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Weighted Model Counting in FO2 with Cardinality Constraints and Counting Quantifiers: A Closed Form Formula

2021-10-12 13:28:50
Sagar Malhotra, Luciano Serafini
arXiv_AI
   
Abstract

Weighted First-Order Model Counting (WFOMC) computes the weighted sum of the models of a first-order logic theory on a given finite domain. First-Order Logic theories that admit polynomial-time WFOMC w.r.t domain cardinality are called domain liftable. We introduce the concept of lifted interpretations as a tool for formulating closed-forms for WFOMC. Using lifted interpretations, we reconstruct the closed-form formula for polynomial-time FOMC in the universally quantified fragment of FO2, earlier proposed by Beame et al. We then expand this closed-form to incorporate cardinality constraints, existential quantifiers, and counting quantifiers (a.k.a C2) without losing domain-liftability. Finally, we show that the obtained closed-form motivates a natural definition of a family of weight functions strictly larger than symmetric weight functions.

Abstract (translated)

URL

https://arxiv.org/abs/2110.05992

PDF

https://arxiv.org/pdf/2110.05992.pdf

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