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  1. The Definition of an Argument.Jacob Parr - unknown
    The author presents a textbook definition of an "argument" and commentaries on two forms of the syllogism , on the reductio , on fitch-style notation , on the formal (in-)validity of the law of excluded middle , and on the rhetoric(s) of neophytic writing .
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  2. Valid Arguments as True Conditionals.Andrea Iacona - 2023 - Mind 132 (526):428-451.
    This paper explores an idea of Stoic descent that is largely neglected nowadays, the idea that an argument is valid when the conditional formed by the conjunction of its premises as antecedent and its conclusion as consequent is true. As it will be argued, once some basic features of our naıve understanding of validity are properly spelled out, and a suitable account of conditionals is adopted, the equivalence between valid arguments and true conditionals makes perfect sense. The account of validity (...)
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  3. Svojstva klasične logike [Properties of Classical Logic].Srećko Kovač - 2013 - Zagreb: Hrvatski studiji Sveučilišta u Zagrebu.
    The content for an advanced logic course is presented, which includes the properties of first-order logic language, soundness and completeness of the first-order logic deductive system, Peano arithmetic, Gödel's incompleteness theorems, higher-order logic and its properties. As a reminder, a brief description of first-order logic is included.
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  4. Logička pitanja i postupci [Logical questions and procedures].Srećko Kovač & Berislav Žarnić - 2008 - Zagreb: KruZak.
    This book is an introduction to elementary logic (classical propositional and first-order logic), comprising brief summaries of the basics of elementary logic, with the emphasis on typical questions and procedure descriptions and with a large number of corresponding exercises and problems. Solutions are given for each problem and exercise, often with commentaries. The first part, Basics of Logic, deals with (a) formal language, models, Venn diagrams for sentences, and translation from natural into formal language and vice versa, (b) deduction and (...)
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  5. Introduction à la théorie de la démonstration : Élimination des coupures, normalisation et preuves de cohérence.Paolo Mancosu, Sergio Galvan & Richard Zach - 2022 - Paris: Vrin.
    Cet ouvrage offre une introduction accessible à la théorie de la démonstration : il donne les détails des preuves et comporte de nombreux exemples et exercices pour faciliter la compréhension des lecteurs. Il est également conçu pour servir d’aide à la lecture des articles fondateurs de Gerhard Gentzen. L’ouvrage introduit également aux trois principaux formalismes en usage : l’approche axiomatique des preuves, la déduction naturelle et le calcul des séquents. Il donne une démonstration claire et détaillée des résultats fondamentaux du (...)
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  6. On a Definition of Logical Consequence.Nils Kürbis - 2022 - Thought: A Journal of Philosophy 11 (2):64-71.
    Bilateralists, who accept that there are two primitive speech acts, assertion and denial, can offer an attractive definition of consequence: Y follows from X if and only if it is incoherent to assert all formulas X and to deny all formulas Y. The present paper argues that this definition has consequences many will find problematic, amongst them that truth coincides with assertibility. Philosophers who reject these consequences should therefore reject this definition of consequence.
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  7. 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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  8. Logic of faith and deed. The idea and an outline of the theoretical conception.Urszula Wybraniec-Skardowska - 2019 - Studia Philosophiae Christianae 55 (2):125-149.
    This paper discusses the theoretical assumptions behind the conception of the logic of faith and deed and outlines its formal-axiomatic frame and its method of construction, which enable us to understand it as a kind of deductive science. The paper is divided into several sections, starting with the logical analysis of the ambiguous terms of ‚faith’ and ‚action’, and focusing in particular on the concepts of religious faith and deed as a type of conscious activity relating to a matter or (...)
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  9. Robotlar ve planlama.Varol Akman & Erkan Tin - 1993 - Elektrik Mühendisliği 391:37-43.
    Planlama --- bir amaca ulaşmak üzere bir aksiyonlar bütünü tasarlamak --- yapay zekadaki en temel problemlerden biridir. Bu yazıda, robotikte planlama konusuna mantıkçı (logicist) yaklaşım ele alınmaktadır. [Planning --- devising a plan of action to reach a given goal --- is a fundamental problem in AI. This paper reviews the logicist approach to planning in robotics.].
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  10. What Follows from the Impossible: Everything or Nothing? (An Interpretation of the ‘Avranches Text’ and the Ars Meliduna).Wolfgang Lenzen - 2021 - History and Philosophy of Logic 43 (4):309-331.
    One of the main controversies of the Logic Schools of the 12th century centered on the question: What follows from the impossible? In this paper arguments for two diametrically opposed positions are examined. The author of the ‘Avranches Text’ who probably belonged to the school of the Parvipontani defended the view that from an impossible proposition everything follows (‘Ex impossibili quodlibet’). In particular he developed a proof to show that by means of so-called ‘disjunctive syllogism’ any arbitrary proposition B can (...)
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  11. Inferential Constants.Camillo Fiore, Federico Pailos & Mariela Rubin - 2022 - Journal of Philosophical Logic 1: 1 - 26.
    A metainference is usually understood as a pair consisting of a collection of inferences, called premises, and a single inference, called conclusion. In the last few years, much attention has been paid to the study of metainferences—and, in particular, to the question of what are the valid metainferences of a given logic. So far, however, this study has been done in quite a poor language. Our usual sequent calculi have no way to represent, e.g. negations, disjunctions or conjunctions of inferences. (...)
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  12. Representing Buridan’s Divided Modal Propositions in First-Order Logic.Jonas Dagys, Živilė Pabijutaitė & Haroldas Giedra - 2021 - History and Philosophy of Logic 43 (3):264-274.
    Formalizing categorical propositions of traditional logic in the language of quantifiers and propositional functions is no straightforward matter, especially when modalities get involved. Starting...
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  13. Mixed Conditional-Categorical Syllogisms from Avicenna to Urmawī.Khaled El-Rouayheb - 2021 - History and Philosophy of Logic 43 (3):232-250.
    A number of medieval Arabic logicians discussed inferences that combine the principles of propositional and term logic, for example: Whenever H is Z then Every J is DNo D is AWhenever H is Z then S...
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  14. Completeness: From Husserl to Carnap.Víctor Aranda - 2022 - Logica Universalis 16 (1):57-83.
    In his Doppelvortrag, Edmund Husserl introduced two concepts of “definiteness” which have been interpreted as a vindication of his role in the history of completeness. Some commentators defended that the meaning of these notions should be understood as categoricity, while other scholars believed that it is closer to syntactic completeness. A detailed study of the early twentieth-century axiomatics and Husserl’s Doppelvortrag shows, however, that many concepts of completeness were conflated as equivalent. Although “absolute definiteness” was principally an attempt to characterize (...)
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  15. 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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  16. Investigations of isotropy and homogeneity of spacetime in first-order logic.Judit X. Madarász, Mike Stannett & Gergely Székely - 2022 - Annals of Pure and Applied Logic 173 (9):103153.
  17. 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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  18. Homotopy model theory.Brice Halimi - 2021 - Journal of Symbolic Logic 86 (4):1301-1323.
    Drawing on the analogy between any unary first-order quantifier and a "face operator," this paper establishes several connections between model theory and homotopy theory. The concept of simplicial set is brought into play to describe the formulae of any first-order language L, the definable subsets of any L-structure, as well as the type spaces of any theory expressed in L. An adjunction result is then proved between the category of o-minimal structures and a subcategory of the category of linearly ordered (...)
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  19. 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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  20. Classical counterpossibles.Rohan French, Patrick Girard & David Ripley - 2022 - Review of Symbolic Logic 15 (1):259-275.
    We present four classical theories of counterpossibles that combine modalities and counterfactuals. Two theories are anti-vacuist and forbid vacuously true counterfactuals, two are quasi-vacuist and allow counterfactuals to be vacuously true when their antecedent is not only impossible, but also inconceivable. The theories vary on how they restrict the interaction of modalities and counterfactuals. We provide a logical cartography with precise acceptable boundaries, illustrating to what extent nonvacuism about counterpossibles can be reconciled with classical logic.
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  21. Embedding Classical Logic in S4.Sophie Nagler - 2019 - Dissertation, Munich Center for Mathematical Philosophy (Mcmp), Lmu Munich
    In this thesis, we will study the embedding of classical first-order logic in first-order S4, which is based on the translation originally introduced in Fitting (1970). The initial main part is dedicated to a detailed model-theoretic proof of the soundness of the embedding. This will follow the proof sketch in Fitting (1970). We will then outline a proof procedure for a proof-theoretic replication of the soundness result. Afterwards, a potential proof of faithfulness of the embedding, read in terms of soundness (...)
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  22. 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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  23. Semantyczna teoria prawdy a antynomie semantyczne [Semantic Theory of Truth vs. Semantic Antinomies].Jakub Pruś - 2021 - Rocznik Filozoficzny Ignatianum 1 (27):341–363.
    The paper presents Alfred Tarski’s debate with the semantic antinomies: the basic Liar Paradox, and its more sophisticated versions, which are currently discussed in philosophy: Strengthen Liar Paradox, Cyclical Liar Paradox, Contingent Liar Paradox, Correct Liar Paradox, Card Paradox, Yablo’s Paradox and a few others. Since Tarski, himself did not addressed these paradoxes—neither in his famous work published in 1933, nor in later papers in which he developed the Semantic Theory of Truth—therefore, We try to defend his concept of truth (...)
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  24. One-step Modal Logics, Intuitionistic and Classical, Part 1.Harold T. Hodes - 2021 - Journal of Philosophical Logic 50 (5):837-872.
    This paper and its sequel “look under the hood” of the usual sorts of proof-theoretic systems for certain well-known intuitionistic and classical propositional modal logics. Section 1 is preliminary. Of most importance: a marked formula will be the result of prefixing a formula in a propositional modal language with a step-marker, for this paper either 0 or 1. Think of 1 as indicating the taking of “one step away from 0.” Deductions will be constructed using marked formulas. Section 2 presents (...)
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  25. $$\mathrm {ZF}$$ ZF Between Classicality and Non-classicality.Sourav Tarafder & Giorgio Venturi - 2021 - Studia Logica 110 (1):189-218.
    We present a generalization of the algebra-valued models of \ where the axioms of set theory are not necessarily mapped to the top element of an algebra, but may get intermediate values, in a set of designated values. Under this generalization there are many algebras which are neither Boolean, nor Heyting, but that still validate \.
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  26. Falsification-Aware Semantics and Sequent Calculi for Classical Logic.Norihiro Kamide - 2021 - Journal of Philosophical Logic 51 (1):99-126.
    In this study, falsification-aware semantics and sequent calculi for first-order classical logic are introduced and investigated. These semantics and sequent calculi are constructed based on a falsification-aware setting for first-order Nelson constructive three-valued logic. In fact, these semantics and sequent calculi are regarded as those for a classical variant of N3. The completeness and cut-elimination theorems for the proposed semantics and sequent calculi are proved using Schütte’s method. Similar results for the propositional case are also obtained.
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  27. Validities, antivalidities and contingencies: A multi-standard approach.Eduardo Barrio & Federico Pailos - 2021 - Journal of Philosophical Logic 51 (1):75-98.
    It is widely accepted that classical logic is trivialized in the presence of a transparent truth-predicate. In this paper, we will explain why this point of view must be given up. The hierarchy of metainferential logics defined in Barrio et al. and Pailos recovers classical logic, either in the sense that every classical inferential validity is valid at some point in the hierarchy ), or because a logic of a transfinite level defined in terms of the hierarchy shares its validities (...)
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  28. Meaning-Preserving Translations of Non-classical Logics into Classical Logic: Between Pluralism and Monism.Gerhard Schurz - 2021 - Journal of Philosophical Logic 51 (1):27-55.
    In order to prove the validity of logical rules, one has to assume these rules in the metalogic. However, rule-circular ‘justifications’ are demonstrably without epistemic value. Is a non-circular justification of a logical system possible? This question attains particular importance in view of lasting controversies about classical versus non-classical logics. In this paper the question is answered positively, based on meaning-preserving translations between logical systems. It is demonstrated that major systems of non-classical logic, including multi-valued, paraconsistent, intuitionistic and quantum logics, (...)
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  29. The unrevisability of logic.Thomas Hofweber - 2021 - Philosophical Perspectives 35 (1):251-274.
    Can it ever be rational to revise one's own logic by one's own lights? In this paper I argue that logic is never rationally revisable, even if one's own logic gives rise to paradoxes and allows one to derive any conclusion whatsoever. Instead of revising logic, we need to revise a certain widely held position in the philosophy of logic, one tied to the standard conception of validity and to the alleged monotonicity of deductive reasoning. I develop the alternative conception (...)
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  30. Recursive axiomatisations from separation properties.Rob Egrot - 2021 - Journal of Symbolic Logic 86 (3):1228-1258.
    We define a fragment of monadic infinitary second-order logic corresponding to an abstract separation property, We use this to define the concept of a separation subclass. We use model theoretic techniques and games to show that separation subclasses whose axiomatisations are recursively enumerable in our second-order fragment can also be recursively axiomatised in their original first-order language. We pin down the expressive power of this formalism with respect to first-order logic, and investigate some questions relating to decidability and computational complexity. (...)
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  31. 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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  32. On Implicational Intermediate Logics Axiomatizable by Formulas Minimal in Classical Logic: A Counter-Example to the Komori–Kashima Problem.Yoshiki Nakamura & Naosuke Matsuda - 2021 - Studia Logica 109 (6):1413-1422.
    The Komori–Kashima problem, that asks whether the implicational intermediate logics axiomatizable by formulas minimal in classical logic are only intuitionistic logic and classical logic, has stood for over a decade. In this paper, we give a counter-example to this problem. Additionally, we also give some open problems derived from this result.
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  33. 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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  34. Adequate predimension inequalities in differential fields.Vahagn Aslanyan - 2022 - Annals of Pure and Applied Logic 173 (1):103030.
    In this paper we study predimension inequalities in differential fields and define what it means for such an inequality to be adequate. Adequacy was informally introduced by Zilber, and here we give a precise definition in a quite general context. We also discuss the connection of this problem to definability of derivations in the reducts of differentially closed fields. The Ax-Schanuel inequality for the exponential differential equation (proved by Ax) and its analogue for the differential equation of the j-function (established (...)
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  35. Logic Works: A Rigorous Introduction to Formal Logic.Lorne Falkenstein, Scott Stapleford & Molly Kao - 2022 - New York: Routledge. Edited by Scott Stapleford & Molly Kao.
    Logic Works is a critical and extensive introduction to logic. It asks questions about why systems of logic are as they are, how they relate to ordinary language and ordinary reasoning, and what alternatives there might be to classical logical doctrines. It considers how logical analysis can be applied to carefully represent the reasoning employed in academic and scientific work, better understand that reasoning, and identify its hidden premises. Aiming to be as much a reference work and handbook for further, (...)
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  36. The Open Future: Why Future Contingents Are All False.Patrick Todd - 2021 - Oxford: Oxford University Press.
    This book launches a sustained defense of a radical interpretation of the doctrine of the open future. Patrick Todd argues that all claims about undetermined aspects of the future are simply false.
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  37. Why Make Things Simple When You Can Make Them Complicated? An Appreciation of Lewis Carroll’s Symbolic Logic.Amirouche Moktefi - 2021 - Logica Universalis 15 (3):359-379.
    Lewis Carroll published a system of logic in the symbolic tradition that developed in his time. Carroll’s readers may be puzzled by his system. On the one hand, it introduced innovations, such as his logic notation, his diagrams and his method of trees, that secure Carroll’s place on the path that shaped modern logic. On the other hand, Carroll maintained the existential import of universal affirmative Propositions, a feature that is rather characteristic of traditional logic. The object of this paper (...)
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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. A Formal-Logical Approach to the Concept of God.Ricardo Sousa Silvestre - 2021 - Manuscrito. Revista Internacional de Filosofia 44 (4):224-260.
    In this paper I try to answer four basic questions: (1) How the concept of God is to be represented? (2) Are there any logical principles governing it? (3) If so, what kind of logic lies behind them? (4) Can there be a logic of the concept of God? I address them by presenting a formal-logical account to the concept of God. I take it as a methodological desideratum that this should be done within the simplest existing logical formalism. I (...)
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  40. Supervaluations and the Strict-Tolerant Hierarchy.Brian Porter - 2021 - Journal of Philosophical Logic 51 (6):1367-1386.
    In a recent paper, Barrio, Pailos and Szmuc (BPS) show that there are logics that have exactly the validities of classical logic up to arbitrarily high levels of inference. They suggest that a logic therefore must be identified by its valid inferences at every inferential level. However, Scambler shows that there are logics with all the validities of classical logic at every inferential level, but with no antivalidities at any inferential level. Scambler concludes that in order to identify a logic, (...)
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  41. One Step is Enough.David Ripley - 2021 - Journal of Philosophical Logic 51 (6):1-27.
    The recent development and exploration of mixed metainferential logics is a breakthrough in our understanding of nontransitive and nonreflexive logics. Moreover, this exploration poses a new challenge to theorists like me, who have appealed to similarities to classical logic in defending the logic ST, since some mixed metainferential logics seem to bear even more similarities to classical logic than ST does. There is a whole ST-based hierarchy, of which ST itself is only the first step, that seems to become more (...)
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  42. Inquisitive bisimulation.Ivano Ciardelli & Martin Otto - 2021 - Journal of Symbolic Logic 86 (1):77-109.
    Inquisitive modal logic, InqML, is a generalisation of standard Kripke-style modal logic. In its epistemic incarnation, it extends standard epistemic logic to capture not just the information that agents have, but also the questions that they are interested in. Technically, InqML fits within the family of logics based on team semantics. From a model-theoretic perspective, it takes us a step in the direction of monadic second-order logic, as inquisitive modal operators involve quantification over sets of worlds. We introduce and investigate (...)
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  43. Hilbert-style axiomatization of first-degree entailment and a family of its extensions.Yaroslav Shramko - 2021 - Annals of Pure and Applied Logic 172 (9):103011.
  44. Three Systems of First Degree Entailment.Richard Bradshaw Angell - 1977 - Journal of Symbolic Logic 42 (1):147.
  45. 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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  46. The kim–pillay theorem for abstract elementary categories.Mark Kamsma - 2020 - Journal of Symbolic Logic 85 (4):1717-1741.
    We introduce the framework of AECats, generalizing both the category of models of some first-order theory and the category of subsets of models. Any AEC and any compact abstract theory forms an AECat. In particular, we find applications in positive logic and continuous logic: the category of models of a positive or continuous theory is an AECat. The Kim–Pillay theorem for first-order logic characterizes simple theories by the properties dividing independence has. We prove a version of the Kim–Pillay theorem for (...)
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  47. The fundamental theorem of central element theory.Mariana Vanesa Badano & Diego Jose Vaggione - 2020 - Journal of Symbolic Logic 85 (4):1599-1606.
    We give a short proof of the fundamental theorem of central element theory. The original proof is constructive and very involved and relies strongly on the fact that the class be a variety. Here we give a more direct nonconstructive proof which applies for the more general case of a first-order class which is both closed under the formation of direct products and direct factors.
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  48. Proof complexity of substructural logics.Raheleh Jalali - 2021 - Annals of Pure and Applied Logic 172 (7):102972.
  49. A Simplified Ordinal Analysis of First-Order Reflection.Toshiyasu Arai - 2020 - Journal of Symbolic Logic 85 (3):1163-1185.
    In this note we give a simplified ordinal analysis of first-order reflection. An ordinal notation system$OT$is introduced based on$\psi $-functions. Provable$\Sigma _{1}$-sentences on$L_{\omega _{1}^{CK}}$are bounded through cut-elimination on operator controlled derivations.
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  50. Axiomatisations of the Genuine Three-Valued Paraconsistent Logics $$mathbf {L3AG}$$ L 3 A G and $$mathbf {L3BG}$$ L 3 B G.Alejandro Hernández-Tello, Miguel Pérez-Gaspar & Verónica Borja Macías - 2021 - Logica Universalis 15 (1):87-121.
    Genuine Paraconsistent logics \ and \ were defined in 2016 by Béziau et al, including only three logical connectives, namely, negation disjunction and conjunction. Afterwards in 2017 Hernández-Tello et al, provide implications for both logics and define the logics \ and \. In this work we continue the study of these logics, providing sound and complete Hilbert-type axiomatic systems for each logic. We prove among other properties that \ and \ satisfy a restricted version of the Substitution Theorem, and that (...)
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