Principles of KLM-style Defeasible Description Logics

The past 25 years have seen many attempts to introduce defeasible-reasoning capabilities into a description logic setting. Many, if not most, of these attempts are based on preferential extensions of description logics, with a significant number of these, in turn, following the so-called KLM approach to defeasible reasoning initially advocated for propositional logic by Kraus, Lehmann, and Magidor. Each of these attempts has its own aim of investigating particular constructions and variants of the (KLM-style) preferential approach. Here our aim is to provide a comprehensive study of the formal foundations of preferential defeasible reasoning for description logics in the KLM tradition. We start by investigating a notion of defeasible subsumption in the spirit of defeasible conditionals as studied by Kraus, Lehmann, and Magidor in the propositional case. In particular, we consider a natural and intuitive semantics for defeasible subsumption, and we investigate KLM-style syntactic properties for both preferen- tial and rational subsumption. Our contribution includes two representation results linking our semantic constructions to the set of preferential and rational properties considered. Besides showing that our seman- tics is appropriate, these results pave the way for more effective decision procedures for defeasible reasoning in description logics. Indeed, we also analyse the problem of non-monotonic reasoning in description logics at the level of entailment and present an algorithm for the computation of rational closure of a defeasible knowledge base. Importantly, our algorithm relies completely on classical entailment and shows that the computational complexity of reasoning over defeasible knowledge bases is no worse than that of reasoning in the underlying classical DL ALC

Introducing Defeasibility into OWL Ontologies

In recent years, various approaches have been developed for repre- senting and reasoning with exceptions in OWL. The price one pays for such ca- pabilities, in terms of practical performance, is an important factor that is yet to be quantified comprehensively. A major barrier is the lack of naturally oc- curring ontologies with defeasible features - the ideal candidates for evaluation. Such data is unavailable due to absence of tool support for representing defea- sible features. In the past, defeasible reasoning implementations have favoured automated generation of defeasible ontologies. While this suffices as a prelimi- nary approach, we posit that a method somewhere in between these two would yield more meaningful results. In this work, we describe a systematic approach to modify real-world OWL ontologies to include defeasible features, and we ap- ply this to the Manchester OWL Repository to generate defeasible ontologies for evaluating our reasoner DIP (Defeasible-Inference Platform). The results of this evaluation are provided together with some insights into where the performance bottle-necks lie for this kind of reasoning. We found that reasoning was feasible on the whole, with surprisingly few bottle-necks in our evaluation

Rational Defeasible Reasoning for Description Logics

In this paper, we extend description logics (DLs) with non-monotonic reasoning fea- tures. We start by investigating a notion of defeasible subsumption in the spirit of defeasible conditionals as studied by Kraus and colleagues in the propositional case. In particular, we consider a natural and intuitive semantics for defeasible subsumption, and we investi- gate syntactic properties (à la Gentzen) for both preferential and rational subsumptions and prove representation results for the description logic ALC. Such representation results pave the way for more effective decision procedures for defeasible reasoning in DLs. We analyse the problem of non-monotonic reasoning in DL at the level of entailment for both TBox and ABox reasoning, and present an adaptation of rational closure for the DL en- vironment. Importantly, we also show that computing it can be reduced to classical ALC entailment. One of the stumbling blocks to evaluating performance scalability of rational closure is the absence of naturally occurring DL-based ontologies with defeasible features. We overcome this barrier by devising an approach to introduce defeasible subsumption into classical real-world ontologies. Such semi-natural defeasible ontologies, together with a purely artificial set, are used to test our rational closure algorithms. We found that performance is scalable on the whole with no major bottlenecks

CJEU case text similarity

Identification of relevant or similar court decisions is a core activity in legal decision making for case law researchers and practitioners. With an ever increasing body of case law, a manual analysis of court decisions can become practically impossible. As a result, some decisions are inevitably overlooked. Alternatively, network analysis may be applied to detect relevant precedents and landmark cases. Previous research suggests that citation networks of court decisions frequently provide relevant precedents and landmark cases. The advent of text similarity measures (both syntactic and semantic) has meant that potentially relevant cases can be identified without the need to manually read them. However, how close do these measures come to approximating the notion of relevance captured in the citation network? In this contribution, we explore this question by measuring the level of agreement of state-of-the-art text similarity algorithms with the citation behavior in the case citation network. For this work, we focus on judgements by the Court of Justice of the European Union (CJEU) as published in the EUR-Lex database. Our results show that while similarity of the full texts of CJEU court decisions does not closely mirror citation behaviour, there is a substantial overlap. In particular, we found that syntactic measures surprisingly outperform semantic measures in approximating the citation network

A Protégé Plug-in for Defeasible Reasoning

Abstract. We discuss two approaches for defeasible reasoning in Description Logics that allow for the statement of defeasible subsumptions of the form “α subsumed by β usually holds”. These approaches are known as prototypical reasoning and presumptive reasoning and are both rooted in the notion of Rational Closure developed by Lehmann and Magidor for the propositional case. Here we recast their definitions in a defeasible DL context and define algorithms for prototypical and presumptive reasoning in defeasible DL knowledge bases. In particular, we present a plug-in for the Protégé ontology editor which implements these algorithms for OWL ontologies. The plug-in is called RaMP and allows the modeller to indicate defeasible information in OWL ontologies and check entailment of defeasible subsumptions from defeasible knowledge bases.

A defeasible reasoning approach for description logic ontologies

National audienceClassical reasoning for logic-based KR (Knowledge Representation) systems is in general, monotonic. That is, there is an assumption in these systems that there is complete information about a domain. This means that they generally cannot deal with any new information arising which contradicts with the current information. This is not an appropriate model for reasoning in many applications. Therefore, alternative non-monotonic systems have been investigated which can reason under uncertainty or with incomplete information. Defeasible reasoning is one particular model for implementing non-monotonic reasoning. It is concerned with representing and reasoning with defeasible (non-strict) facts about a domain. The defeasible counterpart of the strict fact: "All birds fly" is the defeasible fact: "Most birds fly" (or the alternative phrasing "Birds usually fly"). We discuss two approaches for defeasible reasoning in the family of logic-based KR languages known as Description Logics (DLs). They are applicable to particular extensions of DLs that allow for the statement of defeasible sentences similar to the aforementioned examples. The approaches are known as prototypical reasoning and presumptive reasoning and are both rooted in the notion of Rational Closure developed by Lehmann and Magidor for an extension of propositional logic. Here we recast their definitions in a DL context and define algorithms for prototypical and presumptive reasoning for DL knowledge bases (also called DL ontologies) that may contain defeasible sentences. In particular, we present a plug-in for the Protégé ontology editor which implements these algorithms for OWL ontologies - the Web Ontology Language (OWL) is a formal standard of languages whose semantic basis is identical to that of DLs. Our plug-in, RaMP, allows the modeller to indicate defeasible information in OWL ontologies and perform logical inferencing to determine what defeasible conclusions one can draw from these ontologies

Towards Practical Defeasible Reasoning for Description Logics

Abstract. The formalisation of defeasible reasoning in automated systems is becoming increasingly important. Description Logics (DLs) are nowadays the main logical formalism in the field of formal ontologies. Our focus in this paper is to devise a practical implementation for prior work that formalises a version of Rational Closure (an important type of defeasible reasoning) for DLs. We show that the conclusions drawn from it are generally intuitive and desirable. Moreover, we present experimental results showing that using Rational Closure for ontologies of reasonable size is practical.