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.KeywordsModel CheckWord ProblemCommutative SemigroupCongruence ClassGenerator PropositionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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