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QUANTIFIED MODAL RELEVANT LOGICS

Part of: General logic

Published online by Cambridge University Press:  23 April 2021

NICHOLAS FERENZ
NICHOLAS FERENZ*
Affiliation:
UNIVERSITY OF ALBERTA EDMONTON, ALBERTA, CANADA
*
E-mail: ferenz@ualberta.ca
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Abstract

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 “sufficiently classical” in its modal fragment, where frame conditions are given that work for positive fragments of logics. The roles of the Barcan formula and its converse are also investigated.

Keywords

relevant logicmodal relevant logicquantified relevant logicquantified modal relevant logicrelational semanticsgeneral frame semantics

MSC classification

Primary: 03B45: Modal logic (including the logic of norms)
Secondary: 03B47: Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics)
Type
Research Article
Information
The Review of Symbolic Logic , Volume 16 , Issue 1 , March 2023 , pp. 210 - 240
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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