Abduction Problem in Probabilistic Constraint Logic Programming

Abstract

The paper deals with an abduction problem within the approach for handling probabilistic type of uncertainty in the framework of Constraint Logic Programming. The approach is intended for solving real-life logistic problems such as scheduling, manufacturing, planning, considering uncertainty of input information. The Monte-Carlo method used as background engine allows to combine logical inference with probability and straightforward statistical modeling features. We describe particular cases of abduction problem with different kinds of input and output data (probabilities of clauses and bounds of stochastic variables). We also discuss the problem of determining the dependence between input and output domain variables, and show that this dependence is multilinear in the particular case with independent uncertain clauses. Graph with uncertain edges exemplifies the discussion. At last, we demonstrate the use of some of described methods in the pilot application for solving the network based project planning problem in extended non-deterministic formulation.