Automated Reasoning in Modal and Description Logics via SAT Encoding: the Case Study of K(m)/ALC-Satisfiability
This work addresses efficient reasoning for logics used in knowledge representation and semantic web, but it is incremental as it builds on existing encoding ideas.
The paper tackles the problem of automated reasoning for modal and description logics K(m)/ALC, which is PSPACE-complete, by encoding satisfiability into SAT and testing it with state-of-the-art SAT tools. The results show that this approach handles most problems comparable to or better than existing tools in practice.
In the last two decades, modal and description logics have been applied to numerous areas of computer science, including knowledge representation, formal verification, database theory, distributed computing and, more recently, semantic web and ontologies. For this reason, the problem of automated reasoning in modal and description logics has been thoroughly investigated. In particular, many approaches have been proposed for efficiently handling the satisfiability of the core normal modal logic K(m), and of its notational variant, the description logic ALC. Although simple in structure, K(m)/ALC is computationally very hard to reason on, its satisfiability being PSPACE-complete. In this paper we start exploring the idea of performing automated reasoning tasks in modal and description logics by encoding them into SAT, so that to be handled by state-of-the-art SAT tools; as with most previous approaches, we begin our investigation from the satisfiability in K(m). 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.