A Semantic Decomposition of Defeasible Logics

AAAI Conferences

We investigate defeasible logics using a technique which decomposes the semantics of such logics into two parts: a specification of the structure of defeasible reasoning and a semantics for the metalanguage in which the specification is written. We show that Nute's Defeasible Logic corresponds to Kunen's semantics, and develop a defeasible logic from the well-founded semantics of Van Gelder, Ross and Schlipf. We also obtain a new defeasible logic which extends an existing language by modifying the specification of Defeasible Logic. Thus our approach is productive in analysing, comparing and designing defeasible logics.

Resource-driven Substructural Defeasible Logic

arXiv.org Artificial Intelligence

Linear Logic and Defeasible Logic have been adopted to formalise different features relevant to agents: consumption of resources, and reasoning with exceptions. We propose a framework to combine sub-structural features, corresponding to the consumption of resources, with defeasibility aspects, and we discuss the design choices for the framework.

Defeasible Inheritance-Based Description Logics

Journal of Artificial Intelligence Research

Defeasible inheritance networks are a non-monotonic framework that deals with hierarchical knowledge. On the other hand, rational closure is acknowledged as a landmark of the preferential approach to non-monotonic reasoning. We will combine these two approaches and define a new non-monotonic closure operation for propositional knowledge bases that combines the advantages of both. Then we redefine such a procedure for Description Logics (DLs), a family of logics well-suited to model structured information. In both cases we will provide a simple reasoning method that is built on top of the classical entailment relation and, thus, is amenable of an implementation based on existing reasoners. Eventually, we evaluate our approach on well-known landmark test examples.

A Redefinition of Arguments in Defeasible Logic Programming

AAAI Conferences

Defeasible Logic Programming (DELP) is a formalism that extends declarative programming to capture defeasible reasoning. Its inference mechanism, upon a query on a literal in a program, answers by indicating whether or not it is warranted in an argumentation process. While the properties of DELP are well known, some of its basic elements can be redefined in order to shed light on some of the subtleties of the warrant process. We will discuss these alternative definitions and the cases in which they provide a better performance.

DR-Prolog: A System for Reasoning with Rules and Ontologies on the Semantic Web

AAAI Conferences

At present, the highest layer that has reached sufficient maturity is the ontology layer in the form of the description logic based languages, DAML OIL and OWL. The next step in the development of the Semantic Web will be the logic and proof layers. Rule systems can play a twofold role in the Semantic Web initiative: (a) they can serve as extensions of, or alternatives to, description logic based ontology languages; and (b) they can be used to develop declarative systems on top (using) ontologies. Defeasible reasoning is a simple rule-based approach to reasoning with incomplete and inconsistent information. It can represent facts, rules, and priorities among rules. Its main advantage is the combination of enhanced representational capabilities allowing one to reason with incomplete and contradictory information, coupled with low computational complexity compared to mainstream nonmonotonic reasoning. In this paper we report on the implementation of a defeasible reasoning system for reasoning on the Web.