Algebraic Model Counting

TL;DR

This paper introduces algebraic model counting (AMC), a generalization of weighted model counting (WMC), enabling a unified approach to various inference tasks across multiple domains using semiring structures.

Contribution

It generalizes WMC to a semiring framework, connects AMC to knowledge compilation, and identifies conditions for more efficient circuit representations.

Findings

AMC encompasses probabilistic inference, soft constraints, and database analysis.

All AMC tasks can be evaluated with sd-DNNF circuits.

Certain AMC instances allow for more succinct circuit representations.

Abstract

Weighted model counting (WMC) is a well-known inference task on knowledge bases, used for probabilistic inference in graphical models. We introduce algebraic model counting (AMC), a generalization of WMC to a semiring structure. We show that AMC generalizes many well-known tasks in a variety of domains such as probabilistic inference, soft constraints and network and database analysis. Furthermore, we investigate AMC from a knowledge compilation perspective and show that all AMC tasks can be evaluated using sd-DNNF circuits. We identify further characteristics of AMC instances that allow for the use of even more succinct circuits.