Argument-Based Expansion Operators in Possibilistic Defeasible Logic Programming: Characterization and Logical Properties

Abstract

Possibilistic Defeasible Logic Programming (P-DeLP) is a logic programming language which combines features from argumentation theory and logic programming, incorporating as well the treatment of possibilistic uncertainty and fuzzy knowledge at object-language level. Defeasible argumentation in general and P-DeLP in particular provide a way of modelling non-monotonic inference. From a logical viewpoint, capturing defeasible inference relationships for modelling argument and warrant is particularly important, as well as the study of their logical properties. This paper analyzes two non-monotonic operators for P-DeLP which model the expansion of a given program P by adding new weighed facts associated with argument conclusions and warranted literals, resp. Different logical properties for the proposed expansion operators are studied and contrasted with a traditional SLD-based Horn logic. We will show that this analysis provides useful comparison criteria that can be extended and applied to other argumentation frameworks

We want to thank anonymous reviewers for their useful comments. This work was supported by Spanish Projects TIC2003-00950, TIN2004-07933-C03- 01/03, TIN2004-07933-C03-03, by Ram ́ on y Cajal Program (MCyT, Spain) and by CONICET (Argentina).