Towards a New Semantics for Possibilistic Answer Sets

Abstract

Possibilistic Answer Set Programming is an extension of the standard ASP framework that allows for attaching degrees of certainty to the rules in ASP programs. In the literature, several semantics for such PASP-programs have been presented, each of them having particular strengths and weaknesses. In this work we present a new semantics that employs so-called iota-answer sets, a solution concept introduced by Gebser et al. (2009), in order to find solutions for standard ASP programs with odd cycles or auto-blocking rules. This is achieved by considering maximal subsets of a given ASP program for which answer sets exist. The main idea of our work is to integrate iota-semantics into the possibilistic framework in such a way that degrees of certainty are not only assigned to atoms mentioned in the answer sets, but also to the answer sets themselves. Our approach gives more satisfactory solutions and avoids counter-intuitive examples arising in the other approaches. We compare our approach to existing ones and present a translation into the standard ASP framework allowing the computation of solutions by existing tools.