On model checking boolean BI

Authors:
Heng Guo;Hanpin Wang;Zhongyuan Xu;Yongzhi Cao
Affiliations:
Key Laboratory of High Confidence Software Technologies, Ministry of Education, Institute of Software, School of Electronics Engineering and Computer Science, Peking University, Beijing, China;Key Laboratory of High Confidence Software Technologies, Ministry of Education, Institute of Software, School of Electronics Engineering and Computer Science, Peking University, Beijing, China;Key Laboratory of High Confidence Software Technologies, Ministry of Education, Institute of Software, School of Electronics Engineering and Computer Science, Peking University, Beijing, China;Key Laboratory of High Confidence Software Technologies, Ministry of Education, Institute of Software, School of Electronics Engineering and Computer Science, Peking University, Beijing, China
Venue:
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
Year:
2009

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Abstract

The logic of bunched implications (BI), introduced by O'Hearn and Pym, is a substructural logic which freely combines additive and multiplicative implications. Boolean BI (BBI) denotes BI with classical interpretation of additives and its model is the commutative monoid. We show that when the monoid is finitely generated and propositions are recursively defined, or the monoid is infinitely generated and propositions are restricted to generator propositions, the model checking problem is undecidable. In the case of finitely related monoid and generator propositions, the model checking problem is EXPSPACE-complete.