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.


Interdefinability of defeasible logic and logic programming under the well-founded semantics

arXiv.org Artificial Intelligence

We provide a method of translating theories of Nute's defeasible logic into logic programs, and a corresponding translation in the opposite direction. Under certain natural restrictions, the conclusions of defeasible theories under the ambiguity propagating defeasible logic ADL correspond to those of the well-founded semantics for normal logic programs, and so it turns out that the two formalisms are closely related. Using the same translation of logic programs into defeasible theories, the semantics for the ambiguity blocking defeasible logic NDL can be seen as indirectly providing an ambiguity blocking semantics for logic programs. We also provide antimonotone operators for both ADL and NDL, each based on the Gelfond-Lifschitz (GL) operator for logic programs. For defeasible theories without defeaters or priorities on rules, the operator for ADL corresponds to the GL operator and so can be seen as partially capturing the consequences according to ADL. Similarly, the operator for NDL captures the consequences according to NDL, though in this case no restrictions on theories apply. Both operators can be used to define stable model semantics for defeasible theories.


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.


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.