A Presheaf Semantics for Quantified Temporal Logics

Temporal logics encompass a family of formalisms for the verification of computational devices, and its quantified extensions allow to reason about the properties of individual components of a system. The expressiveness of these logics poses problems in identifying a semantics that exploits its features without imposing restrictions on the acceptable behaviours. We address this issue by introducing a counterpart-based semantics and we provide a categorical presentation of such semantics in terms of relational presheaves.