LIRa session: Wesley Fussner

Speaker: Wesley Fussner  (University of Denver)

Date and Time: Thursday, December 14th 2017, 16:00-17:30

Venue: KdVI Seminar Room F3.20, Science Park 107.


Title: Relational semantics for R-mingle

Abstract: The relevance logic R-mingle extends the prototypical relevance logic R by the mingle axiom, and has been proposed by Dunn as a model for reasoning with inconsistent (but complete) information. In contrast to many other logics in the same family, R-mingle is complete with respect to a simple Kripke-style semantics, introduced by Dunn in 1970, that employs a binary accessibility relation. Owing to the success of the ternary, Routley-Meyer relational semantics for other relevance logics, this unusual situation has remained relatively unexplored. Here we introduce an Esakia-style duality for the algebraic models of R-mingle in order to explain this state of affairs, extending Dunn’s binary relational semantics in much the same way that Esakia duality extends the Kripke semantics for intuitionistic logic. Time permitting, we also discuss how this duality theory reveals the relationship between the Dunn and Routley-Meyer semantics.