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  1. Fusion, fission, and Ackermann’s truth constant in relevant logics: A proof-theoretic investigation.Fabio De Martin Polo - forthcoming - In Andrew Tedder, Shawn Standefer & Igor Sedlar (eds.), New Directions in Relevant Logic. Springer.
    The aim of this paper is to provide a proof-theoretic characterization of relevant logics including fusion and fission connectives, as well as Ackermann’s truth constant. We achieve this by employing the well-established methodology of labelled sequent calculi. After having introduced several systems, we will conduct a detailed proof-theoretic analysis, show a cut-admissibility theorem, and establish soundness and completeness. The paper ends with a discussion that contextualizes our current work within the broader landscape of the proof theory of relevant logics.
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  2. Compatibility, compossibility, and epistemic modality.Wesley Holliday & Matthew Mandelkern - forthcoming - Proceedings of the 23rd Amsterdam Colloquium.
    We give a theory of epistemic modals in the framework of possibility semantics and axiomatize the corresponding logic, arguing that it aptly characterizes the ways in which reasoning with epistemic modals does, and does not, diverge from classical modal logic.
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  3. 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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  4. Proof Invariance.Blane Worley - forthcoming - Australasian Journal of Logic.
    We explore depth substitution invariance, or hyperformalism, and extend known results in this realm to justification logics extending weak relevant logics. We then examine the surprising invariance of justifications over formulas and restrict our attention to the substitution of proofs in the original relevant logic. The results of this paper indicate that depth invariance is a recalcitrant feature of the logic and that proof structures in hyperformal logics are quite inflexible.
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  5. A New Logic, a New Information Measure, and a New Information-Based Approach to Interpreting Quantum Mechanics.David Ellerman - 2024 - Entropy Special Issue: Information-Theoretic Concepts in Physics 26 (2).
    The new logic of partitions is dual to the usual Boolean logic of subsets (usually presented only in the special case of the logic of propositions) in the sense that partitions and subsets are category-theoretic duals. The new information measure of logical entropy is the normalized quantitative version of partitions. The new approach to interpreting quantum mechanics (QM) is showing that the mathematics (not the physics) of QM is the linearized Hilbert space version of the mathematics of partitions. Or, putting (...)
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  6. An Alleged Tension between non-Classical Logics and Applied Classical Mathematics.Sebastian Horvat & Iulian D. Toader - 2024 - The Philosophical Quarterly 1:1-19.
    Timothy Williamson has maintained that the applicability of classical mathematics in science raises a problem for the endorsement, in non-mathematical domains, of a wide range of non-classical logics. We show that this is false.
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  7. Discussive Logic. A Short History of the First Paraconsistent Logic.Fabio De Martin Polo - 2023 - In Jens Lemanski & Ingolf Max (eds.), Historia Logicae and its Modern Interpretation. London: College Publications. pp. 267--296.
    In this paper we present an overview, with historical and critical remarks, of two articles by S. Jaúkowski ([20, 21] 1948 and [22, 23] 1949), which contain the oldest known formulation of a paracon- sistent logic. Jaúkowski has built the logic – he termed discussive (D2) – by defining two new connectives and by introducing a modal translation map from D2 systems into Lewis’ modal logic S5. Discussive systems, for their formal details and their orig- inal philosophical justification, have attracted (...)
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  8. Topics in the Proof Theory of Non-classical Logics. Philosophy and Applications.Fabio De Martin Polo - 2023 - Dissertation, Ruhr-Universität Bochum
    Chapter 1 constitutes an introduction to Gentzen calculi from two perspectives, logical and philosophical. It introduces the notion of generalisations of Gentzen sequent calculus and the discussion on properties that characterize good inferential systems. Among the variety of Gentzen-style sequent calculi, I divide them in two groups: syntactic and semantic generalisations. In the context of such a discussion, the inferentialist philosophy of the meaning of logical constants is introduced, and some potential objections – mainly concerning the choice of working with (...)
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  9. Fine on the Possibility of Vagueness.Andreas Ditter - 2023 - In Federico L. G. Faroldi & Frederik Van De Putte (eds.), Kit Fine on Truthmakers, Relevance, and Non-classical Logic. Springer Verlag. pp. 715-734.
    In his paper ‘The possibility of vagueness’ (Fine in Synthese 194(10):3699–3725, 2017), Kit Fine proposes a new logic of vagueness, CL, that promises to provide both a solution to the sorites paradox and a way to avoid the impossibility result from Fine (Philos Perspect 22(1):111–136, 2008). The present paper presents a challenge to his new theory of vagueness. I argue that the possibility theorem stated in Fine (Synthese 194(10):3699–3725, 2017), as well as his solution to the sorites paradox, fail in (...)
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  10. The Paradox Paradox Non-Paradox and Conjunction Fallacy Non-Fallacy.Noah Greenstein - 2023 - Australasian Journal of Logic 20 (3):478-489.
    Brock and Glasgow recently introduced a new definition of paradox and argue that this conception of paradox itself leads to paradox, the so-called Paradox Paradox. I show that they beg the questions during the course of their argument, but, more importantly, do so in a philosophically interesting way: it reveals a counterexample to the equivalence between being a logical truth and having a probability of one. This has consequences regarding norms of rationality, undermining the grounds for the Conjunction Fallacy.
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  11. A fundamental non-classical logic.Wesley Holliday - 2023 - Logics 1 (1):36-79.
    We give a proof-theoretic as well as a semantic characterization of a logic in the signature with conjunction, disjunction, negation, and the universal and existential quantifiers that we suggest has a certain fundamental status. We present a Fitch-style natural deduction system for the logic that contains only the introduction and elimination rules for the logical constants. From this starting point, if one adds the rule that Fitch called Reiteration, one obtains a proof system for intuitionistic logic in the given signature; (...)
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  12. Yamauchi Tokuryū (1890-1982). Philosophie occidentale et pensée bouddhique.Romaric Jannel - 2023 - Paris: Éditions Kimé.
    Philosophe japonais polyglotte au savoir encyclopédique, Yamauchi Tokuryū est à n’en point douter l’un des auteurs les moins étudiés de l’école de Kyōto. La présente étude vient corriger ce qui ne constitue rien d’autre qu’un accident de l’histoire, tant l’ampleur du projet philosophique de Yamauchi est à même de susciter l’intérêt du philosophe, du savant et de l’amateur cultivé. La démarche de ce penseur japonais, disciple de Nishida Kitarō, est remarquable en ce qu’il chercha à proposer un dépassement englobant de (...)
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  13. Modular labelled calculi for relevant logics.Fabio De Martin Polo - 2023 - Australasian Journal of Logic 20 (1):47-87.
    In this article, we perform a detailed proof theoretic investigation of a wide number of relevant logics by employing the well-established methodology of labelled sequent calculi to build our intended systems. At the semantic level, we will characterise relevant logics by employing reduced Routley-Meyer models, namely, relational structures with a ternary relation between worlds along with a unique distinct element considered as the real (or actual) world. This paper realizes the idea of building a variety of modular labelled calculi by (...)
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  14. Against Classical Paraconsistent Metatheory.Koji Tanaka & Patrick Girard - 2023 - Analysis 83 (2):285-294.
    There was a time when 'logic' just meant classical logic. The climate is slowly changing and non-classical logic cannot be dismissed off-hand. However, a metatheory used to study the properties of non-classical logic is often classical. In this paper, we will argue that this practice of relying on classical metatheories is problematic. In particular, we will show that it is a bad practice because the metatheory that is used to study a non-classical logic often rules out the very logic it (...)
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  15. Compatibility and accessibility: lattice representations for semantics of non-classical and modal logics.Wesley Holliday - 2022 - In David Fernández Duque & Alessandra Palmigiano (eds.), Advances in Modal Logic, Vol. 14. College Publications. pp. 507-529.
    In this paper, we study three representations of lattices by means of a set with a binary relation of compatibility in the tradition of Ploščica. The standard representations of complete ortholattices and complete perfect Heyting algebras drop out as special cases of the first representation, while the second covers arbitrary complete lattices, as well as complete lattices equipped with a negation we call a protocomplementation. The third topological representation is a variant of that of Craig, Haviar, and Priestley. We then (...)
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  16. V.A. Yankov on Non-Classical Logics, History and Philosophy of Mathematics.Vandoulakis Ioannis & Alex Citkin (eds.) - 2022 - Springer. Outstanding Contributions to Logic (Volume 24).
    This book is dedicated to V.A. Yankov’s seminal contributions to the theory of propositional logics. His papers, published in the 1960s, are highly cited even today. The Yankov characteristic formulas have become a very useful tool in propositional, modal and algebraic logic. The papers contributed to this book provide the new results on different generalizations and applications of characteristic formulas in propositional, modal and algebraic logics. In particular, an exposition of Yankov’s results and their applications in algebraic logic, the theory (...)
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  17. Empty validity all the way up: an easy road (Proceedings) (12th edition).Estrada-González Luis & Romero-RodrÍguez Christian (eds.) - 2022 - Moscow: Lomonosov Moscow State University.
    There is a tension between the definition of empty logic as a logic with no valid arguments and no valid meta-arguments, on the one hand, and the way in which we have usually interpreted the validity of meta-arguments, on the other. Here we argue that one way to eliminate the tension is understanding the “If. . . then. . . ” in a meta-argument, at least in the case of an empty logic, as a transplication (aka the de Finetti conditional) (...)
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  18. Semantics for Pure Theories of Connexive Implication.Yale Weiss - 2022 - Review of Symbolic Logic 15 (3):591-606.
    In this article, I provide Urquhart-style semilattice semantics for three connexive logics in an implication-negation language (I call these “pure theories of connexive implication”). The systems semantically characterized include the implication-negation fragment of a connexive logic of Wansing, a relevant connexive logic recently developed proof-theoretically by Francez, and an intermediate system that is novel to this article. Simple proofs of soundness and completeness are given and the semantics is used to establish various facts about the systems (e.g., that two of (...)
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  19. 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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  20. Refining Labelled Systems for Modal and Constructive Logics with Applications.Tim Lyon - 2021 - Dissertation, Technischen Universität Wien
    This thesis introduces the "method of structural refinement", which serves as a means of transforming the relational semantics of a modal and/or constructive logic into an 'economical' proof system by connecting two proof-theoretic paradigms: labelled and nested sequent calculi. The formalism of labelled sequents has been successful in that cut-free calculi in possession of desirable proof-theoretic properties can be automatically generated for large classes of logics. Despite these qualities, labelled systems make use of a complicated syntax that explicitly incorporates the (...)
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  21. Interpreting connexive principles in coherence-based probability logic.Niki Pfeifer & Giuseppe Sanfilippo - 2021 - In J. Vejnarová & J. Wilson (eds.), Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2021, LNAI 12897). Cham: pp. 672-687.
    We present probabilistic approaches to check the validity of selected connexive principles within the setting of coherence. Connexive logics emerged from the intuition that conditionals of the form If ∼A, then A, should not hold, since the conditional’s antecedent ∼A contradicts its consequent A. Our approach covers this intuition by observing that for an event A the only coherent probability assessment on the conditional event A|~A is p(A|~A)=0 . Moreover, connexive logics aim to capture the intuition that conditionals should express (...)
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  22. An Incompleteness Theorem for Modal Relevant Logics.Shawn Standefer - 2021 - Notre Dame Journal of Formal Logic 62 (4):669 - 681.
    In this paper, an incompleteness theorem for modal extensions of relevant logics is proved. The proof uses elementary methods and builds upon the work of Fuhrmann.
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  23. La contrastación de teorías inconsistentes no triviales.Luis Felipe Bartolo Alegre - 2020 - Dissertation, Universidad Nacional Mayor de San Marcos
    This dissertation offers a proof of the logical possibility of testing empirical/factual theories that are inconsistent, but non-trivial. In particular, I discuss whether or not such theories can satisfy Popper's principle of falsifiablility. An inconsistent theory Ƭ closed under a classical consequence relation implies every statement of its language because in classical logic the inconsistency and triviality are coextensive. A theory Ƭ is consistent iff there is not a α such that Ƭ ⊢ α ∧ ¬α, otherwise it is inconsistent. (...)
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  24. Now, Imagine an Actually Existing Unicorn: On Russellian Worries for Modal Meinongianism.Andreas de Jong - 2020 - Axiomathes 31 (3):365-380.
    Modal Meinongianism provides the semantics of sentences involving intentional verbs Priest. To that end, Modal Meinongianism employs a pointed non-normal quantified modal logic model. Like earlier Meinongian views Modal Meinongianism has a characterisation principle, that claims that any condition whatsoever is satisfied by some object in some world. Recently, Everett has proposed an argument against QCP that, if successful, gives rise to problems identical to those Russell raised for Naïve Meinongianism, namely that it allows for true contradictions, and allows us (...)
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  25. Três Vezes Não: Um Estudo Sobre as Negações Clássica, Paraconsistente e Paracompleta.Kherian Gracher - 2020 - Dissertation, Federal University of Santa Catarina
    Could there be a single logical system that would allow us to work simultaneously with classical, paraconsistent, and paracomplete negations? These three negations were separately studied in logics whose negations bear their names. Initially we will restrict our analysis to propositional logics by analyzing classical negation, ¬c, as treated by Classical Propositional Logic (LPC); the paraconsistent negation, ¬p, as treated through the hierarchy of Paraconsistent Propositional Calculi Cn (0 ≤ n ≤ ω); and the paracomplete negation, ¬q, as treated by (...)
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  26. Limits of Abductivism About Logic.Ulf Hlobil - 2020 - Philosophy and Phenomenological Research 103 (2):320-340.
    I argue against abductivism about logic, which is the view that rational theory choice in logic happens by abduction. Abduction cannot serve as a neutral arbiter in many foundational disputes in logic because, in order to use abduction, one must first identify the relevant data. Which data one deems relevant depends on what I call one's conception of logic. One's conception of logic is, however, not independent of one's views regarding many of the foundational disputes that one may hope to (...)
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  27. Inquisitive Intuitionistic Logic.Wesley H. Holliday - 2020 - In Nicola Olivetti & Rineke Verbrugge (eds.), Advances in Modal Logic, Vol. 11. College Publications. pp. 329-348.
    Inquisitive logic is a research program seeking to expand the purview of logic beyond declarative sentences to include the logic of questions. To this end, inquisitive propositional logic extends classical propositional logic for declarative sentences with principles governing a new binary connective of inquisitive disjunction, which allows the formation of questions. Recently inquisitive logicians have considered what happens if the logic of declarative sentences is assumed to be intuitionistic rather than classical. In short, what should inquisitive logic be on an (...)
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  28. Yamauchi Tokuryū, un portrait philosophique.Romaric Jannel - 2020 - In Logos et Lemme: Pensée occidentale, pensée orientale. Paris: CNRS Éditions. pp. 7-18.
    Yamauchi Tokuryū, 2020. Logos et Lemme: Pensée occidentale, pensée orientale 『ロゴスとレンマ』(1974). Translated by Augustin Berque with the assistance of Romaric Jannel. Paris: CNRS Éditions.
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  29. Star models and the semantics of infectiousness.Matthew W. G. McClure - 2020 - Undergraduate Philosophy Journal of Australasia 2 (2):35–57.
    The first degree entailment (FDE) family is a group of logics, a many-valued semantics for each system of which is obtained from classical logic by adding to the classical truth-values true and false any subset of {both, neither, indeterminate}, where indeterminate is an infectious value (any formula containing a subformula with the value indeterminate itself has the value indeterminate). In this paper, we see how to extend a version of star semantics for the logics whose many-valued semantics lack indeterminate to (...)
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  30. In the name of paraconsistency.Francisco Miró Quesada Cantuarias & Luis Felipe Bartolo Alegre - 2020 - South American Journal of Logic 6 (2):163-171.
    Logic systems that can handle contradictions were being used for some time without having a general technical name. One of the main proposers of these systems, Newton da Costa, asked Francisco Miró Quesada to suggest him a name for those systems. In the historical letter that here we translate into English for the first time, Miró Quesada suggests three names to da Costa for this purpose: ‘ultraconsistent’, ‘metaconsistent’, and ‘paraconsistent’; explaining their pros and cons. -/- Paper based on a letter (...)
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  31. Las Lógicas Mixtas como escape al Problema del Colapso y al Desafío de Quine.Joaquín Santiago Toranzo Calderón - 2020 - Análisis Filosófico 40 (2):247-272.
    En este trabajo presentaré una forma de evitar los problemas más recurrentes en cierta versión del pluralismo lógico, aquella que defiende que incluso considerando un lenguaje fijo existen múltiples sistemas lógicos legítimos. Para ello, será necesario considerar los puntos de partida del programa pluralista y explicitar los problemas que de ellos surgen, principalmente el Desafío de Quine y el Problema del Colapso. Luego, propondré una modificación respecto de lo que se entiende por consecuencia lógica, para poder considerar una familia de (...)
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  32. Logos et Lemme. Pensée occidentale, pensée orientale.Tokuryū Yamauchi, Augustin Berque & Romaric Jannel - 2020 - Paris: CNRS Éditions.
    Yamauchi Tokuryū, 2020. Logos et Lemme: Pensée occidentale, pensée orientale 『ロゴスとレンマ』(1974). Translated by Augustin Berque with the assistance of Romaric Jannel. Paris: CNRS Éditions.
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  33. Counterpossibles and Normal Defaults in the Filioque Controversy.Jacob Archambault - 2019 - Logica Universalis 13 (4):443-455.
    A counterpossible conditional, or counterpossible for short, is a conditional proposition whose antecedent is impossible. The filioque doctrine is a dogma of western Christian Trinitarian theology according to which the Holy Spirit proceeds from the Father and the Son. The filioque doctrine was the principal theological reason for the Great Schism, the split between Eastern Orthodoxy and western Christianity, which continues today. In the paper, I review one of the earliest medieval defenses of the doctrine in Anselm of Canterbury, and (...)
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  34. Graham Priest on Dialetheism and Paraconsistency.Can Başkent & Thomas Macaulay Ferguson (eds.) - 2019 - Cham, Switzerland: Springer Verlag.
    This book presents the state of the art in the fields of formal logic pioneered by Graham Priest. It includes advanced technical work on the model and proof theories of paraconsistent logic, in contributions from top scholars in the field. Graham Priest’s research has had a considerable influence on the field of philosophical logic, especially with respect to the themes of dialetheism—the thesis that there exist true but inconsistent sentences—and paraconsistency—an account of deduction in which contradictory premises do not entail (...)
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  35. A Duality for Involutive Bisemilattices.Stefano Bonzio, Andrea Loi & Luisa Peruzzi - 2019 - Studia Logica 107 (2):423-444.
    We establish a duality between the category of involutive bisemilattices and the category of semilattice inverse systems of Stone spaces, using Stone duality from one side and the representation of involutive bisemilattices as Płonka sum of Boolean algebras, from the other. Furthermore, we show that the dual space of an involutive bisemilattice can be viewed as a GR space with involution, a generalization of the spaces introduced by Gierz and Romanowska equipped with an involution as additional operation.
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  36. The Logic of Imagination Acts: A Formal System for the Dynamics of Imaginary Worlds.Joan Casas-Roma, Antonia Huertas & M. Elena Rodríguez - 2019 - Erkenntnis (4):1-29.
    Imagination has received a great deal of attention in different fields such as psychology, philosophy and the cognitive sciences, in which some works provide a detailed account of the mechanisms involved in the creation and elaboration of imaginary worlds. Although imagination has also been formalized using different logical systems, none of them captures those dynamic mechanisms. In this work, we take inspiration from the Common Frame for Imagination Acts, that identifies the different processes involved in the creation of imaginary worlds, (...)
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  37. Apontamentos em Filosofia da Lógica.Gilson Maicá de Oliveira - 2019 - Basilíade - Revista de Filosofia 1 (1):101-120.
    Neste artigo discutimos alguns aspectos da lógica nos dias atuais. O propósito central é mostrar a evolução dessa disciplina. Começamos com uma breve introdução onde especificamos o que queremos dizer com o termo “lógica”. A seguir, exporemos e discutiremos o que consideramos ser algumas das principais áreas de investigação da lógica atual. Concluímos o artigo com algumas observações sobre lógicas não clássicas e seus impactos sobre a filosofia. Ao final do texto se encontram mais detalhes que apontam para um aprofundamento (...)
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  38. A Graph-theoretic Method to Define any Boolean Operation on Partitions.David Ellerman - 2019 - The Art of Discrete and Applied Mathematics 2 (2):1-9.
    The lattice operations of join and meet were defined for set partitions in the nineteenth century, but no new logical operations on partitions were defined and studied during the twentieth century. Yet there is a simple and natural graph-theoretic method presented here to define any n-ary Boolean operation on partitions. An equivalent closure-theoretic method is also defined. In closing, the question is addressed of why it took so long for all Boolean operations to be defined for partitions.
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  39. Formalizing Kant’s Rules.Richard Evans, Andrew Stephenson & Marek Sergot - 2019 - Journal of Philosophical Logic 48:1-68.
    This paper formalizes part of the cognitive architecture that Kant develops in the Critique of Pure Reason. The central Kantian notion that we formalize is the rule. As we interpret Kant, a rule is not a declarative conditional stating what would be true if such and such conditions hold. Rather, a Kantian rule is a general procedure, represented by a conditional imperative or permissive, indicating which acts must or may be performed, given certain acts that are already being performed. These (...)
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  40. A Neutral Temporal Deontic STIT Logic.Kees van Berkel & Tim Lyon - 2019 - In P. Blackburn, E. Lorini & M. Guo (eds.), Logic, Rationality, and Interaction. Springer. pp. 340-354.
    In this work we answer a long standing request for temporal embeddings of deontic STIT logics by introducing the multi-agent STIT logic TDS . The logic is based upon atemporal utilitarian STIT logic. Yet, the logic presented here will be neutral: instead of committing ourselves to utilitarian theories, we prove the logic TDS sound and complete with respect to relational frames not employing any utilitarian function. We demonstrate how these neutral frames can be transformed into utilitarian temporal frames, while preserving (...)
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  41. Prioritized sequent-based argumentation.Ofer Arieli, AnneMarie Borg & Christian Straßer - 2018 - In Elisabeth Andre & Sven Koening (eds.), Proceedings of the 17th International Conference on Autonomous Agents and Multiagent Systems. pp. 1105--1113.
  42. On elimination of quantifiers in some non‐classical mathematical theories.Guillermo Badia & Andrew Tedder - 2018 - Mathematical Logic Quarterly 64 (3):140-154.
    Elimination of quantifiers is shown to fail dramatically for a group of well‐known mathematical theories (classically enjoying the property) against a wide range of relevant logical backgrounds. Furthermore, it is suggested that only by moving to more extensional underlying logics can we get the property back.
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  43. Conjunto plitogénico, una extensión de los conjuntos crisp, difusos, conjuntos difusos intuicionistas y neutrosóficos revisitado.Florentin Smarandache - 2018 - Neutrosophic Computing and Machine Learning 3 (1):1-19.
    En el presente artículo, introducimos el conjunto plitogénico (como generalización de conjuntos nítidos, borrosos, intuicionistas, borrosos y neutrosóficos), que es un conjunto cuyos elementos se caracterizan por los valores de muchos atrib utos. Un valor de atributo v tiene un grado correspondiente (difuso, intuicionista difuso o neutrosófico) de pertenencia d (x, v) del elemento x, al conjunto P, con respecto a algunos criterios dados. Para obtener una mejor precisión para los operadores d e agregación plitogénica en el conjunto plitogénico, y (...)
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  44. Game theoretical semantics for some non-classical logics.Can Başkent - 2016 - Journal of Applied Non-Classical Logics 26 (3):208-239.
    Paraconsistent logics are the formal systems in which absurdities do not trivialise the logic. In this paper, we give Hintikka-style game theoretical semantics for a variety of paraconsistent and non-classical logics. For this purpose, we consider Priest’s Logic of Paradox, Dunn’s First-Degree Entailment, Routleys’ Relevant Logics, McCall’s Connexive Logic and Belnap’s four-valued logic. We also present a game theoretical characterisation of a translation between Logic of Paradox/Kleene’s K3 and S5. We underline how non-classical logics require different verification games and prove (...)
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  45. Dynamic Derivations for Sequent-Based Logical Argumentation.Ofer Arieli & Christian Straßer - 2014 - In Simon Parsons, Nir Oren, Chris Reed & Federico Cerutti (eds.), Proceedings COMMA 2014. IOS Press. pp. 89--100.
  46. Logical Pluralism.Gillian Russell - 2014 - In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. Stanford, CA: The Metaphysics Research Lab.
  47. Fibring in the Leibniz Hierarchy.Victor Fernández & Marcelo Coniglio - 2007 - Logic Journal of the IGPL 15 (5-6):475-501.
    This article studies preservation of certain algebraic properties of propositional logics when combined by fibring. The logics analyzed here are classified in protoalgebraic, equivalential and algebraizable. By introducing new categories of algebrizable logics and of deductivizable quasi-varieties, it is stated an isomorphism between these categories. This constitutes an alternative to a similar result found in the literature.
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  48. Modal Logic Kalish-and-Montague Style.Nathan Salmon - 2005 - In _Metaphysics, Mathematics, and Meaning: Philosophical Papers I_. New York: Oxford University Press. pp. 111-118.
  49. Notes tow Ard a formal conversation theory.G. James Jason - 1980 - Grazer Philosophische Studien 10 (1):119-140.
    Dialectic, as commonly approached, is not an analytic study, as the notion is defined in the paper. Where it is analytically approached, the result is pragmatic in nature, as well as syntactic and semantic. This paper lays the foundations of a purely formal analysis of conversations. This study is accordingly called "Conversation Theory". The key notions of "conversation", "dialogue", "conversation game", "rules of response", "epistemic community" and "channel of informations" are defined precisely, and an analysis of how these notions fit (...)
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  50. Semi-Boolean algebras and their applications to intuitionistic logic with dual operations.Cecylia Rauszer - 1974 - Fundamenta Mathematicae 83:219-249.
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