Domain size asymptotics for Markov logic networks
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Abstract (arXiv)
A Markov logic network (MLN) mathbbM determines a probability distribution mathbbPn^mathbbM on the set Wn of structures, or ``possible worlds'', with domain 1, ldots, n. We study the properties of such distributions as n tends to infinity. We show that with mild assumptions on an MLN mathbbM with one soft constraint with an arbitrary positive weight the distribution mathbbPn^mathbbM will behave quite differently from the uniform distribution mathbbPnuni on Wn for all sufficiently large n. For a language with only one relation symbol R which has arity 1 we give an almost complete characterization of the possible asymptotic behaviours of mathbbPn^mathbbM as n → ∞, where mathbbM may be any MLN for this language. The asymptotic behaviour depends on the soft constraints and weights of the MLN. This characterization is used to show that if the language under consideration contains at least one relation symbol of arity 1 then the following holds: (a) There is an MLN mathbbM such that for every lifted Bayesian network (LBN) mathbbG there are infinitely many n such that mathbbM and mathbbG determine different distributions on Wn. (b) There is an LBN mathbbG such that for every MLN mathbbM there are infinitely many n such that mathbbG and mathbbM determine different distributions on Wn. We also show that, in the limit, the weight dimension and the domain size dimension may behave completely differently.
Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 9 of its 37 references that are in the map. First posted on arXiv 4 Sep 2025.
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9 of 37 references.
References · 9
- 2021An asymptotic analysis of probabilistic logic programming, with implications for expressing projective families of distributionscited by 8
- 2023Zero-One Laws of Graph Neural Networkscited by 7
- 2024Almost Surely Asymptotically Constant Graph Neural Networkscited by 7
- 2021Scaling the weight parameters in Markov logic networks and relational logistic regression modelscited by 3
- 2021Asymptotic elimination of partially continuous aggregation functions in directed graphical modelscited by 3
- 2022Probabilities of the Third Type: Statistical Relational Learning and Reasoning with Relative Frequenciescited by 3
- 2022On the relative asymptotic expressivity of inference frameworkscited by 3
- 2024Random expansions of trees with bounded heightcited by 3
- 2025Convergence Laws for Extensions of First-Order Logic with Averagingcited by 1
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Citing papers per year: 2026: 3.
3 papers.