Decidable Reasoning in Terminological Knowledge Representation Systems

Terminological knowledge representation systems (TKRSs) are tools for designing and using knowledge bases that make use of terminological languages (or concept languages). We analyze from a theoretical point of view a TKRS whose capabilities go beyond the ones of presently available TKRSs. The new features studied, often required in practical applications, can be summarized in three main points. First, we consider a highly expressive terminological language, called ALCNR, including general complements of concepts, number restrictions and role conjunction. Second, we allow to express inclusion statements between general concepts, and terminological cycles as a particular case. Third, we prove the decidability of a number of desirable TKRS-deduction services (like satisfiability, subsumption and instance checking) through a sound, complete and terminating calculus for reasoning in ALCNR-knowledge bases. Our calculus extends the general technique of constraint systems. As a byproduct of the proof, we get also the result that inclusion statements in ALCNR can be simulated by terminological cycles, if descriptive semantics is adopted.Comment: See http://www.jair.org/ for any accompanying file

A set-based reasoner for the description logic \shdlssx (Extended Version)

We present a \ke-based implementation of a reasoner for a decidable fragment of (stratified) set theory expressing the description logic \dlssx (\shdlssx, for short). Our application solves the main TBox and ABox reasoning problems for \shdlssx. In particular, it solves the consistency problem for \shdlssx-knowledge bases represented in set-theoretic terms, and a generalization of the \emph{Conjunctive Query Answering} problem in which conjunctive queries with variables of three sorts are admitted. The reasoner, which extends and optimizes a previous prototype for the consistency checking of \shdlssx-knowledge bases (see \cite{cilc17}), is implemented in \textsf{C++}. It supports \shdlssx-knowledge bases serialized in the OWL/XML format, and it admits also rules expressed in SWRL (Semantic Web Rule Language).Comment: arXiv admin note: text overlap with arXiv:1804.11222, arXiv:1707.07545, arXiv:1702.0309

Reasoning about Explanations for Negative Query Answers in DL-Lite

In order to meet usability requirements, most logic-based applications provide explanation facilities for reasoning services. This holds also for Description Logics, where research has focused on the explanation of both TBox reasoning and, more recently, query answering. Besides explaining the presence of a tuple in a query answer, it is important to explain also why a given tuple is missing. We address the latter problem for instance and conjunctive query answering over DL-Lite ontologies by adopting abductive reasoning; that is, we look for additions to the ABox that force a given tuple to be in the result. As reasoning tasks we consider existence and recognition of an explanation, and relevance and necessity of a given assertion for an explanation. We characterize the computational complexity of these problems for arbitrary, subset minimal, and cardinality minimal explanations

A \textsf{C++} reasoner for the description logic \shdlssx (Extended Version)

We present an ongoing implementation of a \ke\space based reasoner for a decidable fragment of stratified elementary set theory expressing the description logic \dlssx (shortly \shdlssx). The reasoner checks the consistency of \shdlssx-knowledge bases (KBs) represented in set-theoretic terms. It is implemented in \textsf{C++} and supports \shdlssx-KBs serialized in the OWL/XML format. To the best of our knowledge, this is the first attempt to implement a reasoner for the consistency checking of a description logic represented via a fragment of set theory that can also classify standard OWL ontologies.Comment: 15 pages. arXiv admin note: text overlap with arXiv:1702.03096, arXiv:1804.1122

Tractable approximate deduction for OWL

Acknowledgements This work has been partially supported by the European project Marrying Ontologies and Software Technologies (EU ICT2008-216691), the European project Knowledge Driven Data Exploitation (EU FP7/IAPP2011-286348), the UK EPSRC project WhatIf (EP/J014354/1). The authors thank Prof. Ian Horrocks and Dr. Giorgos Stoilos for their helpful discussion on role subsumptions. The authors thank Rafael S. Gonçalves et al. for providing their hotspots ontologies. The authors also thank BoC-group for providing their ADOxx Metamodelling ontologies.Peer reviewedPostprin

A Description Logic Framework for Commonsense Conceptual Combination Integrating Typicality, Probabilities and Cognitive Heuristics

We propose a nonmonotonic Description Logic of typicality able to account for the phenomenon of concept combination of prototypical concepts. The proposed logic relies on the logic of typicality ALC TR, whose semantics is based on the notion of rational closure, as well as on the distributed semantics of probabilistic Description Logics, and is equipped with a cognitive heuristic used by humans for concept composition. We first extend the logic of typicality ALC TR by typicality inclusions whose intuitive meaning is that "there is probability p about the fact that typical Cs are Ds". As in the distributed semantics, we define different scenarios containing only some typicality inclusions, each one having a suitable probability. We then focus on those scenarios whose probabilities belong to a given and fixed range, and we exploit such scenarios in order to ascribe typical properties to a concept C obtained as the combination of two prototypical concepts. We also show that reasoning in the proposed Description Logic is EXPTIME-complete as for the underlying ALC.Comment: 39 pages, 3 figure