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Preferential description logics: reasoning in the presence of inconsistencies

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Title: Preferential description logics: reasoning in the presence of inconsistencies
Authors: Deane, Graham
Item Type: Thesis or dissertation
Abstract: The Web Ontology Languages define a rich machine readable language for knowledge representation on the world wide web. The current generation are based on Description Logics, a family of decidable logics that offer low complexity of reasoning. Due to the principle of explosion, from a contradiction anything follows, inconsistencies prevent meaningful inference from classical reasoners. However, locating and repairing inconsistencies can be resource intensive.This thesis presents an inconsistency tolerant semantics for the Description Logic ALC called Preferential ALC (p-ALC). A p-ALC knowledge base is comprised of defeasible and non-defeasible axioms. The defeasible ABox and TBox are labelled with weights that reflect a relative measure of confidence in each axiom and provide a mechanism to "arbitrate" between inconsistencies. Entailment is defined through the notion of preferred interpretations which minimise the total weight of the unsatisfied axioms. We introduce a tableau algorithm for p-ALC in which the open branches correspond to preferred interpretations. We prove that the algorithm is sound, complete and terminates for any input knowledge base and show how it can be used to compute p-ALC entailment by refutation. The proposed p-ALC differs from existing semantics that obtain inferences from inconsistent knowledge bases designed for classical reasoners. For instance: the para-consistent and the repair semantics, lack a mechanism for "arbitration" of inconsistency; and the mechanism included in possibilistic logic results in a logic with a weak consequence relation. We present an implementation of the algorithm using answer set programming (ASP) that is solved incrementally and exploits the optimisation of answer sets to identify preferred interpretations of p-ALC. The well defined semantics of ASP enabled us to prove that the implementation is correct. The implementation is also verified empirically and the performance is evaluated against a set of synthetically generated inconsistent knowledge bases in which inconsistency is introduced.
Content Version: Open Access
Issue Date: Jun-2016
Date Awarded: Sep-2016
URI: http://hdl.handle.net/10044/1/40430
DOI: https://doi.org/10.25560/40430
Supervisor: Broda, Krysia
Russo, Alessandra
Sponsor/Funder: Engineering and Physical Sciences Research Council
Department: Computing
Publisher: Imperial College London
Qualification Level: Doctoral
Qualification Name: Doctor of Philosophy (PhD)
Appears in Collections:Computing PhD theses

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