First-Order Relevant Reasoners in Classical Worlds

Review of Symbolic Logic:1-26 (forthcoming)
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Abstract

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, using non-general frames with Mares–Goldblatt truth conditions. I further detail the relation between the demand that classical possible worlds have Tarskian truth conditions and incompleteness results in quantified relevant logics.

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Nicholas Ferenz
University of Alberta

Citations of this work

One Variable Relevant Logics are S5ish.Nicholas Ferenz - forthcoming - Journal of Philosophical Logic:1-23.

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References found in this work

Quantified Modal Relevant Logics.Nicholas Ferenz - 2023 - Review of Symbolic Logic 16 (1):210-240.
Neighbourhood Semantics for Quantified Relevant Logics.Andrew Tedder & Nicholas Ferenz - 2022 - Journal of Philosophical Logic 51 (3):457-484.
Identity in Mares-Goldblatt Models for Quantified Relevant Logic.Shawn Standefer - 2021 - Journal of Philosophical Logic 50 (6):1389-1415.
General information in relevant logic.Edwin D. Mares - 2009 - Synthese 167 (2):343-362.

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