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FIRST-ORDER RELEVANT REASONERS IN CLASSICAL WORLDS

Part of: General logic

Published online by Cambridge University Press:  21 March 2023

NICHOLAS FERENZ
NICHOLAS FERENZ*
Affiliation:
INSTITUTE OF COMPUTER SCIENCE CZECH ACADEMY OF SCIENCES 182 00 PRAHA 8, CZECH REPUBLIC
*
E-mail: [email protected]
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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.

Keywords

relevant logicepistemic logicnon-Tarskian quantifiersfirst-order epistemic logic

MSC classification

Primary: 03B10: Classical first-order logic 03B42: Logics of knowledge and belief (including belief change) 03B45: Modal logic (including the logic of norms) 03B47: Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics)
Type
Research Article
Information
The Review of Symbolic Logic , Volume 17 , Issue 3 , September 2024 , pp. 793 - 818
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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References

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