We present a general approach to axiomatise separation logics with heaplet semantics with no external features such as nominals/labels. To start with, we design the first (internal) Hilbert-style axiomatisation for the quantifier-free separation logic SL(∗, -*). We instantiate the method by introducing a new separation logic with essential features: it is equipped with the separating conjunction, the predicate ls, and a natural guarded form of first-order quantification. We apply our approach for its axiomatisation. As a by-product of our method, we also establish the exact expressive power of this new logic and we show PSpace-completeness of its satisfiability problem.
@InProceedings{demri_et_al:LIPIcs.CSL.2020.19, author = {Demri, St\'{e}phane and Lozes, Etienne and Mansutti, Alessio}, title = {{Internal Calculi for Separation Logics}}, booktitle = {28th EACSL Annual Conference on Computer Science Logic (CSL 2020)}, pages = {19:1--19:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-132-0}, ISSN = {1868-8969}, year = {2020}, volume = {152}, editor = {Fern\'{a}ndez, Maribel and Muscholl, Anca}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2020.19}, URN = {urn:nbn:de:0030-drops-116625}, doi = {10.4230/LIPIcs.CSL.2020.19}, annote = {Keywords: Separation logic, internal calculus, adjunct/quantifier elimination} }
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