Probability Aggregates in Probability Answer Set Programming

TL;DR

This paper extends probability answer set programming to include probability aggregates, enabling more natural representation of complex probabilistic reasoning tasks with a formal semantics that subsumes previous approaches.

Contribution

It introduces arbitrary probability aggregates into DHPP and defines a comprehensive semantics that generalizes existing probability and classical answer set semantics.

Findings

The new semantics subsumes previous probability answer set semantics.

Probability answer sets are minimal probability models.

The approach handles monotone, antimonotone, and nonmonotone aggregates.

Abstract

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.