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A General Semantics for Quantified Modal Logic

Robert Goldblatt & Edwin D. Mares

In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 227-246 (1998)

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First-Order Relevant Reasoners in Classical Worlds.Nicholas Ferenz - forthcoming - Review of Symbolic Logic:1-26.details Sedlár and Vigiani [18] have developed an approach to propositional epistemic logics wherein (i) an agent’s beliefs are closed under relevant implication and (ii) the agent is located in a classical possible world (i.e., the non-modal fragment is classical). Here I construct first-order extensions of these logics using the non-Tarskian interpretation of the quantifiers introduced by Mares and Goldblatt [12], and later extended to quantified modal relevant logics by Ferenz [6]. Modular soundness and completeness are proved for constant domain semantics, (...) Download Export citation Bookmark 2 citations
Quantified Modal Relevant Logics.Nicholas Ferenz - 2023 - Review of Symbolic Logic 16 (1):210-240.details Here, I combine the semantics of Mares and Goldblatt [20] and Seki [29, 30] to develop a semantics for quantified modal relevant logics extending ${\bf B}$. The combination requires demonstrating that the Mares–Goldblatt approach is apt for quantified extensions of ${\bf B}$ and other relevant logics, but no significant bridging principles are needed. The result is a single semantic approach for quantified modal relevant logics. Within this framework, I discuss the requirements a quantified modal relevant logic must satisfy to be (...) Download Export citation Bookmark 7 citations
Completeness results for some two-dimensional logics of actuality.David R. Gilbert & Edwin D. Mares - 2012 - Review of Symbolic Logic 5 (2):239-258.details We provide a Hilbert-style axiomatization of the logic of , as well as a two-dimensional semantics with respect to which our logics are sound and complete. Our completeness results are quite general, pertaining to all such actuality logics that extend a normal and canonical modal basis. We also show that our logics have the strong finite model property and permit straightforward first-order extensions. Download Export citation Bookmark 2 citations
Robert Goldblatt. Quantifiers, propositions and identity: Admissible semantics for quantified modal and substructural logics. Lecture notes in logic; 38. cambridge: Cambridge university press, 2011. Isbn 978-1-107-01052-9. Pp. XIII + 282. [REVIEW]R. Jones - 2013 - Philosophia Mathematica 21 (1):123-127.details Download Export citation Bookmark
First-order possibility models and finitary completeness proofs.Matthew Harrison-Trainor - 2019 - Review of Symbolic Logic 12 (4):637-662.details This article builds on Humberstone’s idea of defining models of propositional modal logic where total possible worlds are replaced by partial possibilities. We follow a suggestion of Humberstone by introducing possibility models for quantified modal logic. We show that a simple quantified modal logic is sound and complete for our semantics. Although Holliday showed that for many propositional modal logics, it is possible to give a completeness proof using a canonical model construction where every possibility consists of finitely many formulas, (...) Download Export citation Bookmark 1 citation
Reflexive-insensitive modal logics.David R. Gilbert & Giorgio Venturi - 2016 - Review of Symbolic Logic 9 (1):167-180.details Download Export citation Bookmark 13 citations

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