# Is Kripke semantics somewhat canonical?

## Ivan Di Liberti, FLoV

The talk reports on an ongoing conversation with Graham Leigh on the topic of completeness theorem for modal logics, and more generally on the exploration of their semantics. The usual completeness theorem for modal logic is given over Kripke-style semantics. How necessary is this choice? In this talk we will see how such choice seems almost unavoidable. I will discuss how to tune this technology to handle more complex modal logics, and provide modular completeness theorems for them.