Compilation of Propositional Weighted Bases

TL;DR

This paper explores how knowledge compilation techniques can improve inference from propositional weighted bases, identifying both complexity limitations and tractable cases, with applications to model-based diagnosis.

Contribution

It introduces a general compilation framework for propositional weighted bases and analyzes the complexity and tractability of inference within this framework.

Findings

Inference remains complex for prime implicates, Horn, and renamable Horn classes.

DNNF compilation enables tractable inference and model computation.

Polynomial-time computation of preferred models from DNNF compilations.

Abstract

In this paper, we investigate the extent to which knowledge compilation can be used to improve inference from propositional weighted bases. We present a general notion of compilation of a weighted base that is parametrized by any equivalence--preserving compilation function. Both negative and positive results are presented. On the one hand, complexity results are identified, showing that the inference problem from a compiled weighted base is as difficult as in the general case, when the prime implicates, Horn cover or renamable Horn cover classes are targeted. On the other hand, we show that the inference problem becomes tractable whenever DNNF-compilations are used and clausal queries are considered. Moreover, we show that the set of all preferred models of a DNNF-compilation of a weighted base can be computed in time polynomial in the output size. Finally, we sketch how our results can be used in model-based diagnosis in order to compute the most probable diagnoses of a system.