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  1.  19
    Logical Models of Mathematical Texts: The Case of Conventions for Division by Zero.Jan A. Bergstra & John V. Tucker - 2024 - Journal of Logic, Language and Information 33 (4):277-298.
    Arithmetical texts involving division are governed by conventions that avoid the risk of problems to do with division by zero (DbZ). A model for elementary arithmetic texts is given, and with the help of many examples and counter examples a partial description of what may be called traditional conventions on DbZ is explored. We introduce the informal notions of legal and illegal texts to analyse these conventions. First, we show that the legality of a text is algorithmically undecidable. As a (...)
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  2.  27
    Why Sometimes the King of France is Not Bald: Presupposition Denial Without Ambiguity.Leonard Jay Clapp - 2024 - Journal of Logic, Language and Information 33 (4):235-276.
    Contrary to what seems to be predicted by a Strawson-inspired view, in presupposition denials the presupposition triggered by, e.g., ‘the king of France’ seems to be cancelled. To explain this puzzling instance of the projection problem, defenders of a Strawson-inspired view have proposed various ad hoc ambiguities. I develop a version of Segmented Discourse Representation Theory that explains the puzzling presupposition-cancelling phenomenon relying only on independently motivated pragmatic processes. Appealing to Kripke’s “test” for the adequacy of ambiguity motivating counterexamples, I (...)
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  3.  9
    Interpretation of Hybrid Counterfactual Logic into Hybrid Tense Logic: and Comparison of Their Expressive Power on Temporal Sphere Models.Yuichiro Hosokawa - 2024 - Journal of Logic, Language and Information 33 (4):391-418.
    Lewis (Noûs 13:455–476, 1979) claimed that branching-time(-like) models can be derived from his sphere models. However, he did not present any specific construction of branching-time(-like) models from his sphere models formally. Meanwhile, Hosokawa (in: Modern logic of modality and its philosophical range: counterfactuals, Gettier problem, and information flow, Tokyo Metropolitan University, 2018) presented a logico-mathematically strict manner in which sphere models can be reconstructed from branching-time models. Subsequently, Hosokawa (J Logic Lang Inf 32:677–706, 2023) presented a proof-theoretically refined version of (...)
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  4.  8
    A Propositional Cirquent Calculus for Computability Logic.Giorgi Japaridze - 2024 - Journal of Logic, Language and Information 33 (4):363-389.
    Cirquent calculus is a proof system with inherent ability to account for sharing subcomponents in logical expressions. Within its framework, this article constructs an axiomatization $$\text{ CL18 }$$ CL18 of the basic propositional fragment of computability logic—the game-semantically conceived logic of computational resources and tasks. The nonlogical atoms of this fragment represent arbitrary so called static games, and the connectives of its logical vocabulary are negation and the parallel and choice versions of conjunction and disjunction. The main technical result of (...)
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  5.  12
    On Some Dynamics in Conceptual Spaces.Piotr Lisowski & Roman Urban - 2024 - Journal of Logic, Language and Information 33 (4):339-361.
    In this text, we consider Gärdenfors’ conceptual spaces that are separable Hilbert spaces. In particular, the results we obtained apply to finite-dimensional Euclidean spaces. Our main contribution can be formulated as a combination of the theory of opinion dynamics with the theory of conceptual spaces. This combination, in turn, leads us to propose a new model for the time evolution of conceptual spaces. To achieve this goal, we propose some extension of the multidimensional opinion dynamics model of Parsegov, Proskurnikov, Tempo (...)
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  6.  19
    A basic system of paraconsistent Nelsonian logic of conditionals.Grigory K. Olkhovikov - 2024 - Journal of Logic, Language and Information 33 (4):299-337.
    We define a Kripke semantics for a conditional logic based on the propositional logic $$\textsf{N4}$$ N 4, the paraconsistent variant of Nelson’s logic of strong negation; we axiomatize the minimal system induced by this semantics. The resulting logic, which we call $$\textsf{N4CK}$$ N 4 CK, shows strong connections both with the basic intuitionistic logic of conditionals $$\textsf{IntCK}$$ IntCK introduced earlier in (Olkhovikov, 2023) and with the $$\textsf{N4}$$ N 4 -based modal logic $$\textsf{FSK}^d$$ FSK d introduced in (Odintsov and Wansing, 2004) (...)
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  7.  20
    Syllogistic Relevance and Term Logic.J. -Martín Castro-Manzano - 2024 - Journal of Logic, Language and Information 33 (2):89-105.
    Term Functor Logic is a term logic that recovers some important features of the traditional, Aristotelian logic; however, it turns out that it does not preserve all of the Aristotelian properties a valid inference should have insofar as the class of theorems of Term Functor Logic includes some inferences that may be considered irrelevant (e.g. ex falso, verum ad, and petitio principii). By following an Aristotelian or syllogistic notion of relevance, in this contribution we adapt a tableaux method for Term (...)
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  8.  27
    Expressive Power and Intensional Operators.Pablo Cubides Kovacsics & David Rey - 2024 - Journal of Logic, Language and Information 33 (2):107-141.
    In Entities and Indices, M. J. Cresswell argued that a first-order modal language can reach the expressive power of natural-language modal discourse only if we give to the formal language a semantics with indices containing infinite possible worlds and we add to it an infinite collection of operators $${{\varvec{actually}}}_n$$ actually n and $$ Ref _n$$ R e f n which store and retrieve worlds. In the fourth chapter of the book, Cresswell gave a proof that the resulting intensional language, which (...)
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  9.  33
    Rules of Explosion and Excluded Middle: Constructing a Unified Single-Succedent Gentzen-Style Framework for Classical, Paradefinite, Paraconsistent, and Paracomplete Logics.Norihiro Kamide - 2024 - Journal of Logic, Language and Information 33 (2):143-178.
    A unified and modular falsification-aware single-succedent Gentzen-style framework is introduced for classical, paradefinite, paraconsistent, and paracomplete logics. This framework is composed of two special inference rules, referred to as the rules of explosion and excluded middle, which correspond to the principle of explosion and the law of excluded middle, respectively. Similar to the cut rule in Gentzen’s LK for classical logic, these rules are admissible in cut-free LK. A falsification-aware single-succedent Gentzen-style sequent calculus fsCL for classical logic is formalized based (...)
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  10.  14
    Algebraic Completeness of Connexive and Bi-Intuitionistic Multilattice Logics.Yaroslav Petrukhin - 2024 - Journal of Logic, Language and Information 33 (2):179-196.
    In this paper, we introduce the notions of connexive and bi-intuitionistic multilattices and develop on their base the algebraic semantics for Kamide, Shramko, and Wansing’s connexive and bi-intuitionistic multilattice logics which were previously known in the form of sequent calculi and Kripke semantics. We prove that these logics are sound and complete with respect to the presented algebraic structures.
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  11.  20
    Propositional Logic for Infinitive Sentences.Nicola Spinelli - 2024 - Journal of Logic, Language and Information 33 (2):197-234.
    This paper is about sentences of form To be human is to be an animal, To live is to fight, etc. I call them ‘infinitive sentences’. I define an augmented propositional language able to express them and give a matrix-based semantics for it. I also give a tableau proof system, called IL for Infinitive Logic. I prove soundness, completeness and a few basic theorems.
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