A Semantics for Probabilistic Answer Set Programs with Incomplete Stochastic Knowledge.

Some probabilistic answer set programs (PASP) semantics assign probabilities to sets of answer sets and implicitly assume these answer sets to be equiprobable. While this is a common choice in probability theory, it leads to unnatural behaviours with PASPs. We argue that the user should have a level of control over what assumption is used to obtain a probability distribution when the stochastic knowledge is incomplete. To this end, we introduce the Incomplete Knowledge Semantics (IKS) for probabilistic answer set programs. We take inspiration from the field of decision making under ignorance. Given a cost function, represented by a user-defined ordering over answer sets through weak constraints, we use the notion of Ordered Weighted Averaging (OWA) operator to distribute the probability over a set of answer sets accordingly to the user’s level of optimism. The more optimistic (or pessimistic) a user is, the more (or less) probability is assigned to the more optimal answer sets. We present an implementation and showcase the behaviour of this semantics on simple examples. We also highlight the impact that different OWA operators have on weight learning, showing that the equiprobability assumption is not always the best option.