A guide to completeness and complexity for modal logics of knowledge and belief
Artificial Intelligence
Single Step Tableaux for Modal Logics
Journal of Automated Reasoning
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
BDD-Based Decision Procedures for K
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
Journal of Artificial Intelligence Research
Expressive description logics via SAT: the story so far
Proceedings of the 7th International Workshop on Satisfiability Modulo Theories
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In the last two decades, modal and description logics have been applied to numerous areas of computer science, including artificial intelligence, formal verification, database theory, and distributed computing. For this reason, the problem of automated reasoning in modal and description logics has been throughly investigated. In particular, many approaches have been proposed for efficiently handling the satisfiability of the core normal modal logic Km, and of its notational variant, the description logic $\ensuremath{\mathcal{ALC}}$. Although simple in structure, Km/$\ensuremath{\mathcal{ALC}}$ is computationally very hard to reason on, its satisfiability being PSPACE-complete. In this paper we explore the idea of encoding Km/$\ensuremath{\mathcal{ALC}}$-satisfiability into SAT, so that to be handled by state-of-the-art SAT tools. We propose an efficient encoding, and we test it on an extensive set of benchmarks, comparing the approach with the main state-of-the-art tools available. Although the encoding is necessarily worst-case exponential, from our experiments we notice that, in practice, this approach can handle most or all the problems which are at the reach of the other approaches, with performances which are comparable with, or even better than, those of the current state-of-the-art tools.