Anytime Deduction for Probabilistic Logic

Abstract This paper proposes and investigates an approach to deduction in probabilistic logic, using as its medium a language that generalizes the propositional version of Nilsson's probabilistic logic by incorporating conditional probabilities. Unlike many other approaches to deduction in probabilistic logic, this approach is based on inference rules and therefore can produce proofs to explain how conclusions are drawn. We show how these rules can be incorporated into an anytime deduction procedure that proceeds by computing increasingly narrow probability intervals that contain the tightest entailed probability interval. Since the procedure can be stopped at any time to yield partial information concerning the probability range of any entailed sentence, one can make a tradeoff between precision and computation time. The deduction method presented here contrasts with other methods whose ability to perform logical reasoning is either limited or requires finding all truth assignments consistent with the given sentences.

[1]  Jane W.-S. Liu,et al.  Scheduling Real-Time, Periodic Jobs Using Imprecise Results , 1987, RTSS.

[2]  Eric Horvitz,et al.  Reflection and Action Under Scarce Resources: Theoretical Principles and Empirical Study , 1989, IJCAI.

[3]  E. Horvitz,et al.  Reeection and Action under Scarce Resources: Theoretical Principles and Empirical Study 1 Reeection and Flexibility 2 Decision-theoretic Valuation , 1989 .

[4]  Ronald Fagin,et al.  A logic for reasoning about probabilities , 1988, [1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science.

[5]  Nils J. Nilsson,et al.  Probabilistic Logic Revisited , 1993, Artif. Intell..

[6]  Benjamin N. Grosof.  An Inequality Paradigm for Probabilistic Knowledge: The Logic of Conditional Probability Intervals , 1985, UAI.

[7]  Jane W.-S. Liu,et al.  Scheduling Periodic Jobs That Allow Imprecise Results , 1990, IEEE Trans. Computers.

[8]  Didier Dubois,et al.  Combination and Propagation of Uncertainty with Belief Functions - A Reexamination , 1985, IJCAI.

[9]  Jane W.-S. Liu,et al.  An object-oriented query processor that produces monotonically improving approximate answers , 1991, [1991] Proceedings. Seventh International Conference on Data Engineering.

[10]  Eric Horvitz,et al.  Reasoning under Varying and Uncertain Resource Constraints , 1988, AAAI.

[11]  L. C. Gaag.  Computing probability intervals under independency constraints , 1990, UAI.

[12]  Haim Schweitzer,et al.  Probabilities that Imply Certainties , 1990, AAAI.

[13]  Philippe Smets.  Non-standard logics for automated reasoning , 1988 .

[14]  Silvio Ursic,et al.  Generalising fuzzy logic probabilistic inferences , 1986, UAI.

[15]  Susan B. Davidson,et al.  Partial Computation in Real-Time Database Systems , 1988 .

[16]  Aaron Watters,et al.  A semantics for complex objects and approximate queries , 1988, PODS '88.

[17]  Benjamin N. Grosof,et al.  An inequality paradigm for probabilistic knowledge the augmented logic of conditional probability intervals , 1985, UAI 1985.

[18]  Nils J. Nilsson,et al.  Probabilistic Logic * , 2022 .

[19]  J. W. S. Liu,et al.  Monotonically improving approximate answers to relational algebra queries , 1989, [1989] Proceedings of the Thirteenth Annual International Computer Software & Applications Conference.

[20]  John D. Lowrance,et al.  An Inference Technique for Integrating Knowledge from Disparate Sources , 1981, IJCAI.

[21]  Didier Dubois,et al.  Constraint Propagation with Imprecise Conditional Probabilities , 1991, UAI.

[22]  Ryszard S. Michalski,et al.  Variable Precision Logic , 1986, Artif. Intell..

[23]  V. S. Subrahmanian,et al.  Probabilistic reasoning in logic programming , 1991 .

[24]  Mark S. Boddy,et al.  An Analysis of Time-Dependent Planning , 1988, AAAI.

[25]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[26]  Joseph Y. Halpern.  An Analysis of First-Order Logics of Probability , 1989, IJCAI.

[27]  Peter Haddawy,et al.  Modal logics of higher-order probability , 1988, UAI.

[28]  Fahiem Bacchus,et al.  Representing and reasoning with probabilistic knowledge , 1988 .

[29]  Peter Haddawy,et al.  Convergent deduction for probabilistic logic , 1987, Int. J. Approx. Reason..

[30]  John L. Bresina,et al.  Anytime Synthetic Projection: Maximizing the Probability of Goal Satisfaction , 1990, AAAI.

[31]  Peter Haddawy.  Implementation of and Experiments with a Variable Precision Logic Inference System , 1986, AAAI.

[32]  J. Ross Quinlan,et al.  Inferno: A Cautious Approach To Uncertain Inference , 1986, Comput. J..

[33]  Edmund H. Durfee,et al.  Approximate Processing in Real-Time Problem Solving , 1988, AI Mag..