On the Characterization of the Maximal Ideal Recursive Semantics of RP-DeLP

Possibilistic Defeasible Logic Programming (P-DeLP) is a logic programming framework which combines features from argumentation theory and logic programming, in which defeasible rules are attached with weights expressing their relative belief or preference strength. In P-DeLP a conclusion succeeds if there exists an argument that entails the conclusion and this argument is found to be undefeated by a warrant procedure that systematically explores the universe of arguments in order to present an exhaustive synthesis of the relevant chains of pros and cons for the given conclusion. Recently, we have proposed a new warrant recursive semantics for P-DeLP, called Recursive P-DeLP (RP-DeLP for short), based on the claim that the acceptance of an argument should imply also the acceptance of all its subarguments which reflect the different premises on which the argument is based. In RP-DeLP, an output of a program is a pair of sets, a set of warranted and a set of blocked conclusions.Arguments for both warranted and blocked conclusions are recursively based on warranted conclusions but, while warranted conclusions do not generate any conflict with the set of already warranted conclusions and the strict part of program (information we take for granted they hold true), blocked conclusions do. Conclusions that are neither warranted nor blocked correspond to rejected conclusions. This paper explores the relationship between the exhaustive dialectical analysis based semantics of P-DeLP and the recursive based semantics of RP-DeLP, and analyzes a non-monotonic inference operator for RP-DeLP which models the expansion of a given program by adding new weighed facts associated with warranted conclusions.