×

Anytime deduction for probabilistic logic. (English) Zbl 0809.03016

The authors present a set of inference rules that in any reasoning on probabilistic logic (in the sense of Nilsson) based on conditional probabilities will yield the tightest interval of confidence given the information processed up to that point, under the proposed rules. In contrast to Nilsson’s approach, all arguments are based directly on these rules, no systems of linear equations are solved. The rules are based on the familiar ways of assigning intervals in probabilistic logic; however, no consistency proof is offered.

MSC:

03B60 Other nonclassical logic
68T27 Logic in artificial intelligence
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Adams, E.; Levine, H., On the uncertainties transmitted from premises to conclusions in deductive inferences, Synthese, 30, 429-460 (1975) · Zbl 0307.02031
[2] Amarger, S.; Dubois, D.; Prade, H., Constraint propagation with imprecise conditional probabilities, (D’Ambrosio, B.; Smets, P.; Bonissone, P., Proceedings Seventh Conference on Uncertainty in Artificial Intelligence. Proceedings Seventh Conference on Uncertainty in Artificial Intelligence, Los Angeles, CA (1991)), 26-34
[3] Bacchus, F., (Representing and Reasoning With Probabilistic Knowledge (1990), MIT Press: MIT Press Cambridge, MA)
[4] Bundy, A., Incidence calculus: a mechanism for probabilistic reasoning, J. Automated Reasoning, 1, 263-283 (1985) · Zbl 0615.68067
[5] Bundy, A., Correctness criteria of some algorithms for uncertain reasoning using incidence calculus, J. Automated Reasoning, 2, 109-126 (1986) · Zbl 0642.68178
[6] Buneman, P.; Davidson, S. B.; Watters, A., A semantics for complex objects and approximate queries, (Proceedings Seventh Symposium on the Principles of Database Systems (1988)), 305-314
[7] Chung, J. Y.; Liu, J. W.S.; Lin, K. J., Scheduling periodic jobs that allow imprecise results, IEEE Trans. Computers, 39, 2, 1156-1174 (1990)
[8] Davidson, S. B.; Watters, A., Partial computation in real-time database systems, (Proceedings Fifth Workshop on Real-Time Software and Operating Systems (1988)), 117-121
[9] Dean, T.; Boddy, M., An analysis of time-dependent planning, (Proceedings AAAI-88. Proceedings AAAI-88, St. Paul, MN (1988)), 49-54
[10] Drummond, M.; Bresina, J., Anytime synthetic projection: maximizing the probability of goal satisfaction, (Proceedings AAAI-90. Proceedings AAAI-90, Boston, MA (1990)), 138-144
[11] Dubois, D.; Prade, H., Combination and propagation of uncertainty with belief functions, (Proceedings IJCAI-85. Proceedings IJCAI-85, Los Angeles, CA (1985)), 111-113
[12] Inf. Comput., 87, 78-128 (1990) · Zbl 0811.03014
[13] Garvey, T. D.; Lowrance, J. D.; Fischler, M. A., An inference technique for integrating knowledge from disparate sources, (Proceedings IJCAI-81. Proceedings IJCAI-81, Vancouver, BC (1981)), 319-325
[14] Grosof, B. N., An inequality paradigm for probabilistic knowledge: the logic of conditional probability intervals, (Kanal, J. F.; Lemmer, J. F., Uncertainty in Artificial Intelligence (1986), Elsevier Science: Elsevier Science Amsterdam, Netherlands) · Zbl 0608.68076
[15] Haddawy, P., Implementation of and experiments with a variable precision logic inference system, (Proceedings AAAI-86. Proceedings AAAI-86, Philadelphia, PA (1986)), 238-242
[16] Haddawy, P.; Frisch, A., Convergent deduction for probabilistic logic, (Proceedings Third Workshop on Uncertainty in Artificial Intelligence. Proceedings Third Workshop on Uncertainty in Artificial Intelligence, Seattle, WA (1987)), 278-286
[17] Haddawy, P.; Frisch, A. M., Modal logics of higher-order probability, (Shachter, R. D.; Levitt, T. S.; Lemmer, J. F.; Kanal, L. N., Uncertainty in Artificial Intelligence, 4 (1990), Elsevier Science: Elsevier Science Amsterdam, Netherlands), 133-148
[18] Halpern, J. Y., An analysis of first-order logics of probability, Artif. Intell., 46, 311-350 (1991) · Zbl 0723.03007
[19] Horvitz, E. J., Reasoning under varying and uncertain resource constraints, (Proceedings AAAI-88. Proceedings AAAI-88, St. Paul, MN (1988)), 111-116
[20] Horvitz, E. J., Reflection and action under scarce resources: theoretical principles and empirical study, (Proceedings IJCAI-89. Proceedings IJCAI-89, Detroit, MI (1989)), 1121-1127 · Zbl 0714.68087
[21] Lesser, V. R.; Pavlin, J.; Durfee, E., Approhximate processing in real-time problem solving, AI Mag., 9, 1, 49-61 (1988)
[22] Liu, J. W.S.; Lin, K. J.; Natarajan, S., Scheduling real-time, periodic jobs using imprecise results, (Proceedings IEEE Real-Time Systems Symposium. Proceedings IEEE Real-Time Systems Symposium, San Jose, CA (1987))
[23] Michalski, R. S.; Winston, P. H., Variable precision logic, Artif. Intell., 29, 2, 121-146 (1986) · Zbl 0623.68077
[24] Ng, R. T.; Subrahmanian, V. S., A semantical framework for supporting subjective and conditional probabilities in deductive databases, J. Automated Reasoning, 10, 2, 191-235 (1993) · Zbl 0784.68082
[25] Ng, R. T.; Subrahmanian, V. S., Probabilistic reasoning in logic programming, (Ras, Z. W.; Zemankova, M.; Enrich, M. L., Methodologies for Intelligent Systems, 5 (1990), Elsevier Science: Elsevier Science Amsterdam, Netherlands), 9-16
[26] Nilsson, N. J., Probabilistic logic, Artif. Intell., 28, 71-87 (1986) · Zbl 0589.03007
[27] Nilsson, N. J., Probabilistic logic revisited, Artif. Intell., 59, 1-2, 39-42 (1993) · Zbl 1507.68015
[28] Paass, G., Probabilistic logic, (Smets, P.; Mamdani, A.; Dubois, D.; Prade, H., Non-Standard Logics for Automated Reasoning (1988), Academic Press: Academic Press New York), 213-244 · Zbl 0669.03002
[29] Pearl, J., (Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference (1988), Morgan Kaufmann: Morgan Kaufmann San Mateo, CA)
[30] Pittarelli, M., Decision making with linear constraints on probabilities, (Proceedings Fourth Workshop on Uncertainty in Artificial Intelligence. Proceedings Fourth Workshop on Uncertainty in Artificial Intelligence, Minneapolis, MN (1988)), 283-290
[31] Quinlan, J. R., INFERNO: a cautious approach to uncertain inference, Comput. J., 26, 3, 255-269 (1983)
[32] Shvaytser, H., Probabilities that imply certainties, (Proceedings AAAI-90. Proceedings AAAI-90, Boston, MA (1990)), 665-670
[33] Smith, K. P.; Liu, J. W.S., Monotonically improving approximate answers to relational algebra queries, (Proceedings IEEE Compsac. Proceedings IEEE Compsac, Orlando, FL (1989))
[34] Ursic, S., Generalizing fuzzy logic probabilistic inferences, (Proceedings Third Workshop on Uncertainty in Artificial Intelligence. Proceedings Third Workshop on Uncertainty in Artificial Intelligence, Philadelphia, PA (1986)), 303-310 · Zbl 0661.03012
[35] van der Gaag, L., Computing probability intervals under independency constraints, (Proceedings Sixth Conference on Uncertainty in Artificial Intelligence. Proceedings Sixth Conference on Uncertainty in Artificial Intelligence, Cambridge, MA (1990)), 491-497
[36] Vrbsky, S. V.; Liu, J. W.S.; Smith, K. P., An object-oriented query processor that returns monotonically improving approximate answers, (Report UIUCDCS-R-90-1568 (1990), University of Illinois: University of Illinois Urbana-Champaign, IL)
[37] Zweben, M.; Deale, M.; Garan, R., Anytime rescheduling, (Proceedings 1990 DARPA Workshop on Innovative Approaches to Planning, Scheduling, and Control. Proceedings 1990 DARPA Workshop on Innovative Approaches to Planning, Scheduling, and Control, San Diego, CA (1990))
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.