An implementation of nonmonotonic reasoning with c-representations using an SMT solver

Abstract

A qualitative conditional “If A then usually B” establishes a plausible connection between the antecedent A and the consequent B. As a semantics for conditional knowledge bases containing such conditionals, ranking functions order possible worlds by mapping them to a degree of plausibility. c-Representations are special ranking functions that are obtained by assigning individual integer impacts to the conditionals in a knowledge base $R$ and by defining the rank of each possible world as the sum of these impacts of falsified conditionals. c-Inference is the nonmonotonic inference relation taking all c-representations of a given knowledge base $R$ into account. In this paper, we show how c-inference can be realized as a satisfiability modulo theories problem (SMT), which allows an implementation by an appropriate SMT solver. Moreover, we show that this leads to the first implementation fully realizing c-inference because it does not require a predefined upper limit for the impacts assigned to the conditionals. We develop a transformation of the constraint satisfaction problem characterizing c-inference into a solvable-equivalent SMT problem, prove its correctness, and illustrate it by a running example. Furthermore, we provide a corresponding implementation using the SMT solver Z3. We develop and implement a randomized generation scheme for knowledge bases and queries, and evaluate our SMT-based implementation of c-inference with respect to such randomly generated knowledge bases. Our evaluation demonstrates the feasibility of our approach as well as the superiority in comparison to former implementations of c-inference.