Formalizing Argumentative Reasoning in a Possibilistic Logic Programming Setting with Fuzzy Unification

TERESA ALSINET,; CARLOS IVÁN CHESÑEVAR; LLUÍS GODO,; GUILLERMO SIMARI,

INTERNATIONAL JOURNAL OF APPROXIMATE REASONING

Elsevier

Lugar: Amsterdam; Año: 2008 vol. 48 p. 711 - 729

0888-613X

Possibilistic Defeasible Logic Programming (Pdelp) is a logic programming language which combines features from argumentation theory and logic programming, incorporating the treatment of possibilistic uncertainty at the object-language level. In spite of its expressive power, an important limitation in Pdelp is that imprecise, fuzzy information cannot be expressed in the object language. One interesting alternative for solving this limitation is the use of PGLmes, a Possibilistic logic over G"odel logic extended with fuzzy constants. Fuzzy constants in PGL$^+$ allow expressing disjunctive information about the unknown value of a variable, in the sense of a magnitude,  modeled as a (unary) predicate. The aim of this article is twofold: firstly, we formalize DEPGLmes, a possibilistic defeasible logic programming language that extends Pdelp through the use of PGLmes in order to incorporate fuzzy constants and a fuzzy unification mechanism for them. Secondly, we propose a way to handle conflicting arguments in the context of the extended framework.