ESSLLI 2025 course Semantics for first-order modal logics: a modern introduction
Abstract The course in a technical introduction to semantics of
first-order modal logics aimed at students of philosophy, computer science,
linguistics, and mathematics. We shall aim to present the state of the art in
this area within a comprehensive, unified framework. The main focus will be on
the Kripke semantics for first-modal logics, but other, more general, kinds of
semantics shall be considered as tools for proving incompleteness in the Kripke
semantics. The course assumes a solid background in classical first-order logic
(including the completeness theorem) and propositional monomodal logic
(including completeness through the canonical model construction).