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  1. Chess composition as an art.Miro Brada - manuscript
    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.
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  2. Trivalent Conditionals: Stalnaker's Thesis and Bayesian Inference.Paul Égré, Lorenzo Rossi & Jan Sprenger - manuscript
    This paper develops a trivalent semantics for indicative conditionals and extends it to a probabilistic theory of valid inference and inductive learning with conditionals. On this account, (i) all complex conditionals can be rephrased as simple conditionals, connecting our account to Adams's theory of p-valid inference; (ii) we obtain Stalnaker's Thesis as a theorem while avoiding the well-known triviality results; (iii) we generalize Bayesian conditionalization to an updating principle for conditional sentences. The final result is a unified semantic and probabilistic (...)
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  3. Valuations.Jean-Louis Lenard - manuscript
    Is logic empirical? Is logic to be found in the world? Or is logic rather a convention, a product of conventions, part of the many rules that regulate the language game? Answers fall in either camp. We like the linguistic answer. In this paper, we want to analyze how a linguistic community would tackle the problem of developing a logic and show how the linguistic conventions adopted by the community determine the properties of the local logic. Then show how to (...)
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  4. Truth and Subjunctive Theories of Knwledge: No Luck?Johannes Stern - manuscript
    The paper explores applications of Kripke's theory of truth to semantics for anti-luck epistemology, that is, to subjunctive theories of knowledge. Subjunctive theories put forward modal or subjunctive conditions to rule out knowledge by mere luck as to be found in Gettier-style counterexamples to the analysis of knowledge as justified true belief. Because of the subjunctive nature of these conditions the resulting semantics turns out to be non-monotone, even if it is based on non-classical evaluation schemes such as strong Kleene (...)
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  5. Some Strong Conditionals for Sentential Logics.Jason Zarri - manuscript
    In this article I define a strong conditional for classical sentential logic, and then extend it to three non-classical sentential logics. It is stronger than the material conditional and is not subject to the standard paradoxes of material implication, nor is it subject to some of the standard paradoxes of C. I. Lewis’s strict implication. My conditional has some counterintuitive consequences of its own, but I think its pros outweigh its cons. In any case, one can always augment one’s language (...)
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  6. Syntactic characterizations of first-order structures in mathematical fuzzy logic.Guillermo Badia, Pilar Dellunde, Vicent Costa & Carles Noguera - forthcoming - Soft Computing.
    This paper is a contribution to graded model theory, in the context of mathematical fuzzy logic. We study characterizations of classes of graded structures in terms of the syntactic form of their first-order axiomatization. We focus on classes given by universal and universal-existential sentences. In particular, we prove two amalgamation results using the technique of diagrams in the setting of structures valued on a finite MTL-algebra, from which analogues of the Łoś–Tarski and the Chang–Łoś–Suszko preservation theorems follow.
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  7. Many-Valued Logics and Bivalent Modalities.Edson Bezerra & Giorgio Venturi - forthcoming - Logic and Logical Philosophy:1-26.
    In this paper, we investigate the family LS0.5 of many-valued modal logics LS0.5's. We prove that the modalities of necessity and possibility of the logics LS0.5's capture well-defined bivalent concepts of logical validity and logical consistency. We also show that these modalities can be used as recovery operators.
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  8. Twist-Valued Models for Three-Valued Paraconsistent Set Theory.Walter A. Carnielli & Marcelo E. Coniglio - forthcoming - Logic and Logical Philosophy:1.
    We propose in this paper a family of algebraic models of ZFC based on the three-valued paraconsistent logic LPT0, a linguistic variant of da Costa and D’Ottaviano’s logic J3. The semantics is given by twist structures defined over complete Boolean agebras. The Boolean-valued models of ZFC are adapted to twist-valued models of an expansion of ZFC by adding a paraconsistent negation. This allows for inconsistent sets w satisfying ‘not (w = w)’, where ‘not’ stands for the paraconsistent negation. Finally, our (...)
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  9. Non-reflexive Nonsense: Proof-Theory for Paracomplete Weak Kleene Logic.Bruno Da Ré, Damian Szmuc & María Inés Corbalán - forthcoming - Studia Logica:1-17.
    Our aim is to provide a sequent calculus whose external consequence relation coincides with the three-valued paracomplete logic `of nonsense' introduced by Dmitry Bochvar and, independently, presented as the weak Kleene logic K3W by Stephen C. Kleene. The main features of this calculus are (i) that it is non-reflexive, i.e., Identity is not included as an explicit rule (although a restricted form of it with premises is derivable); (ii) that it includes rules where no variable-inclusion conditions are attached; and (iii) (...)
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  10. Paraconsistentization and many-valued logics.Edelcio G. de Souza, Alexandre Costa-Leite & Diogo H. B. Dias - forthcoming - Logic Journal of the IGPL.
    This paper shows how to transform explosive many-valued systems into paraconsistent logics. We investigate mainly the case of three-valued systems exhibiting how non-explosive three-valued logics can be obtained from them.
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  11. Handbook of Three-Valued Logic.Paul Egre & Lorenzo Rossi (eds.) - forthcoming - Cambridge, Massachusetts: The MIT Press.
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  12. The Buddhist Sengzhao’s Roots in Daoism: Ex Contradictione Nihil.Takaharu Oda - forthcoming - Logica Universalis.
    Sengzhao (c.374–414) was a Chinese Neo-Daoist who converted to Mahāyāna Buddhism, and few people doubt his influence on Chinese Buddhist philosophy. In this article, provided his Neo-Daoism (xuanxue) and Madhyamaka Buddhism, I will present how Sengzhao featured a symbolic meaning of ‘void’ (śūnya) as rooted originally in Daoism. The Daoist contradictions, in particular between ‘being’ (you) and ‘nothing [non-being]’ (wu), are essential to the development of his doctrine of ‘no ultimate void’ (不真空論, Buzhenkonglun). To understand what Sengzhao meant by ‘void’, (...)
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  13. Disjoint Logics.Federico Pailos - forthcoming - Logic and Logical Philosophy:1.
    We will present all the mixed and impure disjoint three-valued logics based on the Strong Kleene schema. Some, but not all of them, are (inferentially) empty logics. We will also provide a recipe to build philosophical interpretations for each of these logics, and show why the kind of permeability that characterized them is not such a bad feature.
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  14. Pure Variable Inclusion Logics.Francesco Paoli, Michele Pra Baldi & Damian Szmuc - forthcoming - Logic and Logical Philosophy:1-22.
    The aim of this article is to discuss pure variable inclusion logics, that is, logical systems where valid entailments require that the propositional variables occurring in the conclusion are included among those appearing in the premises, or vice versa. We study the subsystems of Classical Logic satisfying these requirements and assess the extent to which it is possible to characterise them by means of a single logical matrix. In addition, we semantically describe both of these companions to Classical Logic in (...)
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  15. The Conditional in Three-Valued Logic.Jan Sprenger (ed.) - forthcoming - Cambridge, Massachusetts: The MIT Press.
    By and large, the conditional connective in three-valued logic has two different functions. First, by means of a deduction theorem, it can express a specific relation of logical consequence in the logical language itself. Second, it can represent natural language structures such as "if/then'" or "implies''. This chapter surveys both approaches, shows why none of them will typically end up with a three-valued material conditional, and elaborates on connections to probabilistic reasoning.
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  16. The Conditional in Three-Valued Logic.Jan Sprenger - forthcoming - In Paul Egre & Lorenzo Rossi (eds.), Handbook of Three-Valued Logic. Cambridge, Massachusetts: The MIT Press.
    By and large, the conditional connective in three-valued logic has two different functions. First, by means of a deduction theorem, it can express a specific relation of logical consequence in the logical language itself. Second, it can represent natural language structures such as "if/then'' or "implies''. This chapter surveys both approaches, shows why none of them will typically end up with a three-valued material conditional, and elaborates on connections to probabilistic reasoning.
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  17. Beyond Mixed Logics.Joaquín Toranzo Calderón & Federico Pailos - forthcoming - Logic and Logical Philosophy:1-28.
    In order to define some interesting consequence relations, certain generalizations have been proposed in a many-valued semantic setting that have been useful for defining what have been called pure, mixed and ordertheoretic consequence relations. But these generalizations are insufficient to capture some other interesting relations, like other intersective mixed relations or relations with a conjunctive interpretation for multiple conclusions. We propose a broader framework to define these cases, and many others, and to set a common background that allows for a (...)
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  18. Functional completeness and primitive positive decomposition of relations on finite domains.Sergiy Koshkin - 2024 - Logic Journal of the IGPL 32.
    We give a new and elementary construction of primitive positive decomposition of higher arity relations into binary relations on finite domains. Such decompositions come up in applications to constraint satisfaction problems, clone theory and relational databases. The construction exploits functional completeness of 2-input functions in many-valued logic by interpreting relations as graphs of partially defined multivalued ‘functions’. The ‘functions’ are then composed from ordinary functions in the usual sense. The construction is computationally effective and relies on well-developed methods of functional (...)
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  19. Dialetheism and distributed sorites.Ben Blumson - 2023 - Synthese 202 (4):1-18.
    Noniterative approaches to the sorites paradox accept single steps of soritical reasoning, but deny that these can be combined into valid chains of soritical reasoning. The distributed sorites is a puzzle designed to undermine noniterative approaches to the sorites paradox, by deriving an inconsistent conclusion using only single steps, but not chains, of soritical reasoning. This paper shows how a dialetheist version of the noniterative approach, the strict-tolerant approach, also solves the distributed sorites paradox, at no further cost, by accepting (...)
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  20. A PWK-style Argumentation Framework and Expansion.Massimiliano Carrara - 2023 - IfCoLog Journal of Logics and Their Applications 10 (3):485-509.
    In this article we consider argumentation as an epistemic process performed by an agent to extend and revise her beliefs and gain knowledge, according to the information provided by the environment. Such a process can also generate the suspension of the claim under evaluation. How can we account for such a suspension phenomenon in argumentation process? We propose: (1) to distinguish two kinds of suspensions – critical suspension and non-critical suspension – in epistemic change processes; (2) to introduce a Paraconsistent (...)
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  21. Corry Shores (2021) The Logic of Gilles Deleuze: Basic Principles. [REVIEW]Andrej Jovićević - 2023 - Deleuze and Guattari Studies 17 (3):449-456.
  22. Two-sided Sequent Calculi for FDE-like Four-valued Logics.Barteld Kooi & Allard Tamminga - 2023 - Journal of Philosophical Logic 52 (2):495-518.
    We present a method that generates two-sided sequent calculi for four-valued logics like "first degree entailment" (FDE). (We say that a logic is FDE-like if it has finitely many operators of finite arity, including negation, and if all of its operators are truth-functional over the four truth-values 'none', 'false', 'true', and 'both', where 'true' and 'both' are designated.) First, we show that for every n-ary operator * every truth table entry f*(x1,...,xn) = y can be characterized in terms of a (...)
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  23. Gödel on Many-Valued Logic.Tim Lethen - 2023 - Review of Symbolic Logic 16 (3):655-671.
    This paper collects and presents unpublished notes of Kurt Gödel concerning the field of many-valued logic. In order to get a picture as complete as possible, both formal and philosophical notes, transcribed from the Gabelsberger shorthand system, are included.
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  24. Epimorphism between Fine and Ferguson’s Matrices for Angell’s AC.Richard Zach - 2023 - Logic and Logical Philosophy 32 (2):161-179.
    Angell's logic of analytic containment AC has been shown to be characterized by a 9-valued matrix NC by Ferguson, and by a 16-valued matrix by Fine. We show that the former is the image of a surjective homomorphism from the latter, i.e., an epimorphic image. The epimorphism was found with the help of MUltlog, which also provides a tableau calculus for NC extended by quantifiers that generalize conjunction and disjunction.
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  25. Epsilon theorems in intermediate logics.Matthias Baaz & Richard Zach - 2022 - Journal of Symbolic Logic 87 (2):682-720.
    Any intermediate propositional logic can be extended to a calculus with epsilon- and tau-operators and critical formulas. For classical logic, this results in Hilbert’s $\varepsilon $ -calculus. The first and second $\varepsilon $ -theorems for classical logic establish conservativity of the $\varepsilon $ -calculus over its classical base logic. It is well known that the second $\varepsilon $ -theorem fails for the intuitionistic $\varepsilon $ -calculus, as prenexation is impossible. The paper investigates the effect of adding critical $\varepsilon $ - (...)
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  26. Two Decision Procedures for da Costa’s $$C_n$$ C n Logics Based on Restricted Nmatrix Semantics.Marcelo E. Coniglio & Guilherme V. Toledo - 2022 - Studia Logica 110 (3):601-642.
    Despite being fairly powerful, finite non-deterministic matrices are unable to characterize some logics of formal inconsistency, such as those found between mbCcl and Cila. In order to overcome this limitation, we propose here restricted non-deterministic matrices (in short, RNmatrices), which are non-deterministic algebras together with a subset of the set of valuations. This allows us to characterize not only mbCcl and Cila (which is equivalent, up to language, to da Costa's logic C_1) but the whole hierarchy of da Costa's calculi (...)
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  27. G'3 as the logic of modal 3-valued Heyting algebras.Marcelo E. Coniglio, Aldo Figallo-Orellano, Alejandro Hernández-Tello & Miguel Perez-Gaspar - 2022 - IfCoLog Journal of Logics and Their Applications 9 (1):175-197.
    In 2001, W. Carnielli and Marcos considered a 3-valued logic in order to prove that the schema ϕ ∨ (ϕ → ψ) is not a theorem of da Costa’s logic Cω. In 2006, this logic was studied (and baptized) as G'3 by Osorio et al. as a tool to define semantics of logic programming. It is known that the truth-tables of G'3 have the same expressive power than the one of Łukasiewicz 3-valued logic as well as the one of Gödel (...)
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  28. Structural Completeness in Many-Valued Logics with Rational Constants.Joan Gispert, Zuzana Haniková, Tommaso Moraschini & Michał Stronkowski - 2022 - Notre Dame Journal of Formal Logic 63 (3):261-299.
    The logics RŁ, RP, and RG have been obtained by expanding Łukasiewicz logic Ł, product logic P, and Gödel–Dummett logic G with rational constants. We study the lattices of extensions and structural completeness of these three expansions, obtaining results that stand in contrast to the known situation in Ł, P, and G. Namely, RŁ is hereditarily structurally complete. RP is algebraized by the variety of rational product algebras that we show to be Q-universal. We provide a base of admissible rules (...)
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  29. Minimally Nonstandard K3 and FDE.Rea Golan & Ulf Hlobil - 2022 - Australasian Journal of Logic 19 (5):182-213.
    Graham Priest has formulated the minimally inconsistent logic of paradox (MiLP), which is paraconsistent like Priest’s logic of paradox (LP), while staying closer to classical logic. We present logics that stand to (the propositional fragments of) strong Kleene logic (K3) and the logic of first-degree entailment (FDE) as MiLP stands to LP. That is, our logics share the paracomplete and the paraconsistent-cum-paracomplete nature of K3 and FDE, respectively, while keeping these features to a minimum in order to stay closer to (...)
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  30. Reasoning in Commutative Kleene Algebras from *-free Hypotheses.Stepan Kuznetsov - 2022 - In Igor Sedlár (ed.), The Logica Yearbook 2021. College Publications. pp. 99-114.
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  31. Dissolving the paradoxicality paradox.William Nava - 2022 - Australasian Journal of Logic 19 (4):133-146.
    Non-classical solutions to semantic paradox can be associated with conceptions of paradoxicality understood in terms of entailment facts. In a K3-based theory of truth, for example, it is prima facie natural to say that a sentence φ is paradoxical iff φ ∨ ¬φ entails an absurdity. In a recent paper, Julien Murzi and Lorenzo Rossi exploit this idea to introduce revenge paradoxes for a number of non-classical approaches, including K3. In this paper, I show that on no understanding of ‘is (...)
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  32. A Note on the signed occurrences of propositional variables.Thomas Randriamahazaka - 2022 - Australasian Journal of Logic 19 (1).
    This note concerns the positive and negative occurrences of propositional variables. Just like the theory of infectious truth-values provides an algebraic understanding of the position according to which identity of subject-matter between two formulas can approximated syntactically by the identity of propositional variables occurring in these formulas, we develop an algebraic understanding of the similar position which considers signed occurrence instead of mere occurrence. We apply our framework to classical logic, yielding this first semantic characterisation of the logic called SCL (...)
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  33. Peirce and Łukasiewicz on modal and multi-valued logics.Jon Alan Schmidt - 2022 - Synthese 200 (4):1-18.
    Charles Peirce incorporates modality into his Existential Graphs by introducing the broken cut for possible falsity. Although it can be adapted to various modern modal logics, Zeman demonstrates that making no other changes results in a version that he calls Gamma-MR, an implementation of Jan Łukasiewicz's four-valued Ł-modal system. It disallows the assertion of necessity, reflecting a denial of determinism, and has theorems involving possibility that seem counterintuitive at first glance. However, the latter is a misconception that arises from overlooking (...)
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  34. Towards Tractable Approximations to Many-Valued Logics: the Case of First Degree Entailment.Alejandro Solares-Rojas & Marcello D’Agostino - 2022 - In Igor Sedlár (ed.), The Logica Yearbook 2021. College Publications. pp. 57-76.
    FDE is a logic that captures relevant entailment between implication-free formulae and admits of an intuitive informational interpretation as a 4-valued logic in which “a computer should think”. However, the logic is co-NP complete, and so an idealized model of how an agent can think. We address this issue by shifting to signed formulae where the signs express imprecise values associated with two distinct bipartitions of the set of standard 4 values. Thus, we present a proof system which consists of (...)
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  35. The Quantified Argument Calculus with Two- and Three-valued Truth-valuational Semantics.Hongkai Yin & Hanoch Ben-Yami - 2022 - Studia Logica 111 (2):281-320.
    We introduce a two-valued and a three-valued truth-valuational substitutional semantics for the Quantified Argument Calculus (Quarc). We then prove that the 2-valid arguments are identical to the 3-valid ones with strict-to-tolerant validity. Next, we introduce a Lemmon-style Natural Deduction system and prove the completeness of Quarc on both two- and three-valued versions, adapting Lindenbaum’s Lemma to truth-valuational semantics. We proceed to investigate the relations of three-valued Quarc and the Predicate Calculus (PC). Adding a logical predicate T to Quarc, true of (...)
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  36. Non-classical Comparative Logic I: Standard Categorical Logic–from SLe to IFLe.Amer Amikhteh & Seyed Ahmad Mirsanei - 2021 - Logical Studies 12 (1):1-24.
    n this paper, a non-classical axiomatic system was introduced to classify all moods of Aristotelian syllogisms, in addition to the axiom "Every a is an a" and the bilateral rules of obversion of E and O propositions. This system consists of only 2 definitions, 2 axioms, 1 rule of a premise, and moods of Barbara and Datisi. By adding first-degree propositional negation to this system, we prove that the square of opposition holds without using many of the other rules of (...)
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  37. Two-variable logic has weak, but not strong, Beth definability.Hajnal Andréka & István Németi - 2021 - Journal of Symbolic Logic 86 (2):785-800.
    We prove that the two-variable fragment of first-order logic has the weak Beth definability property. This makes the two-variable fragment a natural logic separating the weak and the strong Beth properties since it does not have the strong Beth definability property.
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  38. Lindström theorems in graded model theory.Guillermo Badia & Carles Noguera - 2021 - Annals of Pure and Applied Logic 172 (3):102916.
    Stemming from the works of Petr Hájek on mathematical fuzzy logic, graded model theory has been developed by several authors in the last two decades as an extension of classical model theory that studies the semantics of many-valued predicate logics. In this paper we take the first steps towards an abstract formulation of this model theory. We give a general notion of abstract logic based on many-valued models and prove six Lindström-style characterizations of maximality of first-order logics in terms of (...)
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  39. Degree-Preserving Gödel Logics with an Involution: Intermediate Logics and Paraconsistency.Marcelo E. Coniglio, Francesc Esteva, Joan Gispert & Lluis Godo - 2021 - In Ofer Arieli & Anna Zamansky (eds.), Arnon Avron on Semantics and Proof Theory of Non-Classical Logics. Springer Verlag. pp. 107-139.
    In this paper we study intermediate logics between the logic G≤∼, the degree preserving companion of Gödel fuzzy logic with involution G∼ and classical propositional logic CPL, as well as the intermediate logics of their finite-valued counterparts G≤n∼. Although G≤∼ and G≤ are explosive w.r.t. Gödel negation ¬, they are paraconsistent w.r.t. the involutive negation ∼. We introduce the notion of saturated paraconsistency, a weaker notion than ideal paraconsistency, and we fully characterize the ideal and the saturated paraconsistent logics between (...)
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  40. MTV Logics.Roy T. Cook - 2021 - Journal of Philosophical Logic 51 (6):1477-1519.
    This essay introduces a novel framework to studying many-valued logics – the movable truth value (or MTV ) approach. After setting up the framework, we will show that a vast number of many-valued logics, and in particular many-valued logics that have previously been given very different kinds of semantics, including C, K3, LP, ST, TS, RM fde, and FDE, can all be unified within the MTV -logic approach. This alone is notable, since until now RM fde in particular has resisted (...)
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  41. Deep ST.Thomas M. Ferguson & Elisángela Ramírez-Cámara - 2021 - Journal of Philosophical Logic 51 (6):1261-1293.
    Many analyses of notion of _metainferences_ in the non-transitive logic ST have tackled the question of whether ST can be identified with classical logic. In this paper, we argue that the primary analyses are overly restrictive of the notion of metainference. We offer a more elegant and tractable semantics for the strict-tolerant hierarchy based on the three-valued function for the LP material conditional. This semantics can be shown to easily handle the introduction of _mixed_ inferences, _i.e._, inferences involving objects belonging (...)
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  42. Some Lessons Learned About Adding Conditionals to Certain Many-Valued Logics.Allen P. Hazen & Francis Jeffry Pelletier - 2021 - In Ivo Düntsch & Edwin Mares (eds.), Alasdair Urquhart on Nonclassical and Algebraic Logic and Complexity of Proofs. Springer Verlag. pp. 557-570.
    There are good reasons to want logics, including many-valued logics, to have usable conditionals, and we have explored this in certain logics. However, it turns out that we “accidentally” chose some favourable logics. In this paper, we look at some of the unfavourable logics and describe where usable conditionals can be added and where it is not possible.
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  43. Calculi for Many-Valued Logics.Michael Kaminski & Nissim Francez - 2021 - Logica Universalis 15 (2):193-226.
    We present a number of equivalent calculi for many-valued logics and prove soundness and strong completeness theorems. The calculi are obtained from the truth tables of the logic under consideration in a straightforward manner and there is a natural duality among these calculi. We also prove the cut elimination theorems for the sequent-like systems.
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  44. Many-valued logic and sequence arguments in value theory.Simon Knutsson - 2021 - Synthese 199 (3-4):10793-10825.
    Some find it plausible that a sufficiently long duration of torture is worse than any duration of mild headaches. Similarly, it has been claimed that a million humans living great lives is better than any number of worm-like creatures feeling a few seconds of pleasure each. Some have related bad things to good things along the same lines. For example, one may hold that a future in which a sufficient number of beings experience a lifetime of torture is bad, regardless (...)
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  45. On the Methods of Constructing Hilbert-type Axiom Systems for Finite-valued Propositional Logics of Łukasiewicz.Mateusz M. Radzki - 2021 - History and Philosophy of Logic 43 (1):70-79.
    The article explores the following question: which among the most often examined in the literature method of constructing Hilbert-type axiom systems for finite-valued propositional logics of Łukasi...
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  46. Translating Metainferences Into Formulae: Satisfaction Operators and Sequent Calculi.Ariel Jonathan Roffé & Federico Pailos - 2021 - Australasian Journal of Logic 3.
    In this paper, we present a way to translate the metainferences of a mixed metainferential system into formulae of an extended-language system, called its associated σ-system. To do this, the σ-system will contain new operators (one for each standard), called the σ operators, which represent the notions of "belonging to a (given) standard". We first prove, in a model-theoretic way, that these translations preserve (in)validity. That is, that a metainference is valid in the base system if and only if its (...)
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  47. From Intuitionism to Many-Valued Logics Through Kripke Models.Saeed Salehi - 2021 - In Mojtaba Mojtahedi, Shahid Rahman & MohammadSaleh Zarepour (eds.), Mathematics, Logic, and their Philosophies: Essays in Honour of Mohammad Ardeshir. Springer. pp. 339-348.
    Intuitionistic Propositional LogicIntuitionistic propositional logic is proved to be an infinitely many valued logicMany valued logics by Gödel Publications 1929–1936, Oxford University Press, pp 222–225, 1932), and it is proved by Jaśkowski Jaśkowski, S. to be a countably many valued logicMany valued logics. In this paper, we provide alternative proofs for these theorems by using models of Kripke :1–14, 1959). Gödel’s proof gave rise to an intermediate propositional logic, that is known nowadays as Gödel or the Gödel-Dummett LogicGödel-Dummet Logic, and (...)
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  48. The (Greatest) Fragment of Classical Logic that Respects the Variable-Sharing Principle (in the FMLA-FMLA Framework).Damian E. Szmuc - 2021 - Bulletin of the Section of Logic 50 (4):421-453.
    We examine the set of formula-to-formula valid inferences of Classical Logic, where the premise and the conclusion share at least a propositional variable in common. We review the fact, already proved in the literature, that such a system is identical to the first-degree entailment fragment of R. Epstein's Relatedness Logic, and that it is a non-transitive logic of the sort investigated by S. Frankowski and others. Furthermore, we provide a semantics and a calculus for this logic. The semantics is defined (...)
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  49. A Simple Logical Matrix and Sequent Calculus for Parry’s Logic of Analytic Implication.Damian E. Szmuc - 2021 - Studia Logica 109 (4):791-828.
    We provide a logical matrix semantics and a Gentzen-style sequent calculus for the first-degree entailments valid in W. T. Parry’s logic of Analytic Implication. We achieve the former by introducing a logical matrix closely related to that inducing paracomplete weak Kleene logic, and the latter by presenting a calculus where the initial sequents and the left and right rules for negation are subject to linguistic constraints.
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  50. Meaningless Divisions.Damian Szmuc & Thomas Macaulay Ferguson - 2021 - Notre Dame Journal of Formal Logic 62 (3):399-424.
    In this article we revisit a number of disputes regarding significance logics---i.e., inferential frameworks capable of handling meaningless, although grammatical, sentences---that took place in a series of articles most of which appeared in the Australasian Journal of Philosophy between 1966 and 1978. These debates concern (i) the way in which logical consequence ought to be approached in the context of a significance logic, and (ii) the way in which the logical vocabulary has to be modified (either by restricting some notions, (...)
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