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Languages for Probabilistic Modeling Over Structured and Relational Domains

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Abstract

In this chapter we survey languages that specify probability distributions using graphs, predicates, quantifiers, fixed-point operators, recursion, and other logical and programming constructs. Many of these languages have roots both in probabilistic logic and in the desire to enhance Bayesian networks and Markov random fields. We examine their origins and comment on various proposals up to recent developments in probabilistic programming.

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Notes

  1. 1.

    We might be more even general by introducing “probabilistic quantifiers”, say by writing to mean \(\mathbb {P}\left( \phi \right) \ge \alpha \). We could then nest within other formulas (Halpern 2003). We avoid this generality here.

  2. 2.

    This example is due to my colleague Marcelo Finger (personal communication).

  3. 3.

    Lists of languages can be found at http://probabilistic-programming.org/wiki/Home and https://en.wikipedia.org/wiki/Probabilistic_programming_language.

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Acknowledgements

The author was partially supported by CNPq (grant 308433/2014-9). This work was partially supported by FAPESP (grant 2016/18841-0).

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  1. University of São Paulo, São Paulo, Brazil

    Fabio Gagliardi Cozman

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  1. Fabio Gagliardi Cozman
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Correspondence to Fabio Gagliardi Cozman .

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  1. CRIL-CNRS, Université d’Artois and Institut Universitaire de France, Lens, France

    Pierre Marquis

  2. Aix Marseille Université, Université de Toulon, CNRS, LIS, Marseille, France

    Odile Papini

  3. IRIT, CNRS and Université Paul Sabatier, Toulouse, France

    Henri Prade

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Cozman, F.G. (2020). Languages for Probabilistic Modeling Over Structured and Relational Domains. In: Marquis, P., Papini, O., Prade, H. (eds) A Guided Tour of Artificial Intelligence Research. Springer, Cham. https://doi.org/10.1007/978-3-030-06167-8_9

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