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  1. A cut-free sequent calculus for bi-intuitionistic logic.Rajeev Gore - manuscript
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  2. Polyhedral Completeness of Intermediate Logics: The Nerve Criterion.Sam Adam-day, Nick Bezhanishvili, David Gabelaia & Vincenzo Marra - forthcoming - Journal of Symbolic Logic:1-41.
    We investigate a recently devised polyhedral semantics for intermediate logics, in which formulas are interpreted inn-dimensional polyhedra. An intermediate logic ispolyhedrally completeif it is complete with respect to some class of polyhedra. The first main result of this paper is a necessary and sufficient condition for the polyhedral completeness of a logic. This condition, which we call the Nerve Criterion, is expressed in terms of Alexandrov’s notion of the nerve of a poset. It affords a purely combinatorial characterisation of polyhedrally (...)
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  3. How Much Propositional Logic Suffices for Rosser's Essential Undecidability Theorem?Guillermo Badia, Petr Cintula, Petr Hajek & Andrew Tedder - forthcoming - Review of Symbolic Logic.
    In this paper we explore the following question: how weak can a logic be for Rosser’s essential undecidability result to be provable for a weak arithmetical theory? It is well known that Robinson’s Q is essentially undecidable in intuitionistic logic, and P. Hájek proved it in the fuzzy logic BL for Grzegorczyk’s variant of Q which interprets the arithmetic operations as nontotal nonfunctional relations. We present a proof of essential undecidability in a much weaker substructural logic and for a much (...)
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  4. Bishop's Mathematics: a Philosophical Perspective.Laura Crosilla - forthcoming - In Handbook of Bishop's Mathematics. CUP.
    Errett Bishop's work in constructive mathematics is overwhelmingly regarded as a turning point for mathematics based on intuitionistic logic. It brought new life to this form of mathematics and prompted the development of new areas of research that witness today's depth and breadth of constructive mathematics. Surprisingly, notwithstanding the extensive mathematical progress since the publication in 1967 of Errett Bishop's Foundations of Constructive Analysis, there has been no corresponding advances in the philosophy of constructive mathematics Bishop style. The aim of (...)
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  5. On a Problem of Friedman and its Solution by Rybakov.Jeroen P. Goudsmit - forthcoming - Bulletin of Symbolic Logic:1-48.
    Rybakov (1984a) proved that the admissible rules of IPC are decidable. We give a proof of the same theorem, using the same core idea, but couched in the many notions that have been developed in the mean time. In particular, we illustrate how the argument can be interpreted as using refinements of the notions of exactness and extendibility.
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  6. Another Neighbourhood Semantics for Intuitionistic Logic.Morteza Moniri & Fatemeh Shirmohammadzadeh Maleki - forthcoming - Logic Journal of the IGPL.
    In this paper we first introduce a new neighbourhood semantics for propositional intuitionistic logic. We then naturally extend this semantics to first-order intuitionistic logic. We also study bisimulation between neighbourhood models and prove some of their basic properties for both propositional and first-order intuitionistic logic.
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  7. Natural deduction and normal form for intuitionistic linear logic.S. Negri - forthcoming - Archive for Mathematical Logic.
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  8. Wansing's bi-intuitionistic logic: semantics, extension and unilateralisation.Juan C. Agudelo-Agudelo - 2024 - Journal of Applied Non-Classical Logics 34 (1):31-54.
    The well-known algebraic semantics and topological semantics for intuitionistic logic (Int) is here extended to Wansing's bi-intuitionistic logic (2Int). The logic 2Int is also characterised by a quasi-twist structure semantics, which leads to an alternative topological characterisation of 2Int. Later, notions of Fregean negation and of unilateralisation are proposed. The logic 2Int is extended with a ‘Fregean negation’ connective ∼, obtaining 2Int∼, and it is showed that the logic N4⋆ (an extension of Nelson's paraconsistent logic) results to be the unilateralisation (...)
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  9. The existential fragment of second-order propositional intuitionistic logic is undecidable.Ken-Etsu Fujita, Aleksy Schubert, Paweł Urzyczyn & Konrad Zdanowski - 2024 - Journal of Applied Non-Classical Logics 34 (1):55-74.
    The provability problem in intuitionistic propositional second-order logic with existential quantifier and implication (∃,→) is proved to be undecidable in presence of free type variables (constants). This contrasts with the result that inutitionistic propositional second-order logic with existential quantifier, conjunction and negation is decidable.
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  10. Connecting the revolutionary with the conventional: Rethinking the differences between the works of Brouwer, Heyting, and Weyl.Kati Kish Bar-On - 2023 - Philosophy of Science 90 (3):580–602.
    Brouwer’s intuitionism was a far-reaching attempt to reform the foundations of mathematics. While the mathematical community was reluctant to accept Brouwer’s work, its response to later-developed brands of intuitionism, such as those presented by Hermann Weyl and Arend Heyting, was different. The paper accounts for this difference by analyzing the intuitionistic versions of Brouwer, Weyl, and Heyting in light of a two-tiered model of the body and image of mathematical knowledge. Such a perspective provides a richer account of each story (...)
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  11. 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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  12. Verified completeness in Henkin-style for intuitionistic propositional logic.Huayu Guo, Dongheng Chen & Bruno Bentzen - 2023 - In Bruno Bentzen, Beishui Liao, Davide Liga, Reka Markovich, Bin Wei, Minghui Xiong & Tianwen Xu (eds.), Logics for AI and Law: Joint Proceedings of the Third International Workshop on Logics for New-Generation Artificial Intelligence and the International Workshop on Logic, AI and Law, September 8-9 and 11-12, 2023, Hangzhou. College Publications. pp. 36-48.
    This paper presents a formalization of the classical proof of completeness in Henkin-style developed by Troelstra and van Dalen for intuitionistic logic with respect to Kripke models. The completeness proof incorporates their insights in a fresh and elegant manner that is better suited for mechanization. We discuss details of our implementation in the Lean theorem prover with emphasis on the prime extension lemma and construction of the canonical model. Our implementation is restricted to a system of intuitionistic propositional logic with (...)
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  13. 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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  14. Contrapositionally complemented Heyting algebras and intuitionistic logic with minimal negation.Anuj Kumar More & Mohua Banerjee - 2023 - Logic Journal of the IGPL 31 (3):441-474.
    Two algebraic structures, the contrapositionally complemented Heyting algebra (ccHa) and the contrapositionally |$\vee $| complemented Heyting algebra (c|$\vee $|cHa), are studied. The salient feature of these algebras is that there are two negations, one intuitionistic and another minimal in nature, along with a condition connecting the two operators. Properties of these algebras are discussed, examples are given and comparisons are made with relevant algebras. Intuitionistic Logic with Minimal Negation (ILM) corresponding to ccHas and its extension |${\textrm {ILM}}$|-|${\vee }$| for c|$\vee (...)
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  15. The Gödel-McKinsey-Tarski embedding for infinitary intuitionistic logic and its extensions.Matteo Tesi & Sara Negri - 2023 - Annals of Pure and Applied Logic 174 (8):103285.
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  16. 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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  17. Naive cubical type theory.Bruno Bentzen - 2022 - Mathematical Structures in Computer Science:1-27.
    This article proposes a way of doing type theory informally, assuming a cubical style of reasoning. It can thus be viewed as a first step toward a cubical alternative to the program of informalization of type theory carried out in the homotopy type theory book for dependent type theory augmented with axioms for univalence and higher inductive types. We adopt a cartesian cubical type theory proposed by Angiuli, Brunerie, Coquand, Favonia, Harper, and Licata as the implicit foundation, confining our presentation (...)
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  18. Natural Deduction Systems for Intuitionistic Logic with Identity.Szymon Chlebowski, Marta Gawek & Agata Tomczyk - 2022 - Studia Logica 110 (6):1381-1415.
    The aim of the paper is to present two natural deduction systems for Intuitionistic Sentential Calculus with Identity ( ISCI ); a syntactically motivated \(\mathsf {ND}^1_{\mathsf {ISCI}}\) and a semantically motivated \(\mathsf {ND}^2_{\mathsf {ISCI}}\). The formulation of \(\mathsf {ND}^1_{\mathsf {ISCI}}\) is based on the axiomatic formulation of ISCI. Its rules cannot be straightforwardly classified as introduction or elimination rules; ISCI -specific rules are based on axioms characterizing the identity connective. The system does not enjoy the standard subformula property, but due (...)
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  19. 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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  20. Compatibility and accessibility: lattice representations for semantics of non-classical and modal logics.Wesley Holliday - 2022 - In David Fernández Duque, Alessandra Palmigiano & Sophie Pinchinat (eds.), Advances in Modal Logic, Vol. 14. London: 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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  21. 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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  22. Effect of the Choice of Connectives on the Relation between Classical Logic and Intuitionistic Logic.Tomoaki Kawano, Naosuke Matsuda & Kento Takagi - 2022 - Notre Dame Journal of Formal Logic 63 (2).
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  23. 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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  24. Revisiting Constructive Mingle: Algebraic and Operational Semantics.Yale Weiss - 2022 - In Katalin Bimbo (ed.), Relevance Logics and other Tools for Reasoning. Essays in Honor of J. Michael Dunn. London: College Publications. pp. 435-455.
    Among Dunn’s many important contributions to relevance logic was his work on the system RM (R-mingle). Although RM is an interesting system in its own right, it is widely considered to be too strong. In this chapter, I revisit a closely related system, RM0 (sometimes known as ‘constructive mingle’), which includes the mingle axiom while not degenerating in the way that RM itself does. My main interest will be in examining this logic from two related semantical perspectives. First, I give (...)
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  25. Note on the Intuitionistic Logic of False Belief.Tomasz Witczak - 2022 - Bulletin of the Section of Logic 51 (1):57-71.
    In this paper we analyse logic of false belief in the intuitionistic setting. This logic, studied in its classical version by Steinsvold, Fan, Gilbert and Venturi, describes the following situation: a formula $\varphi$ is not satisfied in a given world, but we still believe in it. Another interpretations are also possible: e.g. that we do not accept $\varphi$ but it is imposed on us by a kind of council or advisory board. From the mathematical point of view, the idea is (...)
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  26. Intuitionistic fixed point logic.Ulrich Berger & Hideki Tsuiki - 2021 - Annals of Pure and Applied Logic 172 (3):102903.
    We study the system IFP of intuitionistic fixed point logic, an extension of intuitionistic first-order logic by strictly positive inductive and coinductive definitions. We define a realizability interpretation of IFP and use it to extract computational content from proofs about abstract structures specified by arbitrary classically true disjunction free formulas. The interpretation is shown to be sound with respect to a domain-theoretic denotational semantics and a corresponding lazy operational semantics of a functional language for extracted programs. We also show how (...)
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  27. Book "Set theory INC^# based on intuitionistic logic with restricted modus ponens rule".Jaykov Foukzon - 2021 - LAP LAMBERT Academic Publishing.
    In this book set theory INC# based on intuitionistic logic with restricted modus ponens rule is proposed. It proved that intuitionistic logic with restricted modus ponens rule can to safe Cantor naive set theory from a triviality.
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  28. Set theory INC# based on intuitionistic logic with restricted modus ponens rule.Jaykov Foukzon (ed.) - 2021 - AP LAMBERT Academic Publishing (June 23, 2021).
    In this book set theory INC# based on intuitionistic logic with restricted modus ponens rule is proposed. It proved that intuitionistic logic with restricted modus ponens rule can to safe Cantor naive set theory from a triviality. Similar results for paraconsistent set theories were obtained in author papers [13]-[16].
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  29. 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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  30. Possibility Semantics.Wesley H. Holliday - 2021 - In Melvin Fitting (ed.), Selected Topics from Contemporary Logics. London: College Publications. pp. 363-476.
    In traditional semantics for classical logic and its extensions, such as modal logic, propositions are interpreted as subsets of a set, as in discrete duality, or as clopen sets of a Stone space, as in topological duality. A point in such a set can be viewed as a "possible world," with the key property of a world being primeness—a world makes a disjunction true only if it makes one of the disjuncts true—which classically implies totality—for each proposition, a world either (...)
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  31. Proof complexity of substructural logics.Raheleh Jalali - 2021 - Annals of Pure and Applied Logic 172 (7):102972.
  32. Games and Bisimulations for Intuitionistic First-Order Kripke Models.Małgorzata Kruszelnicka - 2021 - Studia Logica 109 (5):903-916.
    The aim of this paper is to introduce the notion of a game for intuitionistic first-order Kripke models. We also establish links between notions presented here and the notions of logical equivalence and bounded bisimulation for intuitionistic first-order Kripke models, and the Ehrenfeucht–Fraïssé game for classical first-order structures.
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  33. Normalisation and subformula property for a system of intuitionistic logic with general introduction and elimination rules.Nils Kürbis - 2021 - Synthese 199 (5-6):14223-14248.
    This paper studies a formalisation of intuitionistic logic by Negri and von Plato which has general introduction and elimination rules. The philosophical importance of the system is expounded. Definitions of ‘maximal formula’, ‘segment’ and ‘maximal segment’ suitable to the system are formulated and corresponding reduction procedures for maximal formulas and permutative reduction procedures for maximal segments given. Alternatives to the main method used are also considered. It is shown that deductions in the system convert into normal form and that deductions (...)
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  34. Strong Depth Relevance.Shay Allen Logan - 2021 - Australasian Journal of Logic 18 (6):645-656.
    Relevant logics infamously have the property that they only validate a conditional when some propositional variable is shared between its antecedent and consequent. This property has been strengthened in a variety of ways over the last half-century. Two of the more famous of these strengthenings are the strong variable sharing property and the depth relevance property. In this paper I demonstrate that an appropriate class of relevant logics has a property that might naturally be characterized as the supremum of these (...)
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  35. 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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  36. Intuitionistic mereology.Paolo Maffezioli & Achille C. Varzi - 2021 - Synthese 198 (Suppl 18):4277-4302.
    Two mereological theories are presented based on a primitive apartness relation along with binary relations of mereological excess and weak excess, respectively. It is shown that both theories are acceptable from the standpoint of constructive reasoning while remaining faithful to the spirit of classical mereology. The two theories are then compared and assessed with regard to their extensional import.
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  37. 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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  38. Proof that Intuitionistic Logic is not Three-Valued.Micah Phillips-Gary - 2021 - The Hemlock Papers 18:4-14.
    In this paper, we give an introduction to intuitionistic logic and a defense of it from certain formal logical critiques. Intuitionism is the thesis that mathematical objects are mental constructions produced by the faculty of a priori intuition of time. The truth of a mathematical proposition, then, consists in our knowing how to construct in intuition a corresponding state of affairs. This understanding of mathematical truth leads to a rejection of the principle, valid in classical logic, that a proposition is (...)
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  39. The Naturality of Natural Deduction (II): On Atomic Polymorphism and Generalized Propositional Connectives.Paolo Pistone, Luca Tranchini & Mattia Petrolo - 2021 - Studia Logica 110 (2):545-592.
    In a previous paper we investigated the extraction of proof-theoretic properties of natural deduction derivations from their impredicative translation into System F. Our key idea was to introduce an extended equational theory for System F codifying at a syntactic level some properties found in parametric models of polymorphic type theory. A different approach to extract proof-theoretic properties of natural deduction derivations was proposed in a recent series of papers on the basis of an embedding of intuitionistic propositional logic into a (...)
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  40. Inquisitive Heyting Algebras.Vít Punčochář - 2021 - Studia Logica 109 (5):995-1017.
    In this paper we introduce a class of inquisitive Heyting algebras as algebraic structures that are isomorphic to algebras of finite antichains of bounded implicative meet semilattices. It is argued that these structures are suitable for algebraic semantics of inquisitive superintuitionistic logics, i.e. logics of questions based on intuitionistic logic and its extensions. We explain how questions are represented in these structures and provide several alternative characterizations of these algebras. For instance, it is shown that a Heyting algebra is inquisitive (...)
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  41. Basic Quasi-Boolean Expansions of Relevance Logics.Gemma Robles & José M. Méndez - 2021 - Journal of Philosophical Logic 50 (4):727-754.
    The basic quasi-Boolean negation expansions of relevance logics included in Anderson and Belnap’s relevance logic R are defined. We consider two types of QB-negation: H-negation and D-negation. The former one is of paraintuitionistic or superintuitionistic character, the latter one, of dual intuitionistic nature in some sense. Logics endowed with H-negation are paracomplete; logics with D-negation are paraconsistent. All logics defined in the paper are given a Routley-Meyer ternary relational semantics.
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  42. From Intuitionism to Many-Valued Logics Through Kripke Models.Saeed Salehi - 2021 - In Mojtaba Mojtahedi, Shahid Rahman & Mohammad Saleh Zarepour (eds.), Mathematics, Logic, and their Philosophies: Essays in Honour of Mohammad Ardeshir. Springer. pp. 339-348.
    Intuitionistic Propositional Logic is proved to be an infinitely many valued logic by Gödel (Kurt Gödel collected works (Volume I) Publications 1929–1936, Oxford University Press, pp 222–225, 1932), and it is proved by Jaśkowski (Actes du Congrés International de Philosophie Scientifique, VI. Philosophie des Mathématiques, Actualités Scientifiques et Industrielles 393:58–61, 1936) to be a countably many valued logic. In this paper, we provide alternative proofs for these theorems by using models of Kripke (J Symbol Logic 24(1):1–14, 1959). Gödel’s proof gave (...)
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  43. A Reinterpretation of the Semilattice Semantics with Applications.Yale Weiss - 2021 - Logica Universalis 15 (2):171-191.
    In the early 1970s, Alasdair Urquhart proposed a semilattice semantics for relevance logic which he provided with an influential informational interpretation. In this article, I propose a BHK-inspired reinterpretation of the semantics which is related to Kit Fine’s truthmaker semantics. I discuss and compare Urquhart’s and Fine’s semantics and show how simple modifications of Urquhart’s semantics can be used to characterize both full propositional intuitionistic logic and Jankov’s logic. I then present (quasi-)relevant companions for both of these systems. Finally, I (...)
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  44. Proof Theory for Positive Logic with Weak Negation.Marta Bílková & Almudena Colacito - 2020 - Studia Logica 108 (4):649-686.
    Proof-theoretic methods are developed for subsystems of Johansson’s logic obtained by extending the positive fragment of intuitionistic logic with weak negations. These methods are exploited to establish properties of the logical systems. In particular, cut-free complete sequent calculi are introduced and used to provide a proof of the fact that the systems satisfy the Craig interpolation property. Alternative versions of the calculi are later obtained by means of an appropriate loop-checking history mechanism. Termination of the new calculi is proved, and (...)
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  45. Intuitionism and the Modal Logic of Vagueness.Susanne Bobzien & Ian Rumfitt - 2020 - Journal of Philosophical Logic 49 (2):221-248.
    Intuitionistic logic provides an elegant solution to the Sorites Paradox. Its acceptance has been hampered by two factors. First, the lack of an accepted semantics for languages containing vague terms has led even philosophers sympathetic to intuitionism to complain that no explanation has been given of why intuitionistic logic is the correct logic for such languages. Second, switching from classical to intuitionistic logic, while it may help with the Sorites, does not appear to offer any advantages when dealing with the (...)
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  46. Monadic Intuitionistic and Modal Logics Admitting Provability Interpretations.Kristina Brantley - 2020 - Bulletin of Symbolic Logic 26 (3-4):296-296.
  47. Recovery operators, paraconsistency and duality.Walter A. Carnielli, Marcelo E. Coniglio & Abilio Rodrigues Filho - 2020 - Logic Journal of the IGPL 28 (5):624-656.
    There are two foundational, but not fully developed, ideas in paraconsistency, namely, the duality between paraconsistent and intuitionistic paradigms, and the introduction of logical operators that express meta-logical notions in the object language. The aim of this paper is to show how these two ideas can be adequately accomplished by the Logics of Formal Inconsistency (LFIs) and by the Logics of Formal Undeterminedness (LFUs). LFIs recover the validity of the principle of explosion in a paraconsistent scenario, while LFUs recover the (...)
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  48. The Philosophy of Logic of Francisco Miró Quesada Cantuarias.Newton da Costa, José Carlos Cifuentes & Luis Felipe Bartolo Alegre - 2020 - South American Journal of Logic 6 (2):189-208.
    In this historical article, Newton da Costa discusses Francisco Miró Quesada’s philosophical ideas about logic. He discusses the topics of reason, logic, and action in Miró Quesada’s work, and in the final section he offers his critical view. In particular, he disagrees with Miró Quesada’s stance on the historicity of reason, for whom “reason is essentially absolute”, whereas for da Costa it “is being constructed in the course of history”. Da Costa concludes by emphasizing the importance of Miró Quesada’s theory (...)
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  49. Paracomplete logics which are dual to the paraconsistent logics L3A and L3B.Alejandro Hernández-Tello, Verónica Borja-Macı́as & Marcelo E. Coniglio - 2020 - LANMR 2019: Proceedings of the 12th Latin American Workshop on Logic/Languages, Algorithms and New Methods of Reasoning.
    In 2016 Beziau, introduce a more restricted concept of paraconsistency, namely the genuine paraconsistency. He calls genuine paraconsistent logic those logic rejecting φ, ¬φ |- ψ and |- ¬(φ ∧ ¬φ). In that paper the author analyzes, among the three-valued logics, which of these logics satisfy this property. If we consider multiple-conclusion consequence relations, the dual properties of those above mentioned are: |- φ, ¬φ, and ¬(ψ ∨ ¬ψ) |- . We call genuine paracomplete logics those rejecting the mentioned properties. (...)
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  50. Inquisitive Intuitionistic Logic.Wesley H. Holliday - 2020 - In Nicola Olivetti & Rineke Verbrugge (eds.), Advances in Modal Logic, Vol. 13. London: 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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