Probability Aggregates in Probability Answer Set Programming
  Probability answer set programming is a declarative programming that has been
shown effective for representing and reasoning about a variety of probability
reasoning tasks. However, the lack of probability aggregates, e.g. {\em
expected values}, in the language of disjunctive hybrid probability logic
programs (DHPP) disallows the natural and concise representation of many
interesting problems. In this paper, we extend DHPP to allow arbitrary
probability aggregates. We introduce two types of probability aggregates; a
type that computes the expected value of a classical aggregate, e.g., the
expected value of the minimum, and a type that computes the probability of a
classical aggregate, e.g, the probability of sum of values. In addition, we
define a probability answer set semantics for DHPP with arbitrary probability
aggregates including monotone, antimonotone, and nonmonotone probability
aggregates. We show that the proposed probability answer set semantics of DHPP
subsumes both the original probability answer set semantics of DHPP and the
classical answer set semantics of classical disjunctive logic programs with
classical aggregates, and consequently subsumes the classical answer set
semantics of the original disjunctive logic programs. We show that the proposed
probability answer sets of DHPP with probability aggregates are minimal
probability models and hence incomparable, which is an important property for
nonmonotonic probability reasoning.
