Ilya Shapirovsky
"Locally tabular modal logics"
A logic is called locally tabular if it has only finitely many pairwise non-equivalent formulas in each of its finite-variable fragments. Algebraically, modal logics are equational theories of Boolean algebras with operators, thus a modal logic L is locally tabular iff the variety of L-algebras is locally finite, i.e., every finitely generated L-algebra is finite. Recently, it was shown that local tabularity of modal logics can be characterized in terms of partitions of relational structures of finite height. In my talk, I will formulate this semantic criterion and discuss some of its corollaries. Also, I would like to discuss some open problems on local tabularity and the finite model property of modal logics.
This talk is based on joint work with Valentin Shehtman.
MC 5403