2026-07-23T22:19:23Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:1381 2024-03-06T11:07:29Z ddc:004 open_access

Markov Logic in Infinite Domains Domingos, Pedro Singla, Parag Markov logic networks Gibbs measures first-order logic infinite probabilistic models Markov networks Markov logic combines logic and probability by attaching weights to first-order formulas, and viewing them as templates for features of Markov networks. Unfortunately, in its original formulation it does not have the full power of first-order logic, because it applies only to finite domains. Recently, we have extended Markov logic to infinite domains, by casting it in the framework of Gibbs measures. In this talk I will summarize our main results to date, including sufficient conditions for the existence and uniqueness of a Gibbs measure consistent with an infinite MLN, and properties of the set of consistent measures in the non-unique case. (Many important phenomena, like phase transitions, are modeled by non-unique MLNs.) Under the conditions for existence, we have extended to infinite domains the result in Richardson and Domingos (2006) that first-order logic is the limiting case of Markov logic when all weights tend to infinity. I will also discuss some fundamental limitations of Herbrand interpretations (and representations based on them) for probabilistic modeling of infinite domains, and how to get around them. Finally, I will discuss some of the surprising insights for learning and inference in large finite domains that result from considering the infinite limit. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Pedro Domingos and Parag Singla 2008 Is Part Of Dagstuhl Seminar Proceedings, Volume 7161, Probabilistic, Logical and Relational Learning - A Further Synthesis (2008) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/DagSemProc.07161.6 urn:nbn:de:0030-drops-13811 https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07161.6 eng https://creativecommons.org/licenses/by/4.0/legalcode