An Epistemic Separation Logic with Action Models

Abstract

AbstractIn this paper we present an extension of (bunched) separation logic, Boolean BI, with epistemic and dynamic epistemic modalities. This logic, called action model separation logic ($$\mathrm {AMSL}$$ AMSL ), can be seen as a generalization of public announcement separation logic in which we replace public announcements with action models. Then we not only model public information change (public announcements) but also non-public forms of information change, such as private announcements. In this context the semantics for the connectives $$*$$ ∗ and $$\mathrel {-*}$$ - ∗ from separation logic are epistemic versions of their usual semantics. This is because formulas are interpreted in states, not in resources, and agents may be uncertain between different states representing the same resource. We present the logic $$\mathrm {AMSL}$$ AMSL and its semantics, with a detailed case study that highlights its interest for modeling. We also prove the elimination of the dynamics modalities and discuss some alternative epistemic semantics for the separation connectives.