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  • FIRST-ORDER RELEVANT REASONERS IN CLASSICAL WORLDS

  • Part of
  • NICHOLAS FERENZ
  • Journal:
    The Review of Symbolic Logic / Volume 17 / Issue 3 / September 2024
    Published online by Cambridge University Press:
    21 March 2023, pp. 793-818
    Print publication:
    September 2024
    • Article
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  • 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.