Bisemilattice Semantics for Intuitionistic and Relevant Modal Logics (Yale Weiss)

The Logic and Metaphysics Workshop will meet on October 4th from 4:15-6:15 (NY time) via Zoom for a talk by Yale Weiss (CUNY GC).

Title: Bisemilattice Semantics for Intuitionistic and Relevant Modal Logics

Abstract: In this talk, I consider modal logics extending J (intuitionistic logic) and RMO (sometimes called ‘constructive mingle’). Adapting previous work of Humberstone, all of these systems are given a purely operational bisemilattice semantics and soundness and completeness results are proved. I consider a way of exactly translating each intuitionistic modal system into a relevant modal companion and discuss what, if any, light this sheds on the interpretation of the relevant companions. Various applications are examined (e.g., to developing constructive theories of entailment) and results germane to those applications are proved. I also discuss connections between the present semantic framework and related frameworks, including Fine’s hybrid operational-partial order semantics, inquisitive semantics, and Urquhart’s semilattice semantics.

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