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About this topic
Summary A logical connective is anything that joins smaller logical expressions into larger ones.  There are any number of logical connectives, depending on which logic one is using.  The subcategories here (with the obvious exception of the miscellaneous leaf node) are most appropriate for classical logic, and logics which depart from classical logic only modestly, where there is a widely held intuition (with the exception of the conditional) that the linguistic connectives, "and," "or," and "not," are, at least in most respects, the equivalents of the formal logical connectives, conjunction, disjunction, and negation.  However, even in classical propositional logic, there is the Sheffer stroke and the dagger, which allow the axiomatization of propositional logic with just one connective, but have no clear linguistic equivalent.   As one moves further afield from classical logic, along various dimensions, one will soon discover that the variety of logical connectives is limited only by the mathematical ingenuity of the human mind.  This might help explain why--with the exception of "conditionals"--there are (currently) far more entries in the miscellaneous category than there are in any of the more standard categories.
Key works Given the above variety, as discussed, there are separate key works for each logic, although there are a few multi-volume works which attempt to be all-inclusive and cover the enormous variety of logics, their operators, and their semantics.
Introductions See, key works, above.  Only the best-known logics have works that can fairly be called introductions.
Related
Subcategories
Negation* (224)
Conditionals* (2,383 | 606)
Disjunction* (68)
Conjunction* (40)
See also

Contents
433 found
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  1. A Theory of Analyticity.Matthew J. LaVine - 2016 - Dissertation, University at Buffalo
    In this dissertation, I develop a new theory for distinguishing between analytic and synthetic truths. Despite being a somewhat new combination of views, each individual view in the theory is firmly grounded in a number of earlier theories given throughout the Analytic tradition. For this reason, Chapter 1 gives an introduction to the theories of various Positivists and Wittgensteinians, Quine, and Kripke from a contemporary perspective. Chapter 2 provides an explication and evaluation of the work which began the contemporary discussion (...)
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  2. The Meaning of Logical Connectives and Prior's Tonk Argument.Jeremiah Joven Joaquin - 2024 - Philosophia: International Journal of Philosophy (Philippine e-journal) 25 (1).
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  3. Truth dependence against transparent truth.Susanna Melkonian-Altshuler - 2024 - Asian Journal of Philosophy 3 (1):1-17.
    Beall’s (e.g., 2009, 2021) transparency theory of truth is recognized as a prominent, deflationist solution to the liar paradox. However, it has been neglected by truth theorists who have attempted to show that a deflationist theory of truth can (or cannot) account for truth dependence, i.e., the claim that the truth of a proposition depends on how things described by the proposition are, but how these things are does not depend on the truth of the proposition. Truth theorists interested in (...)
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  4. Logical connectives for two-state semantics.Marta Cialdea Mayer & Luis Fariñas del Cerro - 2023 - Journal of Applied Non-Classical Logics 33 (3-4):520-536.
    1. A. Heyting (1930) introduced an intermediate logic whose semantics is based on a pair of states (‘here’ and ‘there’). This logic was axiomatized by Hosoi (1966), using the sequence of intermedia...
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  5. Do nonlinguistic creatures deploy mental symbols for logical connectives in reasoning?Susan Carey - 2023 - Behavioral and Brain Sciences 46:e267.
    Some nonlinguistic systems of representation display some of the six features of a language-of-thought (LoT) delineated by Quilty-Dunn et al. But they conjecture something stronger: That all six features cooccur homeostatically in nonlinguistic thought. Here I argue that there is no good evidence for nonlinguistic deductive reasoning involving the disjunctive syllogism. Animals and prelinguistic children probably do not make logical inferences.
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  6. Uniqueness of Logical Connectives in a Bilateralist Setting.Sara Ayhan - 2021 - In Martin Blicha & Igor Sedlár (eds.), The Logica Yearbook 2020. College Publications. pp. 1-16.
    In this paper I will show the problems that are encountered when dealing with uniqueness of connectives in a bilateralist setting within the larger framework of proof-theoretic semantics and suggest a solution. Therefore, the logic 2Int is suitable, for which I introduce a sequent calculus system, displaying - just like the corresponding natural deduction system - a consequence relation for provability as well as one dual to provability. I will propose a modified characterization of uniqueness incorporating such a duality of (...)
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  7. The Constituents of the Propositions of Logic.Kevin C. Klement - 2015 - In Donovan WIshon & Bernard Linsky (eds.), Acquaintance, Knowledge, and Logic: New Essays on Bertrand Russell’s _The Problems of Philosophy_. Stanford: CSLI Publications. pp. 189–229.
    In he Problems of Philosophy and other works of the same period, Russell claims that every proposition must contain at least one universal. Even fully general propositions of logic are claimed to contain “abstract logical universals”, and our knowledge of logical truths claimed to be a species of a priori knowledge of universals. However, these views are in considerable tension with Russell’s own philosophy of logic and mathematics as presented in Principia Mathematica. Universals generally are qualities and relations, but if, (...)
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  8. New jump operators on equivalence relations.John D. Clemens & Samuel Coskey - 2022 - Journal of Mathematical Logic 22 (3).
    We introduce a new family of jump operators on Borel equivalence relations; specifically, for each countable group [Formula: see text] we introduce the [Formula: see text]-jump. We study the elementary properties of the [Formula: see text]-jumps and compare them with other previously studied jump operators. One of our main results is to establish that for many groups [Formula: see text], the [Formula: see text]-jump is proper in the sense that for any Borel equivalence relation [Formula: see text] the [Formula: see (...)
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  9. Logical connectives.Varol Akman - 2006 - In A. C. Grayling, Naomi Goulder & Andrew Pyle (eds.), The Continuum Encyclopedia of British Philosophy (4 volumes). London: Continuum. pp. 1939-1940.
    Logical connectives (otherwise known as 'logical constants' or 'logical particles') have seemed challenging to philosophers of language. This article gives a concise account of logical connectives.
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  10. An Expressivist Analysis of the Indicative Conditional with a Restrictor Semantics.John Cantwell - 2021 - Review of Symbolic Logic 14 (2):487-530.
    A globally expressivist analysis of the indicative conditional based on the Ramsey Test is presented. The analysis is a form of ‘global’ expressivism in that it supplies acceptance and rejection conditions for all the sentence forming connectives of propositional logic (negation, disjunction, etc.) and so allows the conditional to embed in arbitrarily complex sentences (thus avoiding the Frege–Geach problem). The expressivist framework is semantically characterized in a restrictor semantics due to Vann McGee, and is completely axiomatized in a logic dubbed (...)
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  11. Poly-Connexivity: Connexive Conjunction and Disjunction.Nissim Francez - 2022 - Notre Dame Journal of Formal Logic 63 (3):343-355.
    This paper motivates the logic PCON, an extension of connexivity to conjunction and disjunction, called poly-connexivity. The motivation arises from differences in intonational stress patterns due to focus, where PCON turns out to be a logic of intentionally stressed connectives in focus.
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  12. Symbolic Logic.Rebeka Ferreira - 2022 - Gig Φ Philosophy.
    Basic Concepts in Logic Identifying & Evaluating Arguments Valid Argument Forms Complex Arguments Propositional Logic: Symbols & Translation Truth Tables: Statements Classifying & Comparing Statements.
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  13. New Relations and Separations of Conjectures About Incompleteness in the Finite Domain.Erfan Khaniki - 2022 - Journal of Symbolic Logic 87 (3):912-937.
    In [20] Krajíček and Pudlák discovered connections between problems in computational complexity and the lengths of first-order proofs of finite consistency statements. Later Pudlák [25] studied more statements that connect provability with computational complexity and conjectured that they are true. All these conjectures are at least as strong as $\mathsf {P}\neq \mathsf {NP}$ [23–25].One of the problems concerning these conjectures is to find out how tightly they are connected with statements about computational complexity classes. Results of this kind had been (...)
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  14. The two halves of disjunctive correctness.Cezary Cieśliński, Mateusz Łełyk & Bartosz Wcisło - 2023 - Journal of Mathematical Logic 23 (2).
    Ali Enayat had asked whether two halves of Disjunctive Correctness ([Formula: see text]) for the compositional truth predicate are conservative over Peano Arithmetic (PA). In this paper, we show that the principle “every true disjunction has a true disjunct” is equivalent to bounded induction for the compositional truth predicate and thus it is not conservative. On the other hand, the converse implication “any disjunction with a true disjunct is true” can be conservatively added to [Formula: see text]. The methods introduced (...)
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  15. Connexive Principles After a ‘Classical’ Turn in Medieval Logic.Spencer C. Johnston - 2021 - History and Philosophy of Logic 43 (3):251-263.
    The aim of this paper is to look at the arguments advanced by three Parisian arts masters about how to understand Prior Analytics II 4 and the more general discussion that medieval authors situate...
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  16. What is a Relevant Connective?Shawn Standefer - 2022 - Journal of Philosophical Logic 51 (4):919-950.
    There appears to be few, if any, limits on what sorts of logical connectives can be added to a given logic. One source of potential limitations is the motivating ideology associated with a logic. While extraneous to the logic, the motivating ideology is often important for the development of formal and philosophical work on that logic, as is the case with intuitionistic logic. One family of logics for which the philosophical ideology is important is the family of relevant logics. In (...)
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  17. Modal Definability: Two Commuting Equivalence Relations.Yana Rumenova & Tinko Tinchev - 2022 - Logica Universalis 16 (1):177-194.
    We prove that modal definability with respect to the class of all structures with two commuting equivalence relations is an undecidable problem. The construction used in the proof shows that the same is true for the subclass of all finite structures. For that reason we prove that the first-order theories of these classes are undecidable and reduce the latter problem to the former.
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  18. On Induction Principles for Partial Orders.Ievgen Ivanov - 2022 - Logica Universalis 16 (1):105-147.
    Various forms of mathematical induction are applicable to domains with some kinds of order. This naturally leads to the questions about the possibility of unification of different inductions and their generalization to wider classes of ordered domains. In the paper we propose a common framework for formulating induction proof principles in various structures and apply it to partially ordered sets. In this framework we propose a fixed induction principle which is indirectly applicable to the class of all posets. In a (...)
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  19. An Unexpected Boolean Connective.Sérgio Marcelino - 2022 - Logica Universalis 16 (1):85-103.
    We consider a 2-valued non-deterministic connective \({\wedge \!\!\!\!\!\vee }\) defined by the table resulting from the entry-wise union of the tables of conjunction and disjunction. Being half conjunction and half disjunction we named it _platypus_. The value of \({\wedge \!\!\!\!\!\vee }\) is not completely determined by the input, contrasting with usual notion of Boolean connective. We call non-deterministic Boolean connective any connective based on multi-functions over the Boolean set. In this way, non-determinism allows for an extended notion of truth-functional connective. (...)
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  20. Coordination and Harmony in Bilateral Logic.Pedro del Valle-Inclan & Julian J. Schlöder - 2023 - Mind 132 (525):192-207.
    Ian Rumfitt (2000) developed a bilateralist account of logic in which the meaning of the connectives is given by conditions on asserted and rejected sentences. An additional set of inference rules, the coordination principles, determines the interaction of assertion and rejection. Fernando Ferreira (2008) found this account defective, as Rumfitt must state the coordination principles for arbitrary complex sentences. Rumfitt (2008) has a reply, but we argue that the problem runs deeper than he acknowledges and is in fact related to (...)
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  21. Default meanings: language’s logical connectives between comprehension and reasoning.David J. Lobina, Josep Demestre, José E. García-Albea & Marc Guasch - 2023 - Linguistics and Philosophy 46 (1):135-168.
    Language employs various coordinators to connect propositions, a subset of which are “logical” in nature and thus analogous to the truth operators of formal logic. We here focus on two linguistic connectives and their negations: conjunction _and_ and (inclusive) disjunction _or_. Linguistic connectives exhibit a truth-conditional component as part of their meaning (their semantics), but their use in context can give rise to various implicatures and presuppositions (the domain of pragmatics) as well as to inferences that go beyond semantic/pragmatic properties (...)
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  22. Complexity of distances: Theory of generalized analytic equivalence relations.Marek Cúth, Michal Doucha & Ondřej Kurka - 2022 - Journal of Mathematical Logic 23 (1).
    We generalize the notion of analytic/Borel equivalence relations, orbit equivalence relations, and Borel reductions between them to their continuous and quantitative counterparts: analytic/Borel pseudometrics, orbit pseudometrics, and Borel reductions between them. We motivate these concepts on examples and we set some basic general theory. We illustrate the new notion of reduction by showing that the Gromov–Hausdorff distance maintains the same complexity if it is defined on the class of all Polish metric spaces, spaces bounded from below, from above, and from (...)
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  23. Equivalence relations and determinacy.Logan Crone, Lior Fishman & Stephen Jackson - 2022 - Journal of Mathematical Logic 22 (1).
    We introduce the notion of -determinacy for Γ a pointclass and E an equivalence relation on a Polish space X. A case of particular interest is the case when E = EG is the shift-action o...
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  24. The domination monoid in o-minimal theories.Rosario Mennuni - 2021 - Journal of Mathematical Logic 22 (1).
    We study the monoid of global invariant types modulo domination-equivalence in the context of o-minimal theories. We reduce its computation to the problem of proving that it is generated by classes...
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  25. Computable Reducibility of Equivalence Relations and an Effective Jump Operator.John D. Clemens, Samuel Coskey & Gianni Krakoff - forthcoming - Journal of Symbolic Logic:1-22.
    We introduce the computable FS-jump, an analog of the classical Friedman–Stanley jump in the context of equivalence relations on the natural numbers. We prove that the computable FS-jump is proper with respect to computable reducibility. We then study the effect of the computable FS-jump on computably enumerable equivalence relations (ceers).
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  26. Suppose and Tell: The Semantics and Heuristics of Conditionals: Timothy Williamson. Oxford: Oxford University Press, 2020. viii + 278 pp. £30.00. ISBN 978-0-19-886066-2.Dorothy Edgington - 2021 - History and Philosophy of Logic 43 (2):188-195.
    Conditional judgements—judgements employing ‘if’—are essential to practical reasoning about what to do, as well as to much reasoning about what is the case. We handle them well enough from an early...
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  27. Equality and Near-Equality in a Nonstandard World.Bruno Dinis - forthcoming - Logic and Logical Philosophy:1-14.
    In the context of nonstandard analysis, the somewhat vague equality relation of near-equality allows us to relate objects that are indistinguishable but not necessarily equal. This relation appears to enable us to better understand certain paradoxes, such as the paradox of Theseus’s ship, by identifying identity at a time with identity over a short period of time. With this view in mind, I propose and discuss two mathematical models for this paradox.
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  28. Bilateral Inversion Principles.Nils Kürbis - 2022 - Electronic Proceedings in Theoretical Computer Science 358:202–215.
    This paper formulates a bilateral account of harmony that is an alternative to one proposed by Francez. It builds on an account of harmony for unilateral logic proposed by Kürbis and the observation that reading the rules for the connectives of bilateral logic bottom up gives the grounds and consequences of formulas with the opposite speech act. I formulate a process I call 'inversion' which allows the determination of assertive elimination rules from assertive introduction rules, and rejective elimination rules from (...)
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  29. Extending the Lambek Calculus with Classical Negation.Michael Kaminski - 2021 - Studia Logica 110 (2):295-317.
    We present an axiomatization of the non-associative Lambek calculus extended with classical negation for which the frame semantics with the classical interpretation of negation is sound and complete.
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  30. The Dynamics of Argumentative Discourse.Carlotta Pavese & Alexander W. Kocurek - 2022 - Journal of Philosophical Logic 51 (2):413-456.
    Arguments have always played a central role within logic and philosophy. But little attention has been paid to arguments as a distinctive kind of discourse, with its own semantics and pragmatics. The goal of this essay is to study the mechanisms by means of which we make arguments in discourse, starting from the semantics of argument connectives such as `therefore'. While some proposals have been made in the literature, they fail to account for the distinctive anaphoric behavior of `therefore', as (...)
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  31. On the modal interpretation of the connective of realisation.A. M. Karczewska - 2021 - Journal of Applied Non-Classical Logics 31 (3-4):221-233.
    The connective of realisation associates propositions with names of contexts, at which they are said to be realised. Realisation is usually understood as relativised truth-connective, thus under mo...
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  32. On the Overlap Between Everything and Nothing.Massimiliano Carrara, Filippo Mancini & Jeroen Smid - forthcoming - Logic and Logical Philosophy.
    Graham Priest has recently proposed a solution to the problem of the One and the Many which involves inconsistent objects and a non-transitive identity relation. We show that his solution entails either that the object everything is identical with the object nothing or that they are mutual parts; depending on whether Priest goes for an extensional or a non-extensional mereology.
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  33. Operands and Instances.Peter Fritz - 2023 - Review of Symbolic Logic 16 (1):188-209.
    Can conjunctive propositions be identical without their conjuncts being identical? Can universally quantified propositions be identical without their instances being identical? On a common conception of propositions, on which they inherit the logical structure of the sentences which express them, the answer is negative both times. Here, it will be shown that such a negative answer to both questions is inconsistent, assuming a standard type-theoretic formalization of theorizing about propositions. The result is not specific to conjunction and universal quantification, but (...)
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  34. Centering and compound conditionals under coherence.A. Gilio, Niki Pfeifer & Giuseppe Sanfilippo - 2017 - In M. B. Ferraro, P. Giordani, B. Vantaggi, M. Gagolewski, Gilgameshgodman Gilgameshgodman, P. Grzegorzewski & O. Hryniewicz (eds.), Soft Methods for Data Science. Cham, Switzerland: pp. 253-260.
    There is wide support in logic, philosophy, and psychology for the hypothesis that the probability of the indicative conditional of natural language, P(if A then B), is the conditional probability of B given A, P(B|A). We identify a conditional which is such that P(if A then B)=P(B|A) with de Finetti’s conditional event, B | A. An objection to making this identification in the past was that it appeared unclear how to form compounds and iterations of conditional events. In this paper, (...)
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  35. Generalized probabilistic modus ponens.Giuseppe Sanfilippo, Niki Pfeifer & Angelo Gilio - 2017 - In A. Antonucci, L. Cholvy & O. Papini (eds.), Symbolic and Quantitative Approaches to Reasoning with Uncertainty (Lecture Notes in Artificial Intelligence, vol. 10369). Cham, Switzerland: pp. 480-490.
    Modus ponens (from A and “if A then C” infer C) is one of the most basic inference rules. The probabilistic modus ponens allows for managing uncertainty by transmitting assigned uncertainties from the premises to the conclusion (i.e., from P(A) and P(C|A) infer P(C)). In this paper, we generalize the probabilistic modus ponens by replacing A by the conditional event A|H. The resulting inference rule involves iterated conditionals (formalized by conditional random quantities) and propagates previsions from the premises to the (...)
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  36. The logical relation of consequence.Basil Evangelidis - 2020 - Humanities Bulletin 3 (2):77-90.
    The present endeavour aims at the clarification of the concept of the logical consequence. Initially we investigate the question: How was the concept of logical consequence discovered by the medieval philosophers? Which ancient philosophical foundations were necessary for the discovery of the logical relation of consequence and which explicit medieval contributions, such as the notion of the formality (formal validity), led to its discovery. Secondly we discuss which developments of modern philosophy effected the turn from the medieval concept of logical (...)
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  37. The fluted fragment with transitive relations.Ian Pratt-Hartmann & Lidia Tendera - 2022 - Annals of Pure and Applied Logic 173 (1):103042.
    The fluted fragment is a fragment of first-order logic (without equality) in which, roughly speaking, the order of quantification of variables coincides with the order in which those variables appear as arguments of predicates. It is known that this fragment has the finite model property. We consider extensions of the fluted fragment with various numbers of transitive relations, as well as the equality predicate. In the presence of one transitive relation (together with equality), the finite model property is lost; nevertheless, (...)
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  38. Metasequents and Tetravaluations.Rohan French - 2021 - Journal of Philosophical Logic 51 (6):1-24.
    In this paper we treat metasequents—objects which stand to sequents as sequents stand to formulas—as first class logical citizens. To this end we provide a metasequent calculus, a sequent calculus which allows us to directly manipulate metasequents. We show that the various metasequent calculi we consider are sound and complete w.r.t. appropriate classes of tetravaluations where validity is understood locally. Finally we use our metasequent calculus to give direct syntactic proofs of various collapse results, closing a problem left open in (...)
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  39. The Inextricable Link Between Conditionals and Logical Consequence.Matheus Silva - manuscript
    There is a profound, but frequently ignored relationship between logical consequence (formal implication) and material implication. The first repeats the patterns of the latter, but with a wider modal reach. It is argued that this kinship between formal and material implication simply means that they express the same kind of implication, but differ in scope. Formal implication is unrestricted material implication. This apparently innocuous observation has some significant corollaries: (1) conditionals are not connectives, but arguments; (2) the traditional examples of (...)
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  40. How Mathematics Isn’t Logic.Roger Wertheimer - 1999 - Ratio 12 (3):279-295.
    View more Abstract If logical truth is necessitated by sheer syntax, mathematics is categorially unlike logic even if all mathematics derives from definitions and logical principles. This contrast gets obscured by the plausibility of the Synonym Substitution Principle implicit in conceptions of analyticity: synonym substitution cannot alter sentence sense. The Principle obviously fails with intercepting: nonuniform term substitution in logical sentences. ‘Televisions are televisions’ and ‘TVs are televisions’ neither sound alike nor are used interchangeably. Interception synonymy gets assumed because logical (...)
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  41. Belnap–Dunn Modal Logic with Value Operators.Yuanlei Lin & Minghui Ma - 2020 - Studia Logica 109 (4):759-789.
    The language of Belnap–Dunn modal logic \ expands the language of Belnap–Dunn four-valued logic with the modal operator \. We introduce the polarity semantics for \ and its two expansions \ and \ with value operators. The local finitary consequence relation \ in the language \ with respect to the class of all frames is axiomatized by a sequent system \ where \. We prove by using translations between sequents and formulas that these languages under the polarity semantics have the (...)
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  42. Problemas semánticos en filosofía de la lógica.Sergio Aramburu - 2021 - Actas y Comunicaciones UNGS 6:193-211.
    Este texto presenta, y en cierta medida analiza, ambigüedades existentes en textos de lógica y filosofía de la lógica (como la interpretación de los llamados principios, postulados, leyes o verdades lógicas, la coexistencia de la tesis de que toda relación presupone la existencia de al menos dos relata y la de que una cosa puede relacionarse consigo misma, o la llamada "paradoja del mentiroso") bajo el supuesto de que, dado que la lógica no es anterior a la semántica, un análisis (...)
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  43. Identity in Mares-Goldblatt Models for Quantified Relevant Logic.Shawn Standefer - 2021 - Journal of Philosophical Logic 50 (6):1389-1415.
    Mares and Goldblatt, 163–187, 2006) provided an alternative frame semantics for two quantified extensions of the relevant logic R. In this paper, I show how to extend the Mares-Goldblatt frames to accommodate identity. Simpler frames are provided for two zero-order logics en route to the full logic in order to clarify what is needed for identity and substitution, as opposed to quantification. I close with a comparison of this work with the Fine-Mares models for relevant logics with identity and a (...)
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  44. What is Identical?Marta Vlasáková - 2021 - Logica Universalis 15 (2):153-170.
    Numerical identity is standardly considered to be a relation between things. This means that two things are identical if they are only one thing. It is not only Wittgenstein who finds this claim rather odd. Another possibility is to understand identity as a relation between names which denote the same thing; or as a relation between the senses of those names which are modes of presentation of the same thing. Or identity statements can be considered as expressions of the fact (...)
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  45. Multiple readability in principle and practice: Existential Graphs and complex symbols.Dirk Schlimm & David Waszek - 2020 - Logique Et Analyse 251:231-260.
    Since Sun-Joo Shin's groundbreaking study (2002), Peirce's existential graphs have attracted much attention as a way of writing logic that seems profoundly different from our usual logical calculi. In particular, Shin argued that existential graphs enjoy a distinctive property that marks them out as "diagrammatic": they are "multiply readable," in the sense that there are several di erent, equally legitimate ways to translate one and the same graph into a standard logical language. Stenning (2000) and Bellucci and Pietarinen (2016) have (...)
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  46. Cardinality of wellordered disjoint unions of quotients of smooth equivalence relations.William Chan & Stephen Jackson - 2021 - Annals of Pure and Applied Logic 172 (8):102988.
  47. Peirce’s Triadic Logic and Its (Overlooked) Connexive Expansion.Alex Belikov - forthcoming - Logic and Logical Philosophy:1.
    In this paper, we present two variants of Peirce’s Triadic Logic within a language containing only conjunction, disjunction, and negation. The peculiarity of our systems is that conjunction and disjunction are interpreted by means of Peirce’s mysterious binary operations Ψ and Φ from his ‘Logical Notebook’. We show that semantic conditions that can be extracted from the definitions of Ψ and Φ agree (in some sense) with the traditional view on the semantic conditions of conjunction and disjunction. Thus, we support (...)
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  48. Variable Sharing in Connexive Logic.Luis Estrada-González & Claudia Lucía Tanús-Pimentel - 2021 - Journal of Philosophical Logic 50 (6):1377-1388.
    However broad or vague the notion of connexivity may be, it seems to be similar to the notion of relevance even when relevance and connexive logics have been shown to be incompatible to one another. Relevance logics can be examined by suggesting syntactic relevance principles and inspecting if the theorems of a logic abide to them. In this paper we want to suggest that a similar strategy can be employed with connexive logics. To do so, we will suggest some properties (...)
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  49. Three Ways of Being Non-Material.Vincenzo Crupi & Andrea Iacona - 2022 - Studia Logica 110:47-93.
    This paper develops a probabilistic analysis of conditionals which hinges on a quantitative measure of evidential support. In order to spell out the interpreta- tion of ‘if’ suggested, we will compare it with two more familiar interpretations, the suppositional interpretation and the strict interpretation, within a formal framework which rests on fairly uncontroversial assumptions. As it will emerge, each of the three interpretations considered exhibits specific logical features that deserve separate consideration.
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  50. On Abstraction in Mathematics and Indefiniteness in Quantum Mechanics.David Ellerman - 2021 - Journal of Philosophical Logic 50 (4):813-835.
    ion turns equivalence into identity, but there are two ways to do it. Given the equivalence relation of parallelness on lines, the #1 way to turn equivalence into identity by abstraction is to consider equivalence classes of parallel lines. The #2 way is to consider the abstract notion of the direction of parallel lines. This paper developments simple mathematical models of both types of abstraction and shows, for instance, how finite probability theory can be interpreted using #2 abstracts as “superposition (...)
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