Identity in Mares-Goldblatt Models for Quantified Relevant Logic

Abstract

Mares and Goldblatt (The Journal of Symbolic Logic, 71(01), 163–187, 2006) provided an alternative frame semantics for two quantified extensions of the relevant logic R. In this paper, I show how to extend the Mares-Goldblatt frames to accommodate identity. Simpler frames are provided for two zero-order logics en route to the full logic in order to clarify what is needed for identity and substitution, as opposed to quantification. I close with a comparison of this work with the Fine-Mares models for relevant logics with identity and a discussion of constant and variable domains.