A Framework for Combining Defeasible Argumentation with Labeled Deduction

In the last years, there has been an increasing demand of a variety of logical systems, prompted mostly by applications of logic in AI and other related areas. Labeled Deductive Systems (LDS) were developed as a flexible methodology to formalize such a kind of complex logical systems. Defeasible argumentation has proven to be a successful approach to formalizing commonsense reasoning, encompassing many other alternative formalisms for defeasible reasoning. Argument-based frameworks share some common notions (such as the concept of argument, defeater, etc.) along with a number of particular features which make it difficult to compare them with each other from a logical viewpoint. This paper introduces LDSar, a LDS for defeasible argumentation in which many important issues concerning defeasible argumentation are captured within a unified logical framework. We also discuss some logical properties and extensions that emerge from the proposed framework.Comment: 15 pages, presented at CMSRA Workshop 2003. Buenos Aires, Argentin

Reasoning about exceptions in ontologies: from the lexicographic closure to the skeptical closure

Reasoning about exceptions in ontologies is nowadays one of the challenges the description logics community is facing. The paper describes a preferential approach for dealing with exceptions in Description Logics, based on the rational closure. The rational closure has the merit of providing a simple and efficient approach for reasoning with exceptions, but it does not allow independent handling of the inheritance of different defeasible properties of concepts. In this work we outline a possible solution to this problem by introducing a variant of the lexicographical closure, that we call skeptical closure, which requires to construct a single base. We develop a bi-preference semantics semantics for defining a characterization of the skeptical closure

Defeasible Logic Programming: An Argumentative Approach

The work reported here introduces Defeasible Logic Programming (DeLP), a formalism that combines results of Logic Programming and Defeasible Argumentation. DeLP provides the possibility of representing information in the form of weak rules in a declarative manner, and a defeasible argumentation inference mechanism for warranting the entailed conclusions. In DeLP an argumentation formalism will be used for deciding between contradictory goals. Queries will be supported by arguments that could be defeated by other arguments. A query q will succeed when there is an argument A for q that is warranted, ie, the argument A that supports q is found undefeated by a warrant procedure that implements a dialectical analysis. The defeasible argumentation basis of DeLP allows to build applications that deal with incomplete and contradictory information in dynamic domains. Thus, the resulting approach is suitable for representing agent's knowledge and for providing an argumentation based reasoning mechanism to agents.Comment: 43 pages, to appear in the journal "Theory and Practice of Logic Programming

A reconstruction of the multipreference closure

The paper describes a preferential approach for dealing with exceptions in KLM preferential logics, based on the rational closure. It is well known that the rational closure does not allow an independent handling of the inheritance of different defeasible properties of concepts. Several solutions have been proposed to face this problem and the lexicographic closure is the most notable one. In this work, we consider an alternative closure construction, called the Multi Preference closure (MP-closure), that has been first considered for reasoning with exceptions in DLs. Here, we reconstruct the notion of MP-closure in the propositional case and we show that it is a natural variant of Lehmann's lexicographic closure. Abandoning Maximal Entropy (an alternative route already considered but not explored by Lehmann) leads to a construction which exploits a different lexicographic ordering w.r.t. the lexicographic closure, and determines a preferential consequence relation rather than a rational consequence relation. We show that, building on the MP-closure semantics, rationality can be recovered, at least from the semantic point of view, resulting in a rational consequence relation which is stronger than the rational closure, but incomparable with the lexicographic closure. We also show that the MP-closure is stronger than the Relevant Closure.Comment: 57 page