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

• Alternative semantics for possibilistic answer set programming are introduced.
• The weight associated with each rule can be treated in two dual ways.
• Existing semantics consider weighted epistemic states.
• The new semantics consider Boolean epistemic states with varying compatibility.
• We contrast both views and find the new approach to be computationally more complex.

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.