Title: Tense logics over lattices
Speaker: Xiaoyang Wang (PKU)
Time: 15:10 ~ 18:00 (May 17)
Abstract: Lattice theory has intimate connections with modal logic via algebraic semantics and lattices of modal logics. However, one less explored direction is to view lattices as relational structures extending partial orders, and study the modal logic over them. In this paper, following the earlier steps of Burgess and van Benthem in the 1980s, we use the basic tense logic and its extensions with infimum and supremum binary modalities to talk about lattices via standard Kripke semantics. As the main results, we obtain a series of complete finite axiomatizations of lattices, (un)bounded lattices over partial orders or strict preorders.