22 February 2022, The Utrecht Logic in Progress Series (TULIPS), Igor Sedlár

Abstract: In Montague–Scott semantics, the modal box operator represents a property of sentential intensions, that is, propositions or sets of possible worlds. It follows that all logics modelled by this kind of semantics are intensional: if A and B necessarily express the same proposition, then so do Box A and Box B. This is obejctionable on many readings of Box, notorious examples being propositional attitudes. A more realistic formalization of such examples, it is argued, calls for hyperintensional modal logics, where Box A and Box are are not necessarily equivalent even for necessarily equivalent A and B.

Different semantic frameworks for hyperintensional modal logics have been formulated. In a recent paper (Hyperintensional logics for everyone. Synthese 198, 933-956, 2021), I have introduced a generalization of Montague–Scott semantics in which the Box operator expresses properties of “semantic contents” which in turn determine propositions in the standard sense. The nature of these contents is left undetermined, which renders the semantic framework rather general.

In the first part of the talk, I will outline the generalized Scott–Montague semantic framework and I will show that many well-known semantics for hyperintensional modalities are special cases. In the second part of the talk, I outline recent joint work with M. Pascucci in which we use the framework to give a semantics for some weak modal logics.