Formalizing argumentative reasoning in a possibilistic 3 logic programming setting with fuzzy unification q

12 Possibilistic Defeasible Logic Programming (P-DeLP) is a logic programming language which combines features from 13 argumentation theory and logic programming, incorporating the treatment of possibilistic uncertainty at the object-lan14 guage level. In spite of its expressive power, an important limitation in P-DeLP is that imprecise, fuzzy information cannot 15 be expressed in the object language. One interesting alternative for solving this limitation is the use of PGL, a possibilistic 16 logic over Gödel logic extended with fuzzy constants. Fuzzy constants in PGL allow expressing disjunctive information 17 about the unknown value of a variable, in the sense of a magnitude, modelled as a (unary) predicate. The aim of this article 18 is twofold: firstly, we formalize DePGL, a possibilistic defeasible logic programming language that extends P-DeLP 19 through the use of PGL in order to incorporate fuzzy constants and a fuzzy unification mechanism for them. Secondly, 20 we propose a way to handle conflicting arguments in the context of the extended framework. 21 2007 Elsevier Inc. All rights reserved.