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  1. Preconditionals.Wesley H. Holliday - manuscript
    In recent work, we introduced a new semantics for conditionals, covering a large class of what we call preconditionals. In this paper, we undertake an axiomatic study of preconditionals and subclasses of preconditionals. We then prove that any bounded lattice equipped with a preconditional can be represented by a relational structure, suitably topologized, yielding a single relational semantics for conditional logics normally treated by different semantics, as well as generalizing beyond those semantics.
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  2. Vagueness and the Connectives.Wesley H. Holliday - manuscript
    Challenges to classical logic have emerged from several sources. According to recent work, the behavior of epistemic modals in natural language motivates weakening classical logic to orthologic, a logic originally discovered by Birkhoff and von Neumann in the study of quantum mechanics. In this paper, we consider a different tradition of thinking that the behavior of vague predicates in natural language motivates weakening classical logic to intuitionistic logic or even giving up some intuitionistic principles. We focus in particular on Fine's (...)
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  3. The ILLTP Library for Intuitionistic Linear Logic.Carlos Olarte, Valeria Correa Vaz De Paiva, Elaine Pimentel & Giselle Reis - manuscript
    Benchmarking automated theorem proving (ATP) systems using standardized problem sets is a well-established method for measuring their performance. However, the availability of such libraries for non-classical logics is very limited. In this work we propose a library for benchmarking Girard's (propositional) intuitionistic linear logic. For a quick bootstrapping of the collection of problems, and for discussing the selection of relevant problems and understanding their meaning as linear logic theorems, we use translations of the collection of Kleene's intuitionistic theorems in the (...)
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  4. A cut-free sequent calculus for bi-intuitionistic logic.Rajeev Gore - manuscript
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  5. On the early history of intuitionistic logic.Anne S. Troelstra - unknown - In Philip Kremer (ed.), Mathematical Logic. pp. 3–17.
  6. Remarks on Stable Formulas in Intuitionistic Logic.Majid Alizadeh & Ali Bibak - forthcoming - Logic and Logical Philosophy:1.
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  7. Degree of Satisfiability in Heyting Algebras.Benjamin Merlin Bumpus & Zoltan A. Kocsis - forthcoming - Journal of Symbolic Logic:1-19.
    We investigate degree of satisfiability questions in the context of Heyting algebras and intuitionistic logic. We classify all equations in one free variable with respect to finite satisfiability gap, and determine which common principles of classical logic in multiple free variables have finite satisfiability gap. In particular we prove that, in a finite non-Boolean Heyting algebra, the probability that a randomly chosen element satisfies $x \vee \neg x = \top $ is no larger than $\frac {2}{3}$. Finally, we generalize our (...)
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  8. Propositional intuitionistic multiple-conclusion calculus via proof graphs.Ruan V. B. Carvalho, Anjolina G. de Oliveira & Ruy J. G. B. de Queiroz - forthcoming - Logic Journal of the IGPL.
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  9. The Logic of Potential Infinity.Roy T. Cook - forthcoming - Philosophia Mathematica.
    Michael Dummett argues that acceptance of potentially infinite collections requires that we abandon classical logic and restrict ourselves to intuitionistic logic. In this paper we examine whether Dummett is correct. After developing two detailed accounts of what, exactly, it means for a concept to be potentially infinite (based on ideas due to Charles McCarty and Øystein Linnebo, respectively), we construct a Kripke structure that contains a natural number structure that satisfies both accounts. This model supports a logic much stronger than (...)
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  10. 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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  11. (1 other version)Fine on the Possibility of Vagueness.Andreas Ditter - forthcoming - In Federico L. G. Faroldi & Frederik Van De Putte (eds.), Outstanding Contributions to Logic: Kit Fine. Springer.
    Fine (2017) 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 (2008). The present paper presents a challenge to his new theory of vagueness. I argue that the possibility theorem stated in Fine (2017), as well as his solution to the sorites paradox, fail in certain reasonable extensions of the language of CL. More specifically, I show that if we extend the (...)
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  12. Univocity of Intuitionistic and Classical Connectives.Branden Fitelson & Rodolfo C. Ertola-Biraben - forthcoming - Bulletin of Symbolic Logic:1-9.
    In this paper, we show (among other things) that the conditional in Frege's Begriffsschrift is ambiguous.
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  13. Proof-theoretic Semantics for Intuitionistic Multiplicative Linear Logic.Alexander V. Gheorghiu, Tao Gu & David J. Pym - forthcoming - Studia Logica:1-61.
    Proof-theoretic semantics (P-tS) is an innovative approach to grounding logical meaning in terms of proofs rather than traditional truth-conditional semantics. The point is not that one provides a proof system, but rather that one articulates meaning in terms of proofs and provability. To elucidate this paradigm shift, we commence with an introduction that contrasts the fundamental tenets of P-tS with the more prevalent model-theoretic approach to semantics. The contribution of this paper is a P-tS for a substructural logic, intuitionistic multiplicative (...)
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  14. Unknowable Truths.Zachary Goodsell, John Hawthorne & Juhani Yli-Vakkuri - forthcoming - Journal of Philosophy.
    In an anonymous referee report written in 1945, Church suggested a sweeping argument against verificiationism, the thesis that every truth is knowable. The argument, which was published with due acknowledgement by Fitch almost two decades later, has generated significant attention as well as some interesting successor arguments. In this paper, we present the most important episodes in this intellectual history using the logic that Church himself favoured, and we give reasons for thinking that the arguments are less than decisive. However, (...)
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  15. Symmetric and conflated intuitionistic logics.Norihiro Kamide - forthcoming - Logic Journal of the IGPL.
    Two new propositional non-classical logics, referred to as symmetric intuitionistic logic (SIL) and conflated intuitionistic logic (CIL), are introduced as indexed and non-indexed Gentzen-style sequent calculi. SIL is regarded as a natural hybrid logic combining intuitionistic and dual-intuitionistic logics, whereas CIL is regarded as a variant of intuitionistic paraconsistent logic with conflation and without paraconsistent negation. The cut-elimination theorems for SIL and CIL are proved. CIL is shown to be conservative over SIL.
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  16. G3-style Sequent Calculi for Gurevich Logic and Its Neighbors.Norihiro Kamide & Sara Negri - forthcoming - Studia Logica:1-29.
    G3-style sequent calculi are introduced for a family of logics with strong negation: Gurevich logic, Nelson logic, intuitionistic propositional logic, Avron logic, De-Omori logic, and classical propositional logic. Structural properties including cut elimination are established for these calculi. In addition, a Glivenko theorem for embedding classical propositional logic into Gurevich logic is shown.
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  17. A Transformative Intuitionist Logic for Examining Negation in Identity-Thinking.Rebecca Kosten - forthcoming - Australasian Journal of Logic.
    Negation often reinforces problematic habits of othering, but rethinking negation can make good on feminist hopes for logic as a transformative space for inclusion. As Plumwood argues in her 1993 paper, not all uses of negation in the context of social identity are inherently problematic, but the widespread implicit use of classical negation has limited our options with respect to representing difference, ultimately reinforcing dualisms that essentialize social differences in problematic ways. In response to these limitations, I take inspiration from (...)
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  18. Normalisation for Negative Free Logics Without and with Definite Descriptions.Nils Kürbis - forthcoming - Review of Symbolic Logic.
    This paper proves normalisation theorems for intuitionist and classical negative free logic, without and with the $\invertediota$ operator for definite descriptions. Rules specific to free logic give rise to new kinds of maximal formulas additional to those familiar from standard intuitionist and classical logic. When $\invertediota$ is added it must be ensured that reduction procedures involving replacements of parameters by terms do not introduce new maximal formulas of higher degree than the ones removed. The problem is solved by a rule (...)
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  19. Predicative Classes and Strict Potentialism.Øystein Linnebo & Stewart Shapiro - forthcoming - Philosophia Mathematica:nkae020.
    While sets are combinatorial collections, defined by their elements, classes are logical collections, defined by their membership conditions. We develop, in a potentialist setting, a predicative approach to (logical) classes of (combinatorial) sets. Some reasons emerge to adopt a stricter form of potentialism, which insists, not only that each object is generated at some stage of an incompletable process, but also that each truth is “made true” at some such stage. The natural logic of this strict form of potentialism is (...)
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  20. Truthmaker Semantics for Intuitionistic Modal Logic.Jon Erling Litland - forthcoming - Topoi.
    A truthmaker for a proposition P is exact if it contains nothing irrelevant to P. What are the exact truthmakers for necessitated propositions? This paper makes progress on this issue by showing how to extend Fine’s truthmaker semantics for intuitionistic logic to an exact truthmaker semantics for intuitionistic modal logic. The project is of interest also to the classical logician: while all distinctively classical theorems may be true, they differ from the intuitionistic ones in how they are made true. This (...)
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  21. 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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  22. Natural deduction and normal form for intuitionistic linear logic.S. Negri - forthcoming - Archive for Mathematical Logic.
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  23. Constructive Validity of a Generalized Kreisel–Putnam Rule.Ivo Pezlar - forthcoming - Studia Logica.
    In this paper, we propose a computational interpretation of the generalized Kreisel–Putnam rule, also known as the generalized Harrop rule or simply the Split rule, in the style of BHK semantics. We will achieve this by exploiting the Curry–Howard correspondence between formulas and types. First, we inspect the inferential behavior of the Split rule in the setting of a natural deduction system for intuitionistic propositional logic. This will guide our process of formulating an appropriate program that would capture the corresponding (...)
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  24. From Explosion to Implosion: A New Justification for the Ex Falso Quodlibet Rule.Ivo Pezlar - forthcoming - Erkenntnis.
    In this paper, we consider the ex falso quodlibet rule (EFQ) as a derived rule and propose a new justification for it based on a rule we call the collapse rule. The collapse rule is a mix between EFQ and disjunctive syllogism (DS). Informally, it says that a choice between a proposition A and ⊥, which is understood as nullary disjunction, is no choice at all and it defaults to A. Thus, we can regard it as capturing the idea of (...)
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  25. Vagueness and Intuitionistic Logic.Ian Rumfitt - forthcoming - In Alexander Miller (ed.), Language, Logic,and Mathematics: Themes from the Philosophy of Crispin Wright. Oxford University Press.
    In his essay ‘“Wang’s Paradox”’, Crispin Wright proposes a solution to the Sorites Paradox (in particular, the form of it he calls the ‘Paradox of Sharp Boundaries’) that involves adopting intuitionistic logic when reasoning with vague predicates. He does not give a semantic theory which accounts for the validity of intuitionistic logic (and the invalidity of stronger logics) in that area. The present essay tentatively makes good the deficiency. By applying a theorem of Tarski, it shows that intuitionistic logic is (...)
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  26. Intuitionistic sets and numbers: small set theory and Heyting arithmetic.Stewart Shapiro, Charles McCarty & Michael Rathjen - forthcoming - Archive for Mathematical Logic.
    It has long been known that (classical) Peano arithmetic is, in some strong sense, “equivalent” to the variant of (classical) Zermelo–Fraenkel set theory (including choice) in which the axiom of infinity is replaced by its negation. The intended model of the latter is the set of hereditarily finite sets. The connection between the theories is so tight that they may be taken as notational variants of each other. Our purpose here is to develop and establish a constructive version of this. (...)
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  27. Proof-Theoretic Validity isn’t Intuitionistic; So What?Will Stafford - forthcoming - Australasian Journal of Philosophy.
    Several recent results bring into focus the superintuitionistic nature of most notions of proof-theoretic validity, but little work has been done evaluating the consequences of these results. Proof-theoretic validity claims to offer a formal explication of how inferences follow from the definitions of logic connectives (which are defined by their introduction rules). This paper explores whether the new results undermine this claim. It is argued that, while the formal results are worrying, superintuitionistic inferences are valid because the treatments of atomic (...)
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  28. Constructive Logic is Connexive and Contradictory.Heinrich Wansing - forthcoming - Logic and Logical Philosophy:1-27.
    It is widely accepted that there is a clear sense in which the first-order paraconsistent constructive logic with strong negation of Almukdad and Nelson, QN4, is more constructive than intuitionistic first-order logic, QInt. While QInt and QN4 both possess the disjunction property and the existence property as characteristics of constructiveness (or constructivity), QInt lacks certain features of constructiveness enjoyed by QN4, namely the constructible falsity property and the dual of the existence property. This paper deals with the constructiveness of the (...)
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  29. Logic in mathematics and computer science.Richard Zach - forthcoming - In Filippo Ferrari, Elke Brendel, Massimiliano Carrara, Ole Hjortland, Gil Sagi, Gila Sher & Florian Steinberger (eds.), Oxford Handbook of Philosophy of Logic. Oxford, UK: Oxford University Press.
    Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as Hilbert developed systems of logic to formalize mathematics. These systems were meant to serve either as themselves foundational, or at least as formal analogs of mathematical reasoning amenable to mathematical study, e.g., in Hilbert’s consistency program. Similar efforts continue, but have been (...)
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  30. Universal proof theory: Feasible admissibility in intuitionistic modal logics.Amirhossein Akbar Tabatabai & Raheleh Jalali - 2025 - Annals of Pure and Applied Logic 176 (2):103526.
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  31. A complete axiomatization of infinitary first-order intuitionistic logic over L κ +, κ.Christian Espíndola - 2025 - Annals of Pure and Applied Logic 176 (1):103506.
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  32. Polyhedral Completeness of Intermediate Logics: The Nerve Criterion.Sam Adam-day, Nick Bezhanishvili, David Gabelaia & Vincenzo Marra - 2024 - Journal of Symbolic Logic 89 (1):342-382.
    We investigate a recently devised polyhedral semantics for intermediate logics, in which formulas are interpreted in n-dimensional polyhedra. An intermediate logic is polyhedrally complete if 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 (...)
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  33. 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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  34. Beyond Knowledge of the Model.Sergei Artemov - 2024 - In Yale Weiss & Romina Birman (eds.), Saul Kripke on Modal Logic. Cham: Springer. pp. 23-41.
    The principle motivation of this work is to display the sense in which the epistemic reading of a Kripke model tacitly requires common knowledge of the model, CKM. This requirement significantly restricts the amount of epistemic situations we are able to consider. We explore possible worlds epistemic models in a general setting without CKM assumptions and show that such models can be identified with observable substructures of Kripke models. We argue that such observable models offer a new level of generality (...)
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  35. Analyticity and Syntheticity in Type Theory Revisited.Bruno Bentzen - 2024 - Review of Symbolic Logic 17 (4).
    I discuss problems with Martin-Löf's distinction between analytic and synthetic judgments in constructive type theory and propose a revision of his views. I maintain that a judgment is analytic when its correctness follows exclusively from the evaluation of the expressions occurring in it. I argue that Martin-Löf's claim that all judgments of the forms a : A and a = b : A are analytic is unfounded. As I shall show, when A evaluates to a dependent function type (x : (...)
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  36. An intuitionistic interpretation of Bishop’s philosophy.Bruno Bentzen - 2024 - Philosophia Mathematica 32 (3):307-331.
    The constructive mathematics developed by Bishop in Foundations of Constructive Analysis succeeded in gaining the attention of mathematicians, but discussions of its underlying philosophy are still rare in the literature. Commentators seem to conclude, from Bishop’s rejection of choice sequences and his severe criticism of Brouwerian intuitionism, that he is not an intuitionist–broadly understood as someone who maintains that mathematics is a mental creation, mathematics is meaningful and eludes formalization, mathematical objects are mind-dependent constructions given in intuition, and mathematical truths (...)
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  37. From Strategies to Derivations and Back: An Easy Completeness Proof for First-Order Intuitionistic Dialogical Logic.Davide Catta - 2024 - In Antonio Piccolomini D'Aragona (ed.), Perspectives on Deduction: Contemporary Studies in the Philosophy, History and Formal Theories of Deduction. Springer Verlag. pp. 397-424.
    In this paper, we give a new proof of the correspondence between the existence of a winning strategy for intuitionistic E-games and Intuistionistic validity for first-order logic. The proof is obtained by a direct mapping between formal E-strategies and derivations in a cut-free complete sequent calculus for first-order intuitionistic logic. Our approach builds on the one developed by Herbelin in his PhD dissertation and greatly simplifies the proof of correspondence given by Felscher in his classic paper.
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  38. Intuitionistic Modal Algebras.Sergio A. Celani & Umberto Rivieccio - 2024 - Studia Logica 112 (3):611-660.
    Recent research on algebraic models of _quasi-Nelson logic_ has brought new attention to a number of classes of algebras which result from enriching (subreducts of) Heyting algebras with a special modal operator, known in the literature as a _nucleus_. Among these various algebraic structures, for which we employ the umbrella term _intuitionistic modal algebras_, some have been studied since at least the 1970s, usually within the framework of topology and sheaf theory. Others may seem more exotic, for their primitive operations (...)
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  39. Intuitionistic Sahlqvist Theory for Deductive Systems.Damiano Fornasiere & Tommaso Moraschini - 2024 - Journal of Symbolic Logic 89 (4):1522-1580.
    Sahlqvist theory is extended to the fragments of the intuitionistic propositional calculus that include the conjunction connective. This allows us to introduce a Sahlqvist theory of intuitionistic character amenable to arbitrary protoalgebraic deductive systems. As an application, we obtain a Sahlqvist theorem for the fragments of the intuitionistic propositional calculus that include the implication connective and for the extensions of the intuitionistic linear logic.
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  40. 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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  41. Modal logic, fundamentally.Wesley H. Holliday - 2024 - In Agata Ciabattoni, David Gabelaia & Igor Sedlár (eds.), Advances in Modal Logic, Vol. 15. London: College Publications.
    Non-classical generalizations of classical modal logic have been developed in the contexts of constructive mathematics and natural language semantics. In this paper, we discuss a general approach to the semantics of non-classical modal logics via algebraic representation theorems. We begin with complete lattices L equipped with an antitone operation ¬ sending 1 to 0, a completely multiplicative operation ◻, and a completely additive operation ◊. Such lattice expansions can be represented by means of a set X together with binary relations (...)
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  42. The Logic ILP for Intuitionistic Reasoning About Probability.Angelina Ilić-Stepić, Zoran Ognjanović & Aleksandar Perović - 2024 - Studia Logica 112 (5):987-1017.
    We offer an alternative approach to the existing methods for intuitionistic formalization of reasoning about probability. In terms of Kripke models, each possible world is equipped with a structure of the form \(\langle H, \mu \rangle \) that needs not be a probability space. More precisely, though _H_ needs not be a Boolean algebra, the corresponding monotone function (we call it measure) \(\mu : H \longrightarrow [0,1]_{\mathbb {Q}}\) satisfies the following condition: if \(\alpha \), \(\beta \), \(\alpha \wedge \beta \), (...)
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  43. Paradoxes, Intuitionism, and Proof-Theoretic Semantics.Reinhard Kahle & Paulo Guilherme Santos - 2024 - In Thomas Piecha & Kai F. Wehmeier (eds.), Peter Schroeder-Heister on Proof-Theoretic Semantics. Springer. pp. 363-374.
    In this note, we review paradoxes like Russell’s, the Liar, and Curry’s in the context of intuitionistic logic. One may observe that one cannot blame the underlying logic for the paradoxes, but has to take into account the particular concept formations. For proof-theoretic semantics, however, this comes with the challenge to block some forms of direct axiomatizations of the Liar. A proper answer to this challenge might be given by Schroeder-Heister’s definitional freedom.
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  44. Intuitionistic Public Announcement Logic with Distributed Knowledge.Ryo Murai & Katsuhiko Sano - 2024 - Studia Logica 112 (3):661-691.
    We develop intuitionistic public announcement logic over intuitionistic \({\textbf{K}}\), \({{\textbf{K}}}{{\textbf{T}}}\), \({{\textbf{K}}}{{\textbf{4}}}\), and \({{\textbf{S}}}{{\textbf{4}}}\) with distributed knowledge. We reveal that a recursion axiom for the distributed knowledge is _not_ valid for a frame class discussed in [ 12 ] but valid for the restricted frame class introduced in [ 20, 26 ]. The semantic completeness of the static logics for this restricted frame class is established via the concept of pseudo-model.
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  45. An Intuitionistically Complete System of Basic Intuitionistic Conditional Logic.Grigory Olkhovikov - 2024 - Journal of Philosophical Logic 53 (5).
    We introduce a basic intuitionistic conditional logic \(\textsf{IntCK}\) that we show to be complete both relative to a special type of Kripke models and relative to a standard translation into first-order intuitionistic logic. We show that \(\textsf{IntCK}\) stands in a very natural relation to other similar logics, like the basic classical conditional logic \(\textsf{CK}\) and the basic intuitionistic modal logic \(\textsf{IK}\). As for the basic intuitionistic conditional logic \(\textsf{ICK}\) proposed in Weiss (_Journal of Philosophical Logic_, _48_, 447–469, 2019 ), \(\textsf{IntCK}\) (...)
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  46. Craig Interpolation Theorem Fails in Bi-Intuitionistic Predicate Logic.Grigory K. Olkhovikov & Guillermo Badia - 2024 - Review of Symbolic Logic 17 (2):611-633.
    In this article we show that bi-intuitionistic predicate logic lacks the Craig Interpolation Property. We proceed by adapting the counterexample given by Mints, Olkhovikov and Urquhart for intuitionistic predicate logic with constant domains [13]. More precisely, we show that there is a valid implication $\phi \rightarrow \psi $ with no interpolant. Importantly, this result does not contradict the unfortunately named ‘Craig interpolation’ theorem established by Rauszer in [24] since that article is about the property more correctly named ‘deductive interpolation’ (see (...)
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  47. The first-order logic of CZF is intuitionistic first-order logic.Robert Passmann - 2024 - Journal of Symbolic Logic 89 (1):308-330.
    We prove that the first-order logic of CZF is intuitionistic first-order logic. To do so, we introduce a new model of transfinite computation (Set Register Machines) and combine the resulting notion of realisability with Beth semantics. On the way, we also show that the propositional admissible rules of CZF are exactly those of intuitionistic propositional logic.
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  48. Intuitionism, Justification Logic, and Doxastic Reasoning.Vincent Alexis Peluce - 2024 - Dissertation, The Graduate Center, City University of New York
    In this Dissertation, we examine a handful of related themes in the philosophy of logic and mathematics. We take as a starting point the deeply philosophical, and—as we argue, deeply Kantian—views of L.E.J. Brouwer, the founder of intuitionism. We examine his famous first act of intuitionism. Therein, he put forth both a critical and a constructive idea. This critical idea involved digging a philosophical rift between what he thought of himself as doing and what he thought of his contemporaries, specifically (...)
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  49. On Combining Intuitionistic and S4 Modal Logic.João Rasga & Cristina Sernadas - 2024 - Bulletin of the Section of Logic 53 (3):321-344.
    We address the problem of combining intuitionistic and S4 modal logic in a non-collapsing way inspired by the recent works in combining intuitionistic and classical logic. The combined language includes the shared constructors of both logics namely conjunction, disjunction and falsum as well as the intuitionistic implication, the classical implication and the necessity modality. We present a Gentzen calculus for the combined logic defined over a Gentzen calculus for the host S4 modal logic. The semantics is provided by Kripke structures. (...)
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  50. A new model construction by making a detour via intuitionistic theories IV: A closer connection between KPω and BI.Kentaro Sato - 2024 - Annals of Pure and Applied Logic 175 (7):103422.
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