Title: Admissible Semantics for Modal Logics

Speaker: Robert Goldblatt (Victoria University of Wellington)

Time: 2025/09/09 (Tuesday) 15:10-17:10

Location: Room 211, Natural ​Sciences Teaching Building (理教), Peking University

Abstract:

In the possible-worlds semantics for modal logic, a proposition is identified with a set of worlds, and the term "admissible semantics" refers to the use of models in which there is a restriction on which sets of worlds can count as propositions. There are axiomatically defined systems of quantified modal logic that cannot be characterised by the kind of models introduced for them by Kripke, even though the propositional fragments of those logics are characterised by their Kripke frames, which are frames in which every set of worlds is admissible as a proposition. We will explain how that this  failure of  completeness under Kripke semantics to lift from the propositional to the quantificational level can be overcome by developing a suitable notion of admissible model for modal logics with quantification, leading to semantic characterisations of such logics in general. This requires a different interpretation of quantifiers that takes into account the admissibility of propositions.