Handling exceptions in a knowledge-based system has been considered as an important issue in many domains of applications, such as medical domain. In this paper, we propose several preferential semantics for plausible subsumption to deal with exceptions in description logic-based knowledge bases. Our preferential semantics are defined in the framework of possibility theory, which is an uncertainty theory devoted to the handling of incomplete information. We consider the properties of these semantics and their relationships. Entailment of these plausible subsumption relative to a knowledge base is also considered. We show the close relationship between two of our semantics and the mutually dual preferential semantics given by Britz, Heidema and Meyer. Finally, we show that our semantics for plausible subsumption can be reduced to standard semantics of an expressive description logic. Thus, the problem of plausible subsumption checking under our semantics can be reduced to the problem of subsumption checking under the classical semantics.
We extend description logics (DLs) with non-monotonic reasoning features. 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 investigate KLM-style syntactic properties for both preferential 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 semantics is appropriate, these results pave the way for more effective decision procedures for defeasible reasoning in DLs. Indeed, we also analyse the problem of non-monotonic reasoning in DLs at the level of entailment and present an algorithm for the computation of rational closure of a defeasible ontology. Importantly, our algorithm relies completely on classical entailment and shows that the computational complexity of reasoning over defeasible ontologies is no worse than that of reasoning in the underlying classical DL ALC.
A description classifier organizes concepts and relations into a taxonomy based on the results of subsumption computations applied to pairs of relation definitions. Until now, description classifiers have only been designed to operate over definitions phrased in highly restricted subsets of the predicate calculus. This paper describes a classifier able to reason with definitions phrased in the full first order predicate calculus, extended with sets, cardinality, equality, scalar inequalities, and predicate variables. The performance of the new classifier is comparable to that of existing description classifiers. Our classifier introduces two new techniques, dual representations and auto-Socratic elaboration, that may be expected to improve the performance of existing description classifiers.
Even though specificity has been one of the most useful conflict resolution strategies for selecting productions, most existing rule-based systems use heuristic approximation such as the number of clauses to measure a rule's specificity. This paper describes an approach for computing a principled specificity relation between rules whose conditions are constructed using predicates defined in a terminological knowledge base. Based on a formal definition about pattern subsumption relation, we first show that a subsumption test between two conjunctive patterns can be viewed as a search problem. Then we describe an implemented pattern classification algorithm that improves the efficiency of the search process by deducing implicit conditions logically implied by a pattern and by reducing the search space using subsumption relationships between predicates. Our approach enhances the maintainability of rule-based systems and the reusability of definitional knowledge.