Tableau reasoning for description logics and its extension to probabilities

• Published in: Annals of mathematics and artificial intelligence Vol. 82; no. 1-3; pp. 101 - 130
• Main Authors: Zese, Riccardo, Bellodi, Elena, Riguzzi, Fabrizio, Cota, Giuseppe, Lamma, Evelina
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.03.2018; Springer; Springer Nature B.V
• Subjects: Algorithms; Analysis; Artificial Intelligence; Complex Systems; Computer Science; Determinism; Knowledge bases (artificial intelligence); Languages; Mathematics; Queries; Reasoning; Semantic web; Semantics; Statistical analysis; Semantic web; 68N17; 68T27; Description logics; 68T37; Prolog; Tableau; 68T30
• ISSN: 1012-2443; 1573-7470
• DOI: 10.1007/s10472-016-9529-3

The increasing popularity of the Semantic Web drove to a widespread adoption of Description Logics (DLs) for modeling real world domains. To help the diffusion of DLs, a large number of reasoning algorithms have been developed. Usually these algorithms are implemented in procedural languages such as Java or C++. Most of the reasoners exploit the tableau algorithm which features non-determinism, that is not easily handled by those languages. Prolog directly manages non-determinism, thus is a good candidate for dealing with the tableau’s non-deterministic expansion rules. We present TRILL, for “Tableau Reasoner for descrIption Logics in proLog”, that implements a tableau algorithm and is able to return explanations for queries and their corresponding probability, and TRILL P , for “TRILL powered by Pinpointing formulas”, which is able to compute a Boolean formula representing the set of explanations for a query. Reasoning on real world domains also requires the capability of managing probabilistic and uncertain information. We show how TRILL and TRILL P can be used to compute the probability of queries to knowledge bases following DISPONTE semantics. Experiments comparing these with other systems show the feasibility of the approach.