Possibilistic Answer Set Programming Revisited

Possibilistic answer set programming (PASP) extends answer set programming (ASP) by attaching to each rule a degree of certainty. While such an extension is important from an application point of view, existing semantics are not well-motivated, and do not always yield intuitive results. To develop a more suitable semantics, we first introduce a characterization of answer sets of classical ASP programs in terms of possibilistic logic where an ASP program specifies a set of constraints on possibility distributions. This characterization is then naturally generalized to define answer sets of PASP programs. We furthermore provide a syntactic counterpart, leading to a possibilistic generalization of the well-known Gelfond-Lifschitz reduct, and we show how our framework can readily be implemented using standard ASP solvers.

💡 Research Summary

The paper addresses a fundamental shortcoming of existing possibilistic answer set programming (PASP) semantics, namely that they can produce unintuitive results when rules are annotated with certainty degrees, especially in the presence of negation‑as‑failure (NAF). The authors propose a new, principled semantics built on a tight connection between classical answer set programming (ASP) and possibilistic logic.

First, they reinterpret a classical ASP program as a set of constraints on a possibility distribution over interpretations. A fact imposes N(a) ≥ 1, a rule a ← b₁,…,bₘ imposes N(a) ≥ min(N(b₁),…,N(bₘ)), where N is the necessity measure (N(p)=1−Π(¬p)). The set of all such constraints Cₚ defines a family of admissible possibility distributions. Among them, the least specific (i.e., least informative) distributions constitute Sₚ. They prove that for any π∈Sₚ, the atoms with necessity 1 form exactly an answer set of the original program, and conversely each answer set yields a unique least‑specific distribution. This provides a semantic characterization of answer sets that is equivalent to the traditional Gelfond‑Lifschitz reduct but expressed entirely in possibilistic terms.

Next, the authors extend this framework to PASP. Each rule r receives a certainty weight n(r)∈