Axiomatising logics with separating conjunctions and modalities

Stephane Demri (1, 2) , Raul Fervari (3, 4) , Alessio Mansutti (1, 2)

1 LSV - Laboratoire Spécification et Vérification
2 CNRS - Centre National de la Recherche Scientifique
3 FaMAF - Facultad de Matemática, Astronomía y Física [Cordoba]
4 Universidad Nacional de Córdoba [Argentina]

Modal separation logics are formalisms that combine modal operators to reason locally, with separating connectives that allow to perform global updates on the models. In this work, we design Hilbert-style proof systems for the modal separation logics MSL(*, <>) and MSL(*, Diff), where * is the separating conjunction, <> is the standard modal operator and Diff is the difference modality. The calculi only use the logical languages at hand (no external features such as labels) and take advantage of new normal forms and of their axiomatisation.

Mots clés: reduction axiom; core formula; Hilbert-style axiomatisation; modal separation logic; separation logic; modal logic; difference operator; logic of elsewhere; connective elimination

Domaines: Informatique [cs]; Intelligence artificielle [cs.AI]; Logique en informatique [cs.LO]

Stephane Demri, Raul Fervari, Alessio Mansutti. Axiomatising logics with separating conjunctions and modalities. 16th European Conference on Logics in Artificial Intelligence (JELIA'19), May 2019, Rende, Italy. ⟨10.1007/978-3-030-19570-0_45⟩. ⟨hal-02362648⟩