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URN: urn:nbn:de:0030-drops-13811
URL: http://drops.dagstuhl.de/opus/volltexte/2008/1381/
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Domingos, Pedro ; Singla, Parag

Markov Logic in Infinite Domains

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Abstract

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.

BibTeX - Entry

@InProceedings{domingos_et_al:DSP:2008:1381,
  author =	{Pedro Domingos and Parag Singla},
  title =	{Markov Logic in Infinite Domains},
  booktitle =	{Probabilistic, Logical and Relational Learning - A Further Synthesis},
  year =	{2008},
  editor =	{Luc de Raedt and Thomas Dietterich and Lise Getoor and Kristian Kersting and Stephen H. Muggleton},
  number =	{07161},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2008/1381},
  annote =	{Keywords: Markov logic networks, Gibbs measures, first-order logic, infinite probabilistic models, Markov networks}
}

Keywords: Markov logic networks, Gibbs measures, first-order logic, infinite probabilistic models, Markov networks
Seminar: 07161 - Probabilistic, Logical and Relational Learning - A Further Synthesis
Issue Date: 2008
Date of publication: 06.03.2008

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