Abstract. The recent quest for tractable logic-based languages arising from the eld of bio-medical ontologies has raised a lot of attention on lightweight (i.e. less expressive but tractable) description logics, like EL and its family. To this extent, automated reasoning techniques in these logics have been developed for computing not only concept subsumptions, but also to pinpoint the set of axioms causing each subsumption. In this paper we build on previous work from the literature and we propose and investigate a simple and novel approach for axiom pinpointing for the logic EL + . The idea is to encode the classi cation of an ontology into a Horn propositional formula, and to exploit the power of Boolean Constraint Propagation and Con ict Analysis from modern SAT solvers to compute concept subsumptions and to perform axiom pinpointing. A preliminary empirical evaluation com rms the potential of the approach.Note: a short version of this paper is currently under submission at CADE-22. Motivations and goalsIn contrast to the trend of the last two decades [3], in which the research in description logic has focused on investigating increasingly expressive logics, the recent quest for tractable logic-based languages arising from the eld of biomedical ontologies has raised a lot of attention on lightweight (i.e. less expressive but tractable) description logics, like EL and its family [1,4,6,16,20,2]. In particular, the logic EL + [4,6,7] extends EL and is of particular relevance due to its algorithmic properties and due to its capability of expressing several important and widely-used bio-medical ontologies, such as Snomed-CT [31,30,32], NCI [29], GeneOntology [9] and the majority of Galen [21]. In fact in EL + not only standard logic problems such as concept subsumption (e.g., is Amputation-of-Finger a subconcept of Amputation-of-Arm in the ontology Snomed-CT? [7]), but also more sophisticated logic problems such as axiom pinpointing (e.g., which minimal sets of axioms in Snomed-CT of the fact that Amputation-of-Finger is a subconcept of Amputation-of-Arm? [7]) are tractable. Importantly, the problem of axiom pinpointing in EL + is of great interest for debugging complex bio-medical ontologies (see, e.g., [7]). To this extent, the problems of concept subsumption and axiom pinpointing in EL + have been thoroughly investigated, and e cient algorithm for these two functionalities have been implemented and tested with success on large ontologies, including Snomed-CT (see e.g. [4,6,7]).The description logic community have spent a considerable e ort in the attempt of extending EL as much as possible, de ning a maximal subset of logical constructors expressive enough to cover the needs of the practical applications above mentioned, but whose standard and even non-standard inference problems remain tractable. Beside the logic EL + [4], on which we focus in this work, many other extension of EL have been studied [1,2].In this paper we build on previous work from the literature of EL + reasoning [4,6,7] and of SAT/SMT [1...

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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 stateof-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.2. We implicitly make the assumption NP = PSpace.

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