Modal Logic Without Possible Worlds: A New Semantics for Modal Logic in Simplicial Complexes

Abstract

In this paper, we set out to give a novel semantics for modal logic in simplicial complexes. The motivation for this semantics will be first the replacement of possible worlds with the idea of an ``agent perspective''. After exploring some of the philosophical implications of such a move, we give a semantics based around this idea. Following this, we explore some of the more interesting consequences of such a system, in particular the soundness of an unusual axiom we call NU^*. After giving soundness and completeness, we conclude by exploring ways to weaken this axiom in our semantics.