Complexity of Contextual Reasoning

Floris Roelofsen and Luciano Serafini

This paper delineates the computational complexity of propositional multi-context systems. We establish NP-membership by translating multi-context systems into bounded modal Kn, and obtain more refined complexity results by achieving the so-called bounded model property: the number of local models needed to satisfy a set of formulas φ in a multi-context system MS is bounded by the number of contexts addressed by φ plus the number of bridge rules in MS. Exploiting this property of multi-context systems, we are able to encode contextual satisfiability into purely propositional satisfiability, providing for the implementation of contextual reasoners based on already existing specialized SAT solvers. Finally, we apply our results to improve complexity bounds for McCarthy’s propositional logic of context — we show that satisfiability in this framework can be settled in nondeterministic polynomial time O(|ψ|2).

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