Hybrid probabilistic programs

Alex Dekhtyar; V. S. Subrahmanian

doi:10.1016/S0743-1066(99)00059-X

Hybrid probabilistic programs

Alex Dekhtyar, V. S. Subrahmanian

Research output: Contribution to journal › Article › peer-review

75 Scopus citations

Abstract

The precise probability of a compound event (e.g. e₁ ∨ e₂, e₁ ∧ e₂) depends upon the known relationships (e.g. independence, mutual exclusion, ignorance of any relationship, etc.) between the primitive events that constitute the compound event. To date, most research on probabilistic logic programming has assumed that we are ignorant of the relationship between primitive events. Likewise, most research in AI (e.g. Bayesian approaches) has assumed that primitive events are independent. In this paper, we propose a hybrid probabilistic logic programming language in which the user can explicitly associate, with any given probabilistic strategy, a conjunction and disjunction operator, and then write programs using these operators. We describe the syntax of hybrid probabilistic programs, and develop a model theory and fixpoint theory for such programs. Last, but not least, we develop three alternative procedures to answer queries, each of which is guaranteed to be sound and complete.

Original language	English (US)
Pages (from-to)	187-250
Number of pages	64
Journal	Journal of Logic Programming
Volume	43
Issue number	3
DOIs	https://doi.org/10.1016/S0743-1066(99)00059-X
State	Published - Jun 2000
Externally published	Yes

Funding

This work was supported by the Army Research Oce under Grants DAAH -04-95-10174, DAAH -04-96-10297, and DAAH 04-96-1-0398, by the Army Research Laboratory under contract number DAAL01-97-K0135, by an NSF Young Investigator award IRI-93-57756, and by an award from Lockheed Martin Advanced Technology Labs. We would like to thank the anonymous reviewers for pointing out a bug in an earlier version of the paper and for a number of useful comments.

Keywords

Logic programming languages
Probabilistic logic
Uncertainty

ASJC Scopus subject areas

Logic

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10.1016/S0743-1066(99)00059-X

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abstract = "The precise probability of a compound event (e.g. e1 ∨ e2, e1 ∧ e2) depends upon the known relationships (e.g. independence, mutual exclusion, ignorance of any relationship, etc.) between the primitive events that constitute the compound event. To date, most research on probabilistic logic programming has assumed that we are ignorant of the relationship between primitive events. Likewise, most research in AI (e.g. Bayesian approaches) has assumed that primitive events are independent. In this paper, we propose a hybrid probabilistic logic programming language in which the user can explicitly associate, with any given probabilistic strategy, a conjunction and disjunction operator, and then write programs using these operators. We describe the syntax of hybrid probabilistic programs, and develop a model theory and fixpoint theory for such programs. Last, but not least, we develop three alternative procedures to answer queries, each of which is guaranteed to be sound and complete.",

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author = "Alex Dekhtyar and Subrahmanian, {V. S.}",

note = "Funding Information: This work was supported by the Army Research Oce under Grants DAAH -04-95-10174, DAAH -04-96-10297, and DAAH 04-96-1-0398, by the Army Research Laboratory under contract number DAAL01-97-K0135, by an NSF Young Investigator award IRI-93-57756, and by an award from Lockheed Martin Advanced Technology Labs. We would like to thank the anonymous reviewers for pointing out a bug in an earlier version of the paper and for a number of useful comments.",

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doi = "10.1016/S0743-1066(99)00059-X",

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N2 - The precise probability of a compound event (e.g. e1 ∨ e2, e1 ∧ e2) depends upon the known relationships (e.g. independence, mutual exclusion, ignorance of any relationship, etc.) between the primitive events that constitute the compound event. To date, most research on probabilistic logic programming has assumed that we are ignorant of the relationship between primitive events. Likewise, most research in AI (e.g. Bayesian approaches) has assumed that primitive events are independent. In this paper, we propose a hybrid probabilistic logic programming language in which the user can explicitly associate, with any given probabilistic strategy, a conjunction and disjunction operator, and then write programs using these operators. We describe the syntax of hybrid probabilistic programs, and develop a model theory and fixpoint theory for such programs. Last, but not least, we develop three alternative procedures to answer queries, each of which is guaranteed to be sound and complete.

AB - The precise probability of a compound event (e.g. e1 ∨ e2, e1 ∧ e2) depends upon the known relationships (e.g. independence, mutual exclusion, ignorance of any relationship, etc.) between the primitive events that constitute the compound event. To date, most research on probabilistic logic programming has assumed that we are ignorant of the relationship between primitive events. Likewise, most research in AI (e.g. Bayesian approaches) has assumed that primitive events are independent. In this paper, we propose a hybrid probabilistic logic programming language in which the user can explicitly associate, with any given probabilistic strategy, a conjunction and disjunction operator, and then write programs using these operators. We describe the syntax of hybrid probabilistic programs, and develop a model theory and fixpoint theory for such programs. Last, but not least, we develop three alternative procedures to answer queries, each of which is guaranteed to be sound and complete.

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Hybrid probabilistic programs

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