A Complete Axiomatisation for Quantifier-Free Separation Logic
Abstract
We present the first complete axiomatisation for quantifier-free separation logic. The logic is equipped with the standard concrete heaplet semantics and the proof system has no external feature such as nominals/labels. It is not possible to rely completely on proof systems for Boolean BI as the concrete semantics needs to be taken into account. Therefore, we present the first internal Hilbert-style axiomatisation for quantifier-free separation logic. The calculus is divided in three parts: the axiomatisation of core formulae where Boolean combinations of core formulae capture the expressivity of the whole logic, axioms and inference rules to simulate a bottom-up elimination of separating connectives, and finally structural axioms and inference rules from propositional calculus and Boolean BI with the magic wand.
Keywords
Cite
@article{arxiv.2006.05156,
title = {A Complete Axiomatisation for Quantifier-Free Separation Logic},
author = {Stéphane Demri and Étienne Lozes and Alessio Mansutti},
journal= {arXiv preprint arXiv:2006.05156},
year = {2023}
}