Speaker: Elaine Pimentel (University College London)
Date and Time: Friday, November 21st 2025, 16:00-17:30 (NOTE the unusual weekday)
Venue: ILLC Seminar Room F1.15, Science Park 107 and online.
Title: The Modal Cube Revisited: Semantics without Worlds
Abstract. We present a non-deterministic semantic framework for all modal logics in the modal cube, extending prior works by Kearns and others. Our approach introduces modular and uniform multi-valued non-deterministic matrices (Nmatrices) for each logic, where necessitation is captured by the systematic use of level valuations. The semantics is grounded in an eight-valued system and provides a sound and complete decision procedure for each modal logic, extending and refining earlier semantics as particular cases. Additionally, we propose a novel model-theoretic perspective that links our framework to relational (Kripke-style) semantics, addressing longstanding conjectures regarding the correspondence between modal axioms and semantic conditions within non-deterministic settings. The result is a philosophically robust and technically modular alternative to standard possible-world semantics.