Semantics for possibilistic answer set programs: Uncertain rules versus rules with uncertain conclusions

Abstract

Although Answer Set Programming (ASP) is a powerful framework for declarative problem solving, it cannot in an intuitive way handle situations in which some rules are uncertain, or in which it is more important to satisfy some constraints than others. Possibilistic ASP (PASP) is a natural extension of ASP in which certainty weights are associated with each rule. In this paper we contrast two different views on interpreting the weights attached to rules. Under the first view, weights reflect the certainty with which we can conclude the head of a rule when its body is satisfied. Under the second view, weights reflect the certainty that a given rule restricts the considered epistemic states of an agent in a valid way, i.e. it is the certainty that the rule itself is correct. The first view gives rise to a set of weighted answer sets, whereas the second view gives rise to a weighted set of classical answer sets.

The Possibilistic Horn Non-Clausal Knowledge Bases

“…Recapitulating, Rule (7) indicates that if the Horn-NC Σ has two formulas such that one is a unit clause ℓ : α and the other Π : β has the pattern of the right conjunct in the numerator, then Π can be replaced with the formula in the denominator. In practice, applying (7) amounts to just removing C(¬ℓ) from Π and updating the necessity weight.…”

“…We now denote Π the right conjunct in the numerator of (7) and by Π ≻ (∨ C(¬ℓ) D(¬ℓ) ) denote that (∨ C(¬ℓ) D(¬ℓ) ) is a sub-formula of Π. Rule (7) above can be compacted, giving rise to a more concise formulation of UR Σ :…”

“…After the works in possibilistic logic programming, a succession of works on possibilistic answer set programming has been carried out, started by [48] and continued with e.g. [51,52,18,19,6,7]. Although, like in possibilistic logic programming, they also focus on the clausal form, there exists an exception as indicated in the Introduction.…”

A Unified Framework for Nonmonotonic Reasoning with Vagueness and Uncertainty

“…Thus this type of constraints are added to the program for every atom that does not occur in the head of any rule. 5 Iterative approach to answer sets:…”

“…Hence, possibilistic or probabilistic logic may be used for capturing this uncertainty. In [5] the authors have demonstrated the application of possibilistic answer set programming to design an intelligent triage system for emergency cases at accident sites.…”