Efficient Knowledge Compilation Beyond Weighted Model Counting

TL;DR

This paper introduces Second Level Algebraic Model Counting (2AMC), a framework for complex inference tasks in probabilistic logic programming, and proposes methods to improve knowledge compilation efficiency by exploiting problem structure.

Contribution

The paper develops a generic 2AMC framework, proposes a novel approach to omit unnecessary constraints, and introduces a static constraint generation strategy to enhance knowledge compilation efficiency.

Findings

The proposed methods improve the efficiency of solving 2AMC problems.

Exploiting logical structure reduces circuit size and complexity.

Empirical results show practical benefits on benchmark tasks.

Abstract

Quantitative extensions of logic programming often require the solution of so called second level inference tasks, i.e., problems that involve a third operation, such as maximization or normalization, on top of addition and multiplication, and thus go beyond the well-known weighted or algebraic model counting setting of probabilistic logic programming under the distribution semantics. We introduce Second Level Algebraic Model Counting (2AMC) as a generic framework for these kinds of problems. As 2AMC is to (algebraic) model counting what forall-exists-SAT is to propositional satisfiability, it is notoriously hard to solve. First level techniques based on Knowledge Compilation (KC) have been adapted for specific 2AMC instances by imposing variable order constraints on the resulting circuit. However, those constraints can severely increase the circuit size and thus decrease the efficiency of such approaches. We show that we can exploit the logical structure of a 2AMC problem to omit parts of these constraints, thus limiting the negative effect. Furthermore, we introduce and implement a strategy to generate a sufficient set of constraints statically, with a priori guarantees for the performance of KC. Our empirical evaluation on several benchmarks and tasks confirms that our theoretical results can translate into more efficient solving in practice. Under consideration for acceptance in TPLP.