Simplified Semantics for Further Relevant Logics II: Propositional Constants

Tore Fjetland Øgaard

doi:10.12775/LLP.2024.022

Authors

Tore Fjetland Øgaard Department of Philosophy, University of Bergen https://orcid.org/0000-0002-7082-991X

DOI:

https://doi.org/10.12775/LLP.2024.022

Keywords

relevant logics, simplified Routley-Meyer semantics, propositional constants

Abstract

It is shown how to model propositional constants within the simplified Routley-Meyer semantics. Various axioms and rules allowing the definition of modal operators, implicative negations, enthymematical conditionals, and propositions expressing various infinite conjunctions and disjunctions are set forth and shown to correspond to specific frame conditions. Two propositional constants which are both often designated as “the Ackermann constant” are shown to capture two such “infinite” propositions: The conjunction of every logical law and the conjunction of every truth –what Anderson and Belnap called the “world” constant.

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