Compressed Constraints in Probabilistic Logic and Their Revision
This work tackles computational efficiency issues in probabilistic logic for researchers and practitioners dealing with large-scale inference problems, representing an incremental improvement through compression techniques.
The paper addresses the impracticality of exact methods in probabilistic logic entailments due to large constraint systems by introducing a three-valued logic to create compressed constraint systems with dramatically fewer variables, while maintaining the same solution sets and discussing techniques for calculating posterior probability point estimates.
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.