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First-Order Classical Modal Logic [PDF]
Studia Logica, 2006 This paper focuses on extending to the first order case the semantical program for modalities first introduced by Dana Scott and Richard Montague. We focus on the study of neighborhood frames with constant domains and we offer in the first part of the paper a series of new completeness results for salient classical systems of first order modal logic.
Arló-Costa, Horacio, Pacuit, Eric
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On Presburger arithmetic extended with non-unary counting quantifiers [PDF]
Logical Methods in Computer Science, 2023 We consider a first-order logic for the integers with addition. This logic extends classical first-order logic by modulo-counting, threshold-counting and exact-counting quantifiers, all applied to tuples of variables (here, residues are given as terms ...
Peter Habermehl, Dietrich Kuske
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Game semantics for first-order logic [PDF]
Logical Methods in Computer Science, 2010 We refine HO/N game semantics with an additional notion of pointer (mu-pointers) and extend it to first-order classical logic with completeness results.
Olivier Laurent
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A Paradox for the Existence Predicate
Bulletin of the Section of Logic, 2022 In this paper, a paradox is shown to arise in the context of classical logic from prima facie highly plausible assumptions for the existence predicate as applied to definite descriptions.
Uwe Meixner
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Bisimulation in Inquisitive Modal Logic [PDF]
Electronic Proceedings in Theoretical Computer Science, 2017 Inquisitive modal logic, InqML, is a generalisation of standard Kripke-style modal logic. In its epistemic incarnation, it extends standard epistemic logic to capture not just the information that agents have, but also the questions that they are ...
Ivano Ciardelli, Martin Otto
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Systematic Verification of the Modal Logic Cube in Isabelle/HOL [PDF]
Electronic Proceedings in Theoretical Computer Science, 2015 We present an automated verification of the well-known modal logic cube in Isabelle/HOL, in which we prove the inclusion relations between the cube's logics using automated reasoning tools. Prior work addresses this problem but without restriction to the
Christoph Benzmüller +2 more
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Combining First-Order Classical and Intuitionistic Logic
Electronic Proceedings in Theoretical Computer Science, 2022 In Proceedings NCL 2022, arXiv:2204 ...
Toyooka, Masanobu, Sano, Katsuhiko
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Löwenheim-Skolem theorems for non-classical first-order algebraizable logics [PDF]
Logic Journal of IGPL, 2016 This article is a contribution to the model theory of non-classical first-order predicate logics. In a wide framework of firstorder systems based on algebraizable logics, we study several notions of homomorphisms between models and find suitable definitions of elementary homomorphism, elementary substructure and elementary equivalence.
Dellunde P. +2 more
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Satisfiability vs. Finite Satisfiability in Elementary Modal Logics [PDF]
Electronic Proceedings in Theoretical Computer Science, 2012 We study elementary modal logics, i.e. modal logic considered over first-order definable classes of frames. The classical semantics of modal logic allows infinite structures, but often practical applications require to restrict our attention to finite ...
Jakub Michaliszyn +2 more
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, 2022 One is often said to be reasoning well when they are reasoning logically. Many attempts to say what logical reasoning is have been proposed, but one commonly proposed system is first-order classical logic. This Element will examine the basics of first-order classical logic and discuss some surrounding philosophical issues. The first half of the Element
Shapiro, Stewart, Kouri-Kissel, Teresa
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