Probabilistic satisfiability: algorithms with the presence and absence of a phase transition

Finger, Marcelo; Bona, Glauber De

doi:10.1007/s10472-015-9466-6

Cited by 22 publications

(40 citation statements)

References 30 publications

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“…The same holds for the problem of answering selection queries in PST KBs that, as shown in Section 4, can be addressed by solving suitable instances of the consistency checking problem. Recent approaches to solve PSAT using SAT (Finger & Bona, 2011) or Integer Linear Programming (Cozman & di Ianni, 2015) for column selection report experiments showing a phase transition behaviour (first observed by Finger and Bona for PSAT) depending on the fraction between the number of clauses and propositional variables as well as the number of probability assignments. Using these techniques PSAT instances with hundreds of propositional variables and clauses can be solved in reasonable time.…”

Section: Probabilistic Logicmentioning

confidence: 96%

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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Section: Probabilistic Logicmentioning

confidence: 96%

Knowledge Representation in Probabilistic Spatio-Temporal Knowledge Bases

Parisi¹,

Grant²

2016

jair

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“…This linear programming approach can be easily extended to handle conditional probabilities under the semantics we are using [16]. Recent advances in algorithms for PSAT solving can be found in [17,9,28].…”

Section: Preliminariesmentioning

confidence: 99%

“…Nevertheless, column generation methods can handle large problems [26,24], and several approaches have recently appeared [28,9,17,7]. Note that this linear programming approach can be applied to other probabilistic logics (see, for instance, [1] and [23]).…”

Section: Preliminariesmentioning

confidence: 99%

Measuring inconsistency in probabilistic logic: rationality postulates and Dutch book interpretation

Bona

Finger

2015

Artificial Intelligence

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Inconsistency measures have been proposed as a way to manage inconsistent knowledge bases in the AI community. To deal with inconsistencies in the context of conditional probabilistic logics, rationality postulates and computational efficiency have driven the formulation of inconsistency measures. Independently, investigations in formal epistemology have used the betting concept of Dutch book to measure an agent's degree of incoherence. In this paper, we show the impossibility of joint satisfiability of the proposed postulates, proposing to replace them by more suitable ones. Thus we reconcile the rationality postulates for inconsistency measures in probabilistic bases and show that several inconsistency measures suggested in the literature and computable with linear programs satisfy the reconciled postulates. Additionally, we give an interpretation for these feasible measures based on the formal epistemology concept of Dutch book, bridging the views of two so far separate communities in AI and Philosophy. In particular, we show that incoherence degrees in formal epistemology may lead to novel approaches to inconsistency measures in the AI view.

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“…PSAT is a particular case of PSAT-IP, but the latter can be polynomially reduced to the former, at least when probability bounds are rational, by employing techniques as the atomic normal form, from Finger and De Bona, 2011). Example 2.2.1.…”

Section: Deciding the Consistency Of Probabilistic Basesmentioning

confidence: 99%

“…Despite the exponential number of columns, column generation methods can be used to handle them implicitly (Jaumard et al, 1991;Kavvadias and Papadimitr , 1990), keeping the computation efficient enough to solve large knowledge bases -thousands of probabilities in Hansen and Perron, 2008). An open source implementation of a PSAT solver through column generation from Finger and De Bona (2011) is available at http://psat.sourceforge.net.…”

Section: 2mentioning

confidence: 99%

Measuring inconsistency in probabilistic knowledge bases

Bona¹

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Probabilistic satisfiability: algorithms with the presence and absence of a phase transition

Cited by 22 publications

References 30 publications

Knowledge Representation in Probabilistic Spatio-Temporal Knowledge Bases

Knowledge Representation in Probabilistic Spatio-Temporal Knowledge Bases

Measuring inconsistency in probabilistic logic: rationality postulates and Dutch book interpretation

Measuring inconsistency in probabilistic knowledge bases

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