A KLM Perspective on Defeasible Reasoning for Description Logics

In this paper we present an approach to defeasible reasoning for the description logic ALC. The results discussed here are based on work done by Kraus, Lehmann and Magidor (KLM) on defeasible conditionals in the propositional case. We consider versions of a preferential semantics for two forms of defeasible subsumption, and link these semantic constructions formally to KLM-style syntactic properties via representation results. In addition to showing that the semantics is appropriate, these results pave the way for more effective decision procedures for defeasible reasoning in description logics. With the semantics of the defeasible version of ALC in place, we turn to the investigation of an appropriate form of defeasible entailment for this enriched version of ALC. This investigation includes an algorithm for the computation of a form of defeasible entailment known as rational closure in the propositional case. Importantly, the algorithm relies completely on classical entailment checks and shows that the computational complexity of reasoning over defeasible ontologies is no worse than that of the underlying classical ALC. Before concluding, we take a brief tour of some existing work on defeasible extensions of ALC that go beyond defeasible subsumption

Optimizing the computation of overriding

We introduce optimization techniques for reasoning in DLN---a recently introduced family of nonmonotonic description logics whose characterizing features appear well-suited to model the applicative examples naturally arising in biomedical domains and semantic web access control policies. Such optimizations are validated experimentally on large KBs with more than 30K axioms. Speedups exceed 1 order of magnitude. For the first time, response times compatible with real-time reasoning are obtained with nonmonotonic KBs of this size

A polynomial Time Subsumption Algorithm for Nominal Safe ELO under Rational Closure

Description Logics (DLs) under Rational Closure (RC) is a well-known framework for non-monotonic reasoning in DLs. In this paper, we address the concept subsumption decision problem under RC for nominal safe ELO⊥, a notable and practically important DL representative of the OWL 2 profile OWL 2 EL. Our contribution here is to define a polynomial time subsumption procedure for nominal safe ELO⊥ under RC that relies entirely on a series of classical, monotonic EL⊥ subsumption tests. Therefore, any existing classical monotonic EL⊥ reasoner can be used as a black box to implement our method. We then also adapt the method to one of the known extensions of RC for DLs, namely Defeasible Inheritance-based DLs without losing the computational tractability

Defeasible Reasoning in SROEL: from Rational Entailment to Rational Closure

In this work we study a rational extension $SROEL^R T$ of the low complexity description logic SROEL, which underlies the OWL EL ontology language. The extension involves a typicality operator T, whose semantics is based on Lehmann and Magidor's ranked models and allows for the definition of defeasible inclusions. We consider both rational entailment and minimal entailment. We show that deciding instance checking under minimal entailment is in general $\Pi^P_2$-hard, while, under rational entailment, instance checking can be computed in polynomial time. We develop a Datalog calculus for instance checking under rational entailment and exploit it, with stratified negation, for computing the rational closure of simple KBs in polynomial time.Comment: Accepted for publication on Fundamenta Informatica

A connection method for a defeasible extension of ALCH\mathcal{ALCH}

This paper proposes a connection method \`a la Bibel for an exception-tolerant family of description logics (DLs). As for the language, we assume the DL $\mathcal{ALCH}$ extended with two typicality operators: one on (complex) concepts and one on role names. The language is a variant of defeasible DLs, as broadly studied in the literature over the past decade, in which most of these can be embedded. We revisit the definition of the matrix representation of a knowledge base and establish the conditions for a given axiom to be provable. We show that the calculus terminates and is sound and complete w.r.t. a DL version of the preferential semantics widely adopted in non-monotonic reasoning

Revising Description Logic Terminologies to Handle Exceptions: a First Step

Abstract. We propose a methodology to revise a Description Logic knowledge base when detecting exceptions. Our approach relies on the methodology for debugging a Description Logic terminology, addressing the problem of diagnosing incoherent ontologies by identifying a mini-mal subset of axioms responsible for an inconsistency. In the approach we propose, once the source of the inconsistency has been localized, the identified axioms are revised in order to obtain a consistent knowledge base including the detected exception. To this aim, we make use of a non-monotonic extension of the Description Logic ALC based on the com-bination of a typicality operator and the well established nonmonotonic mechanism of rational closure, which allows to deal with prototypical properties and defeasible inheritance.

Arbitrary Ranking of Defeasible Subsumption

In this paper we propose an algorithm that generalises existing procedures for the implementation of defeasible reasoning in the framework of Description Logics (DLs). One of the well-known approaches to defeasible reasoning, the so-called KLM approach, is based on constructing specific rankings of defeasible information, and using these rankings to determine priorities in case of conflicting information. Here we propose a procedure that allows us to input any possible ranking of the defeasible concept inclusions contained in the knowledge base. We analyse and investigate the forms of defeasible reasoning obtained when conclusions drawn are obtained using these rankings