Minimal Model Counting via Knowledge Compilation

TL;DR

This paper introduces a new knowledge compilation method that efficiently counts minimal models of Boolean formulas, advancing reasoning capabilities in AI by extending beyond decision problems to model counting.

Contribution

It presents a novel knowledge compilation form specifically designed for counting minimal models, integrating justification and answer set counting theories.

Findings

The proposed method enables efficient counting of minimal models.

It extends existing decision-focused approaches to model counting.

Experimental results demonstrate improved performance over previous techniques.

Abstract

Counting the number of models of a Boolean formula is a fundamental problem in artificial intelligence and reasoning. Minimal models of a Boolean formula are critical in various reasoning systems, making the counting of minimal models essential for detailed inference tasks. Existing research primarily focused on decision problems related to minimal models. In this work, we extend beyond decision problems to address the challenge of counting minimal models. Specifically, we propose a novel knowledge compilation form that facilitates the efficient counting of minimal models. Our approach leverages the idea of justification and incorporates theories from answer set counting.