Compressed Constraints in Probabilistic Logic and Their Revision

TL;DR

This paper introduces a three-valued logic approach to simplify probabilistic logic entailment problems by creating compressed constraint systems, making exact solutions more feasible for larger problems.

Contribution

It proposes a novel three-valued logic method that reduces the complexity of probabilistic constraint systems while preserving their solution sets.

Findings

Compressed constraint systems have fewer variables than traditional systems.

The approach maintains the same solution sets as two-valued systems.

Techniques for calculating posterior probabilities are discussed.

Abstract

In probabilistic logic entailments, even moderate size problems can yield linear constraint systems with so many variables that exact methods are impractical. This difficulty can be remedied in many cases of interest by introducing a three valued logic (true, false, and "don't care"). The three-valued approach allows the construction of "compressed" constraint systems which have the same solution sets as their two-valued counterparts, but which may involve dramatically fewer variables. Techniques to calculate point estimates for the posterior probabilities of entailed sentences are discussed.