Towards Practical First-Order Model Counting

TL;DR

This paper introduces Crane2, an automated first-order model counting method that compiles function definitions into C++ code, enabling scalable counting for very large domains, significantly surpassing previous methods.

Contribution

Crane2 automates the knowledge compilation process for first-order model counting, allowing scalable and efficient counting for large domains without manual intervention.

Findings

Crane2 scales to domain sizes over 500,000 times larger than previous methods.

Automated compilation into C++ enables practical application of first-order model counting.

Experimental results demonstrate significant performance improvements.

Abstract

First-order model counting (FOMC) is the problem of counting the number of models of a sentence in first-order logic. Since lifted inference techniques rely on reductions to variants of FOMC, the design of scalable methods for FOMC has attracted attention from both theoreticians and practitioners over the past decade. Recently, a new approach based on first-order knowledge compilation was proposed. This approach, called Crane, instead of simply providing the final count, generates definitions of (possibly recursive) functions that can be evaluated with different arguments to compute the model count for any domain size. However, this approach is not fully automated, as it requires manual evaluation of the constructed functions. The primary contribution of this work is a fully automated compilation algorithm, called Crane2, which transforms the function definitions into C++ code equipped with arbitrary-precision arithmetic. These additions allow the new FOMC algorithm to scale to domain sizes over 500,000 times larger than the current state of the art, as demonstrated through experimental results.