Probability logic.

Hailperin, Theodore

doi:10.1305/ndjfl/1093870625

Cited by 99 publications

(50 citation statements)

References 7 publications

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“…Probabilistic logic programming has been studied for almost 25 years [8,7,18,16,13,14,4]. For most of these years, researchers have known that the probability in- tervals associated with PLP queries can be inordinately wide, often giving very little information to the user about the truth or falsity of the query and, as illustrated in our stock example, making it difficult for the user to make decisions.…”

Section: Resultsmentioning

confidence: 99%

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Using Histograms to Better Answer Queries to Probabilistic Logic Programs

2009

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Probabilistic logic programs (PLPs) define a set of probability distribution functions (PDFs) over the set of all Herbrand interpretations of the underlying logical language. When answering a query Q, a lower and upper bound on Q is obtained by optimizing (min and max) an objective function subject to a set of linear constraints whose solutions are the PDFs mentioned above. A common critique not only of PLPs but many probabilistic logics is that the difference between the upper bound and lower bound is large, thus often providing very little useful information in the query answer. In this paper, we provide a new method to answer probabilistic queries that tries to come up with a histogram that "maps" the probability that the objective function will have a value in a given interval, subject to the above linear constraints. This allows the system to return to the user a histogram where he can directly "see" what the most likely probability range for his query will be. We prove that computing these histograms is #P -hard, and show that computing these histograms is closely related to polyhedral volume computation. We show how existing randomized algorithms for volume computation can be adapted to the computation of such histograms. A prototype experimental implementation is discussed.

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Section: Resultsmentioning

confidence: 99%

“…While these early frameworks were fuzzy in nature, Ng and Subrahmanian [16] introduced probabilistic logic programs by building on top of probabilistic logics studied earlier by several authors such as Hailperin [8], Fagin et al [7], and Nilsson [18]. There has been much subsequent work in this vein [13,14,4].…”

Section: Introductionmentioning

confidence: 99%

Using Histograms to Better Answer Queries to Probabilistic Logic Programs

2009

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“…There are limits to this strategy, since some multi-premise deductive arguments won't even be guaranteed to preserve warrant/justification in cases where all the premises are highly warranted/justified. But, there is a fully general theory of ''probability logic'', which furnishes such results for many classically deductively valid argument forms (Hailperin 1996). To my mind, this (to some extent) softens the impact of Pollock's objection to thinking of degree of justification or degree of warrant as a PROB.…”

Section: Some Remarks On Pollock's Critique Of Bayesian Epistemologymentioning

confidence: 90%

“…There is quite a long tradition of what is known as probability logic (PL). In recent years, probability-logicians like Adams (1975Adams ( , 1996 and Hailperin (1996) have done a great deal of work on various notions of ''probabilistic validity''. Two important points about (PL) are in order here.…”

Section: Some Remarks On Pollock's Critique Of Bayesian Epistemologymentioning

confidence: 99%

Pollock on probability in epistemology

Fitelson

2009

Philos Stud

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“…(Membership). We show that checking the consistency of K can be reduced to deciding an instance φ K of (an extension to) the Probabilistic Satisfiability (PSAT) problem (Hailperin, 1984;Nilsson, 1986), which is in NP (Georgakopoulos, Kavvadias, & Papadimitriou, 1988). Given a set of m clauses C 1 , .…”

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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Probability logic.

Cited by 99 publications

References 7 publications

Using Histograms to Better Answer Queries to Probabilistic Logic Programs

Using Histograms to Better Answer Queries to Probabilistic Logic Programs

Pollock on probability in epistemology

Knowledge Representation in Probabilistic Spatio-Temporal Knowledge Bases

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