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

Practical reasoning for defeasable description logics.

Doctor of Philosophy in Mathematics, Statistics and Computer Science. University of KwaZulu-Natal, Durban 2016.Description Logics (DLs) are a family of logic-based languages for formalising ontologies. They have useful computational properties allowing the development of automated reasoning engines to infer implicit knowledge from ontologies. However, classical DLs do not tolerate exceptions to speci ed knowledge. This led to the prominent research area of nonmonotonic or defeasible reasoning for DLs, where most techniques were adapted from seminal works for propositional and rst-order logic. Despite the topic's attention in the literature, there remains no consensus on what \sensible" defeasible reasoning means for DLs. Furthermore, there are solid foundations for several approaches and yet no serious implementations and practical tools. In this thesis we address the aforementioned issues in a broad sense. We identify the preferential approach, by Kraus, Lehmann and Magidor (KLM) in propositional logic, as a suitable abstract framework for de ning and studying the precepts of sensible defeasible reasoning. We give a generalisation of KLM's precepts, and their arguments motivating them, to the DL case. We also provide several preferential algorithms for defeasible entailment in DLs; evaluate these algorithms, and the main alternatives in the literature, against the agreed upon precepts; extensively test the performance of these algorithms; and ultimately consolidate our implementation in a software tool called Defeasible-Inference Platform (DIP). We found some useful entailment regimes within the preferential context that satisfy all the KLM properties, and some that have scalable performance in real world ontologies even without extensive optimisation

Quo Vadis KLM-style Defeasible Reasoning?

The field of defeasible reasoning has a variety of frameworks, all of which are constructed with the view of codifying the patterns of common-sense reasoning inherent to human reasoning. One of these frameworks was first described by Kraus, Lehmann and Magidor, and is accordingly referred to as the KLM framework. Initially defined in propo- sitional logic, it has since been imported into description and modal log- ics, and implemented into many defeasible reasoning engines. However, there are many ways in which this framework may be advanced theoreti- cally, and many opportunities for it to be applied. This paper covers some of the most prominent areas of future work and possible applications of this framework, with the intention that anyone who has recently famil- iarized themselves with this approach may then have an understanding of the kind of work in which they could engage

Development of a Logic Layer in the Semantic Web: Research Issues

The ontology layer of the semantic web is now mature enough (i.e. standards like RDF, RDFs, OWL, OWL 2) and the next step is to work on a logic layer for the development of advanced reasoning capabilities for knowledge extraction and efficient decision making. Adding logic to the web means using rules to make inferences. Rules are a means of expressing business processes, policies, contracts etc but most of the studies have focused on the use of monotonic logics in layered development of the semantic web which provides no mechanism for representing or handling incomplete or contradictory information respectively. This paper discusses argumentation, semantic web and defeasible logic programming with their distinct features and identifies the different research issues that need to be addressed in order to realize defeasible argumentative reasoning in the semantic web applications

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

Explanation for defeasible entailment

Explanation facilities are an essential part of tools for knowledge representation and reasoning systems. Knowledge representation and reasoning systems allow users to capture information about the world and reason about it. They are useful in understanding entailments which allow users to derive implicit knowledge that can be made explicit through inferences. Additionally, explanations also assist users in debugging and repairing knowledge bases when conflicts arise. Understanding the conclusions drawn from logic-based systems are complex and requires expert knowledge, especially when defeasible knowledge bases are taken into account for both expert and general users. A defeasible knowledge base represents statements that can be retracted because they refer to information in which there are exceptions to stated rules. That is, any defeasible statement is one that may be withdrawn upon learning of an exception. Explanations for classical logics such as description logics which are well-known formalisms for reasoning about information in a given domain are provided through the notion of justifications. Simply providing or listing the statements that are responsible for an entailment in the classical case is enough to justify an entailment. However, when looking at the defeasible case where entailed statements can be retracted, this is not adequate because the way in which entailment is performed is more complicated than the classical case. In this dissertation, we combine explanations with a particular approach to dealing with defeasible reasoning. We provide an algorithm to compute justification-based explanations for defeasible knowledge bases. It is shown that in order to accurately derive justifications for defeasible knowledge bases, we need to establish the point at which conflicts arise by using an algorithm to come up with a ranking of defeasible statements. This means that only a portion of the knowledge is considered because the statements that cause conflicts are discarded. The final algorithm consists of two parts; the first part establishes the point at which the conflicts occur and the second part uses the information obtained from the first algorithm to compute justifications for defeasible knowledge bases

Compliance checking in reified IO logic via SHACL

Reified Input/Output (I/O) logic[21] has been recently proposed to model real-world norms in terms of the logic in [11]. This is massively grounded on the notion of reification, and it has specifically designed to model meaning of natural language sentences, such as the ones occurring in existing legislation. This paper presents a methodology to carry out compliance checking on reified I/O logic formulae. These are translated in SHACL (Shapes Constraint Language) shapes, a recent W3C recommendation to validate and reason with RDF triplestores. Compliance checking is then enforced by validating RDF graphs describing states of affairs with respect to these SHACL shapes