Automated non-monotonic reasoning in System P

Abstract

This paper presents a novel approach to automated reasoning in System P. System P axiomatizes a set of core properties that describe reasoning with defeasible assertions (defaults) of the form: if α then normally (usually or typically) β. A logic with approximate conditional probabilities is used for modeling default rules. That representation enables reducing the satisfiability problem for default reasoning to the (non)linear programming problem. The complexity of the obtained instances requires the application of optimization approaches. The main heuristic that we use is the Bee Colony Optimization (BCO). As an alternative to BCO, we use Simplex method and Fourier-Motzkin Elimination method to solve linear programming problems. All approaches are tested on a set of default reasoning examples that can be found in literature. The general impression is that Fourier-Motzkin Elimination procedure is not suitable for practical use due to substantially high memory usage and time consuming execution, the Simplex method is able to provide useful results for some of the tested examples, while heuristic approach turns out to be the most appropriate in terms of both success rate and time needed for reaching conclusions. In addition, the BCO method was tested on a set of randomly generated examples of larger dimensions, illustrating its practical usability.