Lifted Inference with Tree Axioms

Author:

van Bremen Timothy1,Kuželka Ondřej2

Affiliation:

1. KU Leuven

2. Czech Technical University in Prague

Abstract

We consider the problem of weighted first-order model counting (WFOMC): given a first-order sentence ϕ and domain size n ∈ ℕ, determine the weighted sum of models of ϕ over the domain {1, ..., n}. Past work has shown that any sentence using at most two logical variables admits an algorithm for WFOMC that runs in time polynomial in the given domain size (Van den Broeck 2011; Van den Broeck, Meert, and Darwiche 2014). In this paper, we extend this result to any two-variable sentence ϕ with the addition of a tree axiom, stating that some distinguished binary relation in ϕ forms a tree in the graph-theoretic sense.

Publisher

International Joint Conferences on Artificial Intelligence Organization

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. On Exact Sampling in the Two-Variable Fragment of First-Order Logic;2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS);2023-06-26

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