A Connection Calculus for the Description Logic $$ {\mathcal{ALC}} $$ [chapter]

Fred Freitas, Jens Otten
2016 Lecture Notes in Computer Science  
The problem of reasoning over ontologies written in Description Logic (DL) [1] has received strong interest, particularly after the Semantic Web inception. The necessity of creating reasoners to deal with OWL (Ontology Web Language) [2], in its various versions, posed interesting research questions for inference systems, making the problem earn the reputation of being complex, whose users see solutions as black boxes. Consequently, not many inference systems became well known to the public;
more » ... ed, tableaux methods [1] took over the field. Apart from the reasoning algorithms, many other practical issues have been brought about, stemming from the natural features of the Web, that ask for certain requirements for inferencing. Among them, the use of memory is certainly an important asset for a good reasoning performance. Therefore, methods that do not require a huge amount of memory may be promising. This paper tries to tackle this issue by adapting a reasoning method that makes a parsimonious usage of memory. The inference system proposed here is based on the connection calculus [3], which is a clear and effective inference method applied successfully over first order logic (FOL). Its main features meet with the demands: it keeps only one copy of each logical sentence in memory and it does not derive new sentences from the stored ones. The formal system, the ALC Connection Method (ALC CM), displays some desirable features for a DL reasoner,: it is able to perform all DL inference services, namely, subsumption, unsatisfiability (or inconsistency), equivalence and disjointness. As the most widespread DL tableaux systems, ALC CM reduces them to subsumption or validity -the dual of unsatisfiability, used in most DL systems (interested readers should check that information at [7]). The rest of the article is organized as follows. Section 2 defines one of the most basic description logic languages, ALC (Attributive Concept Language with Complements) [1], together with the disjunctive normal formal used by the method. ALC was chosen as the starting of the work, because it constitutes the foundation of many other Description Logics. Section 3 brings a proposed ALC ontologies' matrix normal form that fits to the connection method. Section 4 describes the ALC adapted connection method and states the key logical properties for inference systems (soundness, completeness and termination). Section 5 brings discussion in the light of representation and reasoning, and section 6 presents future work and conclusions.
doi:10.1007/978-3-319-34111-8_30 fatcat:4wwdnwqx6naafewbj5wfu265hy