Model Checking with Probabilistic Tabled Logic Programming

TL;DR

This paper introduces a novel probabilistic model checking approach using probabilistic logic programming, enabling analysis of complex systems with a new inference algorithm that handles infinite explanations efficiently.

Contribution

It presents the first formulation of probabilistic model checking as query evaluation over probabilistic logic programs, with a new inference algorithm for infinite explanation sets.

Findings

Implemented in XSB Prolog, the approach encodes probabilistic model checkers for various temporal logics.

The method produces competitive results compared to native model checkers.

Handles a broad class of probabilistic models and temporal logics.

Abstract

We present a formulation of the problem of probabilistic model checking as one of query evaluation over probabilistic logic programs. To the best of our knowledge, our formulation is the first of its kind, and it covers a rich class of probabilistic models and probabilistic temporal logics. The inference algorithms of existing probabilistic logic-programming systems are well defined only for queries with a finite number of explanations. This restriction prohibits the encoding of probabilistic model checkers, where explanations correspond to executions of the system being model checked. To overcome this restriction, we propose a more general inference algorithm that uses finite generative structures (similar to automata) to represent families of explanations. The inference algorithm computes the probability of a possibly infinite set of explanations directly from the finite generative structure. We have implemented our inference algorithm in XSB Prolog, and use this implementation to encode probabilistic model checkers for a variety of temporal logics, including PCTL and GPL (which subsumes PCTL*). Our experiment results show that, despite the highly declarative nature of their encodings, the model checkers constructed in this manner are competitive with their native implementations.