Two Transformations of Clauses into Constraints and Their Properties for Cost-Based Hypothetical Reasoning

This paper describes two ways to transform propositional clauses into mathematical constraints, and gives an overview of mathematical optimization approaches to inference. The first transformation, which translates constraints into linear inequalities, has been applied to cost-based abduction in the past and showed good performance. The second one, which produces nonlinear equalities, is commonly used in other representations, such as SAT. We clarify their differences and advantages, and show the radical performance transition of linear inequalities. We are mainly targeting at cost-based hypothetical reasoning (or abduction), but through preprocessing, the discussion has generality.