Lukasiewicz, T., and Kern-Isberner, G. 1999. Probabilistic logic programming under maximum entropy. In Hunter, A., and Parsons, S., eds., Proceedings of the Fifth European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty, 279--292. London, UK: Springer.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... Curie Individual Fellowship of the European Community (Disclaimer: The authors are solely responsible for information communicated and the European Commission is not responsible for any views or results expressed) We are very grateful to the reviewers of the ECSQARU 99 abstract of this paper [48], whose constructive comments helped to improve our work. Copyright c 2002 by the authors INFSYS RR 1843 02 12 I Contents 1 Introduction 1 2 Preliminaries 4 2.1 Probabilistic Background . 4 2.2 Syntax of Probabilistic Logic ....

T. Lukasiewicz and G. Kern-Isberner. Probabilistic logic programming under maximum entropy. In Proceedings ECSQARU-99, volume 1638 of LNCS/LNAI, pages 279--292. Springer, 1999.

....inferential weakness. For this reason, many recent approaches towards integrating logic and probabilities combine logic based formalisms with Bayesian networks [33, 32, 13, 27, 15] Another way to overcome the inferential weakness of logical entailment is to use the principle of maximum entropy [24] or the principle of sequential maximum entropy [21] where the latter is closely related to Bayesian networks. The maximum entropy approach, however, has the drawback that it does not properly model imprecision in our knowledge base. That is, maximum entropy always produces a single joint ....

....we presented algorithms for probabilistic logic programming under inheritance with overriding, and we analyzed its propositional complexity. A very interesting topic of future research is to investigate the relationship to probabilistic logic programming under maximum entropy as presented in [24], where we also have some form of inheritance with overriding. A Appendix: Proofs Theorems 5.1, 5.2, 5.3, and 6.1 are special cases of Theorems 6.1, 6.2, 6.3, and 7.1, respectively, in [23] The membership results shown in Tables 1 and 2 follow from respective membership results for more general ....

T. Lukasiewicz and G. Kern-Isberner. Probabilistic logic programming under maximum entropy. In Proc. ECSQARU-99, LNCS 1638, pp. 279--292. 1999.

....inferential weakness. For this reason, many recent approaches towards integrating logic and probabilities combine logic based formalisms with Bayesian networks [33, 32, 12, 27, 14] Another way to overcome the inferential weakness of logical entailment is to use the principle of maximum entropy [24] or the principle of sequential maximum entropy [20] where the latter is closely related to Bayesian networks. The maximum entropy approach, however, has the drawback that it does not properly model imprecision in our knowledge base. That is, maximum entropy always produces a single joint ....

....we presented algorithms for probabilistic logic programming under inheritance with overriding, and we analyzed its propositional complexity. A very interesting topic of future research is to investigate the relationship to probabilistic logic programming under maximum entropy as presented in [24], where we also have some form of inheritance with overriding. Acknowledgements I am very grateful to Gabriele Kern Isberner for valuable comments on an earlier version of this paper. Many thanks also the anonymous reviewers for their useful comments. This work has been supported by a DFG grant ....

T. Lukasiewicz and G. Kern-Isberner. Probabilistic logic programming under maximum entropy. In Proc. ECSQARU-99, LNCS 1638, pp. 279--292. 1999.

....inferential weakness. For this reason, many recent approaches towards integrating logic and probabilities combine logic based formalisms with Bayesian networks [33, 32, 13, 27, 15] Another way to overcome the inferential weakness of logical entailment is to use the principle of maximum entropy [24] or the principle of sequential maximum entropy [21] where the latter is closely related to Bayesian networks. The maximum entropy approach, however, has the drawback that it does not properly model imprecision in our knowledge base. That is, maximum entropy always produces a single joint ....

....we presented algorithms for probabilistic logic programming under inheritance with overriding, and we analyzed its propositional complexity. A very interesting topic of future research is to investigate the relationship to probabilistic logic programming under maximum entropy as presented in [24], where we also have some form of inheritance with overriding. A Appendix: Proofs Theorems 5.1, 5.2, 5.3, and 6.1 are special cases of Theorems 6.1, 6.2, 6.3, and 7.1, respectively, in [23] The membership results shown in Tables 1 and 2 follow from respective membership results for more general ....

T. Lukasiewicz and G. Kern-Isberner. Probabilistic logic programming under maximum entropy. In Proc. ECSQARU-99, LNCS 1638, pp. 279--292. 1999.

....notion of consequence under positive correlation or the stronger notion of consequence under maximum entropy. The former carries us immediately to nice computational properties (as shown in Section 9) while the latter can be realized by a generalization of the technique introduced in Section 7. 3 [50]. Note also that there is a refinement of the principle of maximum entropy that encodes Bayesian network oriented conditional independencies [48] 11 Summary and Conclusion We presented a new approach to probabilistic logic programming with a possible worlds semantics in which classical program ....

T. Lukasiewicz and G. Kern-Isberner. Probabilistic logic programming under maximum entropy. In Proceedings of the 5th European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty, volume 1638 of LNAI, pages 279--292. Springer, 1999.

....of sequential maximum entropy to credal networks. We especially showed that this application is equivalent to a number of small local entropy maximizations. A very interesting topic of future research is to apply the results of this work to the framework of probabilistic logic programming [31, 15, 27]. Moreover, it would be interesting to use the principle of sequential maximum entropy in order to add causality to probabilistic default reasoning with conditional constraints [26] INFSYS RR 1843 00 03 Table 1: Some Conditionals in KB and KB KB KB (A = a 1 j ) 0:2; 0:7] 0:5] A = ....

T. Lukasiewicz and G. Kern-Isberner. Probabilistic logic programming under maximum entropy. In Proceedings ECSQARU-99, LNAI 1638, pp. 279--292. Springer, 1999.

....of sequential maximum entropy to credal networks. We especially showed that this application is equivalent to a number of small local entropy maximizations. A very interesting topic of future research is to apply the results of this work to the framework of probabilistic logic programming [32, 15, 28]. Moreover, it would be interesting to use the principle of sequential maximum entropy in order to add causality to probabilistic default reasoning with conditional constraints [27] Acknowledgments I am very grateful to Fabio Gagliardi Cozman, Gabriele Kern Isberner, and Richard Neapolitan for ....

T. Lukasiewicz and G. Kern-Isberner. Probabilistic logic programming under maximum entropy. In Proceedings ECSQARU-99, LNAI 1638, pp. 279--292. Springer, 1999.

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Lukasiewicz, T., and Kern-Isberner, G. 1999. Probabilistic logic programming under maximum entropy. In Hunter, A., and Parsons, S., eds., Proceedings of the Fifth European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty, 279--292. London, UK: Springer.

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