Lifted inference with tree axioms

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...

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Bibliographic Details
Published in:	Artificial intelligence Vol. 324; p. 103997
Main Authors:	van Bremen, Timothy, Kuželka, Ondřej
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01.11.2023
Subjects:	Logic Statistical-relational learning Weighted first-order model counting Statistical-relational learning Logic Weighted first-order model counting
ISSN:	0004-3702, 1872-7921
Online Access:	Get full text
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Summary:	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 [1,2]. The same property was later also shown to hold for C2, the two-variable fragment with counting quantifiers [3]. In this paper, we further expand this result to any C2 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.
ISSN:	0004-3702 1872-7921
DOI:	10.1016/j.artint.2023.103997