On Minimality and Integrity Constraints in Probabilistic Abduction

Abduction is a type of logical inference that can be successfully combined with probabilistic reasoning. However, the role of integrity constraints has not received much attention when performing logical-probabilistic inference. The contribution of our paper is a probabilistic abductive framework based on the distribution semantics for normal logic programs that handles negation as failure and integrity constraints in the form of denials. Integrity constraints are treated as evidence from the perspective of probabilistic inference. An implementation is provided that computes alternative (non-minimal) abductive solutions, using an appropriately modified abductive system, and generates the probability of a query, for given solutions. An example application of the framework is given, where gene network topologies are abduced according to biological expert knowledge, to probabilistically explain observed gene expressions. The example shows the practical utility of the proposed framework.