Simplified Semantics for Further Relevant Logics I: Unreduced Semantics for E and Π′

Tore Fjetland Øgaard

doi:10.12775/LLP.2024.021

Authors

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

DOI:

https://doi.org/10.12775/LLP.2024.021

Keywords

converse conditional, E, fusion, γ, relevant logics, simplified Routley-Meyer semantics, unreduced frames

Abstract

This paper shows that the relevant logics E and Π′ are strongly sound and complete with regards to a version of the “simplified” Routley-Meyer semantics. Such a semantics for E has been thought impossible. Although it is impossible if an admissible rule of E  the rule of restricted assertion or equivalently Ackermann’s δ-rule  is solely added as a primitive rule, it is very much possible when E is axiomatized in the way Anderson and Belnap did.

The simplified semantics for E and Π′ requires unreduced frames. Contra what has been claimed, however, no additional frame component is required over and above what’s required to model other relevant logics such as T and R. It is also shown how to modify the tonicity requirements of the ternary relation so as to allow for the standard truth condition for both fusion – the intensional conjunction ◦ – as well as the converse conditional ←.

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