TY - JOUR

T1 - Probabilistic logic programming

AU - Ng, Raymond

AU - Subrahmanian, V. S.

N1 - Funding Information:
We thank Fahiem Bacchus, Howard Blair, Wiktor Marek, Michael Kifer, and Maarten van Emden for numerous fruitful discussions and constructive comments on the manuscript. V. S. S. also thanks the Oflice of Graduate Studies and Research of the University of Maryland for financial support in the summer of 1990. R. N. thanks Timos Sellis for financial support. The research was partially sponsored by the National Science Foundation under Grants IRI-8719458 and IRI-9109755, and by the Army Research Office under Grant Number DAAL-03-92-G-0225.

PY - 1992/12

Y1 - 1992/12

N2 - Of all scientific investigations into reasoning with uncertainty and chance, probability theory is perhaps the best understood paradigm. Nevertheless, all studies conducted thus far into the semantics of quantitative logic programming have restricted themselves to non-probabilistic semantic characterizations. In this paper, we take a few steps towards rectifying this situation. We define a logic programming language that is syntactically similar to the annotated logics of Blair and Subrahmanian (Theoret. Comput. Sci.68 (1987), 35-54; J. Non-Classical Logic5 (1988), 45-73) but in which the truth values are interpreted probabilistically. A probabilistic model theory and fixpoint theory is developed for such programs. This probabilistic model theory satisfies the requirements proposed by Fenstad (in "Studies in Inductive Logic and Probabilities" (R. C. Jeffrey, Ed.), Vol. 2, pp. 251-262, Univ. of California Press, Berkeley, 1980) for a function to be called probabilistic. The logical treatment of probabilities is complicated by two facts: first, that the connectives cannot be interpreted truth-functionally when truth values are regarded as probabilities; second, that negation-free definite-clause-like sentences can be inconsistent when interpreted probabilistically. We address these issues here and propose a formalism for probabilistic reasoning in logic programming. To our knowledge, this is the first probabilistic characterization of logic programming semantics.

AB - Of all scientific investigations into reasoning with uncertainty and chance, probability theory is perhaps the best understood paradigm. Nevertheless, all studies conducted thus far into the semantics of quantitative logic programming have restricted themselves to non-probabilistic semantic characterizations. In this paper, we take a few steps towards rectifying this situation. We define a logic programming language that is syntactically similar to the annotated logics of Blair and Subrahmanian (Theoret. Comput. Sci.68 (1987), 35-54; J. Non-Classical Logic5 (1988), 45-73) but in which the truth values are interpreted probabilistically. A probabilistic model theory and fixpoint theory is developed for such programs. This probabilistic model theory satisfies the requirements proposed by Fenstad (in "Studies in Inductive Logic and Probabilities" (R. C. Jeffrey, Ed.), Vol. 2, pp. 251-262, Univ. of California Press, Berkeley, 1980) for a function to be called probabilistic. The logical treatment of probabilities is complicated by two facts: first, that the connectives cannot be interpreted truth-functionally when truth values are regarded as probabilities; second, that negation-free definite-clause-like sentences can be inconsistent when interpreted probabilistically. We address these issues here and propose a formalism for probabilistic reasoning in logic programming. To our knowledge, this is the first probabilistic characterization of logic programming semantics.

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U2 - 10.1016/0890-5401(92)90061-J

DO - 10.1016/0890-5401(92)90061-J

M3 - Article

AN - SCOPUS:38249009397

SN - 0890-5401

VL - 101

SP - 150

EP - 201

JO - Information and Computation

JF - Information and Computation

IS - 2

ER -