First-Order Relevant Reasoners in Classical Worlds

0572117 - ÚI 2025 GB eng J - Journal Article
Ferenz, Nicholas
First-Order Relevant Reasoners in Classical Worlds.
Review of Symbolic Logic. Online 21 March 2023 (2024), č. článku PII S1755020323000096. ISSN 1755-0203. E-ISSN 1755-0211
Institutional support: RVO:67985807
Keywords : relevant logic * epistemic logic * non-Tarskian quantifiers * first-order epistemic logic
Impact factor: 0.6, year: 2022
Method of publishing: Limited access

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.
Permanent Link: https://hdl.handle.net/11104/0342944