Simulation of Two Dimensions in Unimodal Logics.
Ilya Borisovich Shapirovsky · Advances in Modal Logic · 2010
In this paper, we prove undecidability and the lack of finite model property for a certain class of unimodal logics. To do this, we adapt the technique from [7], where products of transitive modal logics were investigated, for the unimodal case. As a particular corollary, we present an undecidable unimodal fragment of Halpern and Shoham’s Interval Temporal Logic.