Probabilistic Termination of CHRiSM Programs

Termination analysis has received considerable attention in Logic Programming for several decades. In recent years, probabilistic extensions of Logic Programming languages have become increasingly important. Languages like PRISM, CP-Logic, ProbLog, and

CHRiSM

have been introduced and proved very useful for addressing problems in which a combination of logical and probabilistic reasoning is required. As far as we know, the termination of probabilistic logical programs has not received any attention in the community so far.

Termination of a probabilistic program is not a crisp notion. Given a query, such a program does not simply either terminate or not terminate, but it terminates with a certain probability.

In this paper, we explore this problem in the context of

CHRiSM

, a probabilistic extension of CHR. We formally introduce the notion of probabilistic termination. We study this concept on the basis of a number of case studies. We provide some initial sufficient conditions to characterize probabilistically terminating programs and queries. We also discuss some challenging examples that reveal the complexity and interest of more general settings. The paper is intended as a first step in a challenging and important new area in the analysis of Logic Programs.