Probabilistic Satisfiability

Hansen, Pierre; Jaumard, Brigitte

doi:10.1007/978-94-017-1737-3_8

Cited by 42 publications

(53 citation statements)

References 105 publications

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“…Alternatively, we might define the coherence of an RBN as the existence of at least one input structure, out of a given class, resulting in an acyclic ground Bayesian network. This is closer to the satisfiability-like notion of coherence discussed by de Finetti and closer to work on probabilistic logic [27,28].…”

Section: A Weaker Form Of Coherencesupporting

confidence: 69%

“…The simplest formulation of coherence checking takes a set of events and their probabilities and asks whether there can be a probability measure over an appropriate sample space [1]. This sort of problem is akin to inference in propositional probabilistic logic [28]. Unsurprisingly, similar inference problems have been studied in connection with first-order probabilistic logic [27].…”

Section: Discussionmentioning

confidence: 99%

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On the Coherence of Probabilistic Relational Formalisms

Bona

Cozman

2018

Entropy

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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.

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Section: A Weaker Form Of Coherencesupporting

confidence: 69%

Section: Discussionmentioning

confidence: 99%

On the Coherence of Probabilistic Relational Formalisms

Bona

Cozman

2018

Entropy

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“…Proposition 13 implies that the problem of determining p β T,AF (A) is equivalent to the classical probabilistic entailment problem (Jaumard, Hansen, & Poggi, 1991;Hansen & Jaumard, 2000;Lukasiewicz, 2000). We can directly exploit this relationship to make some observations on the computational complexity of some problems related to p β T,AF (A).…”

Section: Partial Probability Assessmentsmentioning

confidence: 99%

Probabilistic Reasoning with Abstract Argumentation Frameworks

Hunter¹,

Thimm²

2017

jair

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argumentation offers an appealing way of representing and evaluating arguments and counterarguments. This approach can be enhanced by considering probability assignments on arguments, allowing for a quantitative treatment of formal argumentation. In this paper, we regard the assignment as denoting the degree of belief that an agent has in an argument being acceptable. While there are various interpretations of this, an example is how it could be applied to a deductive argument. Here, the degree of belief that an agent has in an argument being acceptable is a combination of the degree to which it believes the premises, the claim, and the derivation of the claim from the premises. We consider constraints on these probability assignments, inspired by crisp notions from classical abstract argumentation frameworks and discuss the issue of probabilistic reasoning with abstract argumentation frameworks. Moreover, we consider the scenario when assessments on the probabilities of a subset of the arguments are given and the probabilities of the remaining arguments have to be derived, taking both the topology of the argumentation framework and principles of probabilistic reasoning into account. We generalise this scenario by also considering inconsistent assessments, i.e., assessments that contradict the topology of the argumentation framework. Building on approaches to inconsistency measurement, we present a general framework to measure the amount of conflict of these assessments and provide a method for inconsistency-tolerant reasoning.

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“…The reduction shown in the membership proof, from the consistency checking problem to PSAT, would allow us to define additional tractable cases if the PSAT instances resulting from such a reduction were tractable. However, as will be discussed in Section 6, the tractable cases that have been identified for PSAT (Georgakopoulos et al, 1988;Andersen & Pretolani, 2001) do not carry over to our framework.…”

Section: Checking Consistency Is Np-completementioning

confidence: 99%

Knowledge Representation in Probabilistic Spatio-Temporal Knowledge Bases

Parisi¹,

Grant²

2016

jair

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We represent knowledge as integrity constraints in a formalization of probabilistic spatiotemporal knowledge bases. We start by defining the syntax and semantics of a formalization called PST knowledge bases. This definition generalizes an earlier version, called SPOT, which is a declarative framework for the representation and processing of probabilistic spatio-temporal data where probability is represented as an interval because the exact value is unknown. We augment the previous definition by adding a type of non-atomic formula that expresses integrity constraints. The result is a highly expressive formalism for knowledge representation dealing with probabilistic spatio-temporal data. We obtain complexity results both for checking the consistency of PST knowledge bases and for answering queries in PST knowledge bases, and also specify tractable cases. All the domains in the PST framework are finite, but we extend our results also to arbitrarily large finite domains.

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Probabilistic Satisfiability

Cited by 42 publications

References 105 publications

On the Coherence of Probabilistic Relational Formalisms

On the Coherence of Probabilistic Relational Formalisms

Probabilistic Reasoning with Abstract Argumentation Frameworks

Knowledge Representation in Probabilistic Spatio-Temporal Knowledge Bases

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