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Open AccessArticle

On the Coherence of Probabilistic Relational Formalisms

Escola Politécnica, Universidade de São Paulo, São Paulo 05508-010, Brazil
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Entropy 2018, 20(4), 229; https://doi.org/10.3390/e20040229
Received: 22 February 2018 / Revised: 23 March 2018 / Accepted: 24 March 2018 / Published: 27 March 2018
(This article belongs to the Special Issue Foundations of Statistics)
There are several formalisms that enhance Bayesian networks by including relations amongst individuals as modeling primitives. For instance, Probabilistic Relational Models (PRMs) use diagrams and relational databases to represent repetitive Bayesian networks, while Relational Bayesian Networks (RBNs) employ first-order probability formulas with the same purpose. We examine the coherence checking problem for those formalisms; that is, the problem of guaranteeing that any grounding of a well-formed set of sentences does produce a valid Bayesian network. This is a novel version of de Finetti’s problem of coherence checking for probabilistic assessments. We show how to reduce the coherence checking problem in relational Bayesian networks to a validity problem in first-order logic augmented with a transitive closure operator and how to combine this logic-based approach with faster, but incomplete algorithms. View Full-Text
Keywords: relational Bayesian networks; probabilistic relational models; coherence checking relational Bayesian networks; probabilistic relational models; coherence checking
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De Bona, G.; Cozman, F.G. On the Coherence of Probabilistic Relational Formalisms. Entropy 2018, 20, 229.

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