the theory of binary relations, called the theory of relation algebras, He asked whether every model of his abstract theory could be represented as a concrete algebra of binary relations. He and Jonsson obtained some initial, positive results for special classes of abstract relation algebras. But Lyndon showed, in 1950, that in general the answer to Tarski's question is negative. Monk proved later that the answer remains negative even (...) if one adjoins finitely many new axioms to Tarski's system. In this paper we describe a far-reaching generalization of the positive results of Jonsson and Tarski, as well as of some later, related results of Maddux. We construct a class of concrete models of Tarski's axioms-called coset relation algebras-that are very close in spirit to algebras of binary relations, but are built using systems of groups and cosets instead of elements of a base set. The models include all algebras of binary relations, and many non-representable relation algebras as well, We prove that every atomic relation algebra satisfying a certain measurability condition-a condition generalizing the conditions imposed by Jonsson and Tarski-is essentially isomorphic to a coset relation algebra. The theorem raises the possibility of providing a positive solution to Tarski's problem by using coset relation algebras instead of the standard algebras of binary relations. (shrink)

As a research team focused on vulnerable youth, we increasingly need to find ways to acknowledge non‐binary genders in health research. Youth have become more vocal about expanding notions of gender beyond traditional categories of boy/man and girl/woman. Integrating non‐binary identities into established research processes is a complex undertaking in a culture that often assumes gender is a binary variable. In this article, we present the challenges at every stage of the research process and questions we have (...) asked ourselves to consider non‐binary genders in our work. As researchers, how do we interrogate the assumptions that have made non‐binary lives invisible? What challenges arise when attempting to transform research practices to incorporate non‐binary genders? Why is it crucial that researchers consider these questions at each step of the research process? We draw on our own research experiences to highlight points of tensions and possibilities for change. Improving access to inclusive health‐care for non‐binary people, and non‐binary youth in particular, is part of creating a more equitable healthcare system. We argue that increased and improved access to inclusive health‐care can be supported by research that acknowledges and includes people of all genders. (shrink)

In my paper, I attempt a phenomenological analysis of the lived experience of intersexuality, which I view from the perspective of the problem of indeterminacy concerning the horizon of the givenness of homeworld founded on the broader basis of the pre-givenness of lifeworld. These horizons define the structure of the sedimentation of subjective experience, as well as the layers of cultural meanings sedimented in the lifeworld. The sedimented layers of self-experience and of the shared lifeworld function as a sphere of (...) indeterminacy, that is the horizons of constituted phenomena. In this sense all intentional acts have the nature of horizontal indeterminacy, the layers of which are revealed in the genetic question (Rückfrage) directed toward them. Horizontal indeterminacy also accounts for the distinction between homeworld and alienworld, which appears as something unobvious and unexpected against the obviousness of the homeworld, at the same time thematizing the latter. One of the elements of the sedimented conceptual system, functioning as the horizon of indeterminacy of both self-experience and the pre-reflective life-world, is the notion of human corporeality as given in the binary sexuality/gender. A unique opportunity for phenomenological insight into the constitution of the phenomenon of sex/gender is provided by Hida Viloria's lived experience of intersexuality. Her lived body, originally experienced pre-reflectively as a transparent medium and a perfectly handy tool of undisturbed intentionality, unproblematized also in the sexual activities, gradually undergoes alienation under the objectifying gaze determined by the binary pattern of sexuality. Becoming an alienated object, her body loses its transparency. Viloria begins to experience her corporeality and identity in a way determined by the sedimented "ideology" of sex and gender, trying on the "constructs" of masculine and feminine identities, eventually overcoming alienation and, in a process of secondary self-identification, reclaiming her lived body in its intersexuality and her identity in its non-binary gender fluidity. (shrink)

The pigeon-inspired optimization algorithm is a category of a newly proposed swarm intelligence-based algorithm that belongs to the population-based solution technique. The MKP is a class of complex optimization problems that have many practical applications in the fields of engineering and sciences. Due to the practical applications of MKP, numerous algorithmic-based methods like local search and population-based search algorithms have been proposed to solve the MKP in the past few decades. This paper proposes a modified binary pigeon-inspired optimization algorithm (...) named (Modified-BPIO) for the 0 - 1 multidimensional knapsack problem (MKP). The utilization of the binary pigeon-inspired optimization (BPIO) for solving the multidimensional knapsack problem came with huge success. However, it can be observed that the BPIO converges prematurely due to lost diversity during the search activities. Given the above, the crossover operator is integrated with the landmark component of the BPIO to improve the diversity of the solution space. The MKP benchmarks from the Operations Research (OR) library are utilized to test the performance of the proposed binary method. Experimentally, it is concluded that the proposed Modified-BPIO has a better performance when compared with the BPIO and existing state-of-the-arts that worked on the same MKP benchmarks. (shrink)

From the early eighteenth century onward, primacy for the invention of binary numeration and arithmetic was almost universally credited to the German polymath Gottfried Wilhelm Leibniz (1646–1716). Then, in 1922, Frank Vigor Morley (1899–1980) noted that an unpublished manuscript of the English mathematician, astronomer, and alchemist Thomas Harriot (1560–1621) contained the numbers 1 to 8 in binary. Morley’s only comment was that this foray into binary was “certainly prior to the usual dates given for binary numeration”. (...) Almost thirty years later, John William Shirley (1908–1988) published reproductions of two of Harriot’s undated manuscript pages, which, he claimed, showed that Harriot had invented binary numeration “nearly a century before Leibniz’s time”. But while Shirley correctly asserted that Harriot had invented binary numeration, he made no attempt to explain how or when Harriot had done so. Curiously, few since Shirley’s time have attempted to answer these questions, despite their obvious importance. After all, Harriot was, as far as we know, the first to invent binary. Accordingly, answering the how and when questions about Harriot’s invention of binary is the aim of this short paper. (shrink)

What endogenous factors contribute to minority (Red Queen) or majority (Red King) domination under conditions of coercive bargaining? We build on previous work demonstrating minority disadvantage in non-coercive bargaining games to show that under neutral initial conditions, majorities are advantaged in high conflict situations, and minorities are advantaged in low conflict games. These effects are a function of the relationship between (1) relative proportions of the majority and minority groups and (2) costs of conflict. Although both Red King and Red (...) Queen effects can occur, we further show that agents’ increased initial propensity toward conflict advantages majorities. (shrink)

B. Kooi and A. Tamminga present a correspondence analysis for extensions of G. Priest’s logic of paradox. Each unary or binary extension is characterizable by a special operator and analyzable via a sound and complete natural deduction system. The present paper develops a sound and complete proof searching technique for the binary extensions of the logic of paradox.

Using the method of correspondence analysis, Tamminga obtains sound and complete natural deduction systems for all the unary and binary truth-functional extensions of Kleene’s strong three-valued logic K3. In this paper, we extend Tamminga’s result by presenting an original finite, sound and complete proof-searching technique for all the truth-functional binary extensions of K3.

The aim of this paper is to provide a contribution to the natural logic program which explores logics in natural language. The paper offers two logics called \ \) and \ \) for dealing with inference involving simple sentences with transitive verbs and ditransitive verbs and quantified noun phrases in subject and object position. With this purpose, the relational logics are introduced and a model-theoretic proof of decidability for they are presented. In the present paper we develop algebraic semantics of (...) the logics using congruence theory. (shrink)