Tense Logics over Lattices

Proceeding PaperWoLLIC
Xiaoyang Wang, Yanjing Wang
Proceedings of WoLLIC 2022
Publication year: 2022

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 extension with infimum and supremum binary modalities and nominals to talk about lattices based on Kripke semantics. As the main results and also the first steps of a general research program, we obtain a series of complete finite axiomatizations of lattices and (un)bounded lattices.

Propositional dynamic logic as a logic of belief revision

Proceeding PaperWoLLIC
Van Eijck, Jan and Wang, Yanjing
In Proceedings of WOLLIC 2008, 2008
Publication year: 2008