Lukasiewicz, T.: 2002b, `Probabilistic default reasoning with conditional constraints'. Ann. Math. Artif. Intell. 34(1--3), 35--88.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....as long as we condition on non zero events. Furthermore, the new formalisms can be used in place of probabilistic entailment under coherence, when we also want to have an inheritance of logical knowledge. Finally, another important application is probabilistic belief revision. A companion paper [43] presents similar probabilistic generalizations of entailment in Pearl s System Z and of Lehmann s lexicographic entailment. These formalisms, however, are quite different from the ones in this paper. In detail, the new formalisms in [43] add an inheritance of probabilistic knowledge and a ....

....is probabilistic belief revision. A companion paper [43] presents similar probabilistic generalizations of entailment in Pearl s System Z and of Lehmann s lexicographic entailment. These formalisms, however, are quite different from the ones in this paper. In detail, the new formalisms in [43] add an inheritance of probabilistic knowledge and a strategy for resolving inconsistencies to entailment in model theoretic probabilistic logic. For this reason, they are generally much stronger than entailment in model theoretic probabilistic logic. Thus, they are especially useful where the ....

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T. Lukasiewicz. Probabilistic default reasoning with conditional constraints. Ann. Math. Artif. Intell., 34(1-- 3):35--88, 2002.

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Lukasiewicz, T.: 2002b, `Probabilistic default reasoning with conditional constraints'. Ann. Math. Artif. Intell. 34(1--3), 35--88.

....as long as we condition on non zero events. Furthermore, the new formalisms can be used in place of probabilistic entailment under coherence, when we also want to have an inheritance of logical knowledge. Finally, another important application is probabilistic belief revision. A companion paper [44] presents similar probabilistic generalizations of entailment in Pearl s System and of Lehmann s lexicographic entailment. These formalisms, however, are quite different from the ones in this paper. In detail, the new formalisms in [44] add an inheritance of probabilistic knowledge and a strategy ....

....is probabilistic belief revision. A companion paper [44] presents similar probabilistic generalizations of entailment in Pearl s System and of Lehmann s lexicographic entailment. These formalisms, however, are quite different from the ones in this paper. In detail, the new formalisms in [44] add an inheritance of probabilistic knowledge and a strategy for resolving inconsistencies to entailment in model theoretic probabilistic logic. For this reason, they are generally much stronger than entailment in model theoretic probabilistic logic. Thus, they are especially useful where the ....

[Article contains additional citation context not shown here]

T. Lukasiewicz. Probabilistic default reasoning with conditional constraints. Ann. Math. Artif. Intell., 34(1--3):35--88, 2002.

....complexity and algorithms for probabilistic reasoning under coherence have been presented in a companion paper [BIA 01] Note that a companion paper [LUK 02b] continues this line of research on the relationship between coherence based and model theoretic probabilistic reasoning. In the spirit of [LUK 02a] it introduces probabilistic generalizations of Pearl s entailment [PEA 90] and Lehmann s lexicographic entailment [LEH 95] which lie between g coherent entailment and logical entailment. As for the relationship between probabilistic reasoning under coherence and default , we showed that ....

LUKASIEWICZ T., "Probabilistic default reasoning with conditional constraints", Ann. Math. Artif. Intell., vol. 34, num. 1--3, 2002, p. 35--88.

.... paper can be summarized as follows: We present a probabilistic extension of the description logic 0(2 , 0 , called P 0(2 ,3 4 , which is based on the notion of probabilistic lexicographic entailment; this approach is motivated by recent advances to probabilistic default reasoning [22,23]. Note especially that probabilistic lexicographic entailment has very nice properties for the use in probabilistic reasoning with generic and assertional (i.e. Abox) probabilistic knowledge [22,23] P 0(2 ,3 4 allows to express default knowledge as a special case of generic probabilistic ....

.... entailment; this approach is motivated by recent advances to probabilistic default reasoning [22,23] Note especially that probabilistic lexicographic entailment has very nice properties for the use in probabilistic reasoning with generic and assertional (i.e. Abox) probabilistic knowledge [22,23]. P 0(2 ,3 4 allows to express default knowledge as a special case of generic probabilistic knowledge, where reasoning with such default knowledge is based on the sophisticated notion of lexicographic entailment by Lehmann [20] We present sound and complete techniques for probabilistic ....

[Article contains additional citation context not shown here]

T. Lukasiewicz. Probabilistic default reasoning with conditional constraints. Ann. Math. Artif. Intell., 34(1--3):35--88, 2002.

....properties of the new probabilistic formalisms. Moreover, we provide algorithms for computing tight consequences under the new formalisms, and draw a precise picture of the complexity of probabilistic reasoning under the new formalisms. More generally, in the same spirit as a companion paper [50], this paper sheds light on exciting new formalisms for probabilistic reasoning beyond the well known standard ones. Dipartimento di Informatica e Sistemistica, Universita di Roma La Sapienza , Via Salaria 113, 00198 Roma, Italy. E mail: lukasiewicz dis.uniroma1.it. Alternate address: Institut ....

....coincide with model theoretic probabilistic entailment as long as we condition on non zero events. Moreover, the new formalisms can be used in place of probabilistic entailment under coherence, when we also want to have some restricted form of inheritance of logical knowledge. A companion paper [50] presents similar probabilistic generalizations of Pearl s entailment in System and of Lehmann s lexicographic entailment. These formalisms, however, are quite different from the ones in this paper. In detail, the new formalisms in [50] add an inheritance of probabilistic knowledge and a ....

[Article contains additional citation context not shown here]

T. Lukasiewicz. Probabilistic default reasoning with conditional constraints. Ann. Math. Artif. Intell., 34(1--3):35--88, 2002.

....through a value##### that describes the strength of the inheritance of purely probabilistic knowledge. In the special cases of##### and##### , the notions of entailment coincide with the probabilistic notions of entailment recently introduced by the author in [45] and [46], respectively. We show that the notions of entailment have similar properties as their classical counterparts. In particular, they both satisfy the rationality postulates of System and the property of Rational Monotonicity. Moreover, entailment is weaker than entailment, and ....

....it has been shown that probabilistic entailment under coherence is a generalization of classical default , while model theoretic probabilistic entailment is well known to be a generalization of model theoretic entailment in classical propositional logics. Recently, the author has shown in [45, 46] that other formalisms for default reasoning from conditional knowledge bases can be extended to the probabilistic framework of conditional constraints, in order to overcome some serious drawbacks of model theoretic and coherence based probabilistic logic. The literature contains several ....

[Article contains additional citation context not shown here]

T. Lukasiewicz. Probabilistic default reasoning with conditional constraints. Ann. Math. Artif. Intell., 34(1--3):35--88, 2002.

....methods from objectoriented programming languages are used to enable flexible and large scale knowledge representation with Bayesian networks. Another promising way towards stronger entailment relations are the recent approaches to probabilistic default reasoning with conditional constraints in [47] and to probabilistic logic programming under inheritance with overriding in [44] These approaches are based on new notions of entailment for reasoning with conditional constraints, which are obtained from the classical notion of logical entailment by adding inheritance with overriding, using ....

....interval that follows from the above program for Tweety has legs, given that Tweety is a penguin is given by . The new notions of entailment have very nice nonmonotonic properties, and they can also be used in reasoning from statistical knowledge and degrees of belief [47]. A companion paper [46] explores related notions of entailment for conditioning on zero events. A further way to overcome the inferential weakness of model theoretic logical entailment is to use the principle of maximum entropy. In general, the available probabilistic knowledge does not suffice ....

T. Lukasiewicz. Probabilistic default reasoning with conditional constraints. Ann. Math. Artif. Intell., 34(1-- 3):35--88, 2002.

....of web ontology languages so far. In this paper, we propose such an extension. We present a probabilistic extension of the description logic , called P 1 2( which is based on the notion of probabilistic lexicographic entailment, a recent approach to probabilistic default reasoning [21, 22]. The description logic P 1 2( also allows to express default knowledge as a special case of generic probabilistic knowledge, where reasoning with such default knowledge is based on the sophisticated notion of lexicographic entailment by Lehmann [19] There are several related approaches ....

.... inverse roles) allows to represent both generic probabilistic knowledge about concepts and roles, and also assertional probabilistic knowledge about concept and role instances; is based on probabilistic lexicographic entailment from recent approaches to probabilistic default reasoning [21, 22] as underlying probabilistic reasoning formalism. The main contributions of this paper can be summarized as follows: We present a probabilistic extension of the description logic , called P 1 2( which is based on the notion of probabilistic lexicographic entailment; this approach is ....

[Article contains additional citation context not shown here]

T. Lukasiewicz. Probabilistic default reasoning with conditional constraints. Ann. Math. Artif. Intell., 34(1-- 3):35--88, 2002.

....results on complexity and algorithms for probabilistic reasoning under coherence have been presented in a companion paper [6] Note that a companion paper [30] continues this line of research on the relationship between coherencebased and model theoretic probabilistic reasoning. In the spirit of [31], it introduces probabilistic generalizations of Pearl s entailment in System ( 35] and Lehmann s lexicographic entailment [26] which lie between g coherent entailment and logical entailment. As for the relationship between probabilistic reasoning under coherence and default reasoning in ....

T. Lukasiewicz. Probabilistic default reasoning with conditional constraints. Ann. Math. Artif. Intell., 34(1-- 3):35--88, 2002.

....research is to explore how other notions of coherence are related to modeltheoretic probabilistic logic and to default reasoning. It would also be interesting to develop coherence based probabilistic extensions of notions of default reasoning different from system P (for example, in the spirit of [28]) 7 Appendix A: Proofs for Section 3 Proof of Theorem 3.2. Let P n = f( 1 j 1 ) l 1 ; u 1 ] n j n ) l n ; u n ]g P with n 1. Define the imprecise probability assessment (L; A) on E n = f 1 j 1 ; n j n g by A( i j i ) l i ; u i ] for all i 2 f1; ng. By ....

T. Lukasiewicz. Probabilistic default reasoning with conditional constraints. to appear in Ann. Math. Artif. Intell., 2002.

....entailment in probabilistic logic does not follow the principle of inheritance with overriding. It is thus a natural idea to strengthen logical entailment by adding inheritance with overriding. In this paper, we realize this idea by using recent approaches to probabilistic default reasoning from [22, 23]. INFSYS RR 1843 01 05 3 The main contributions of this paper can be summarized as follows: We present probabilistic logic programming under inheritance with overriding, which is based on recent approaches to probabilistic default reasoning from [22, 23] We describe general nonmontonic ....

.... probabilistic default reasoning from [22, 23] INFSYS RR 1843 01 05 3 The main contributions of this paper can be summarized as follows: We present probabilistic logic programming under inheritance with overriding, which is based on recent approaches to probabilistic default reasoning from [22, 23]. We describe general nonmontonic properties of entailment under inheritance with overriding. We present algorithms for probabilistic logic programming under inheritance with overriding. We analyze the computational complexity of probabilistic logic programming under inheritance with ....

[Article contains additional citation context not shown here]

T. Lukasiewicz. Probabilistic default reasoning with conditional constraints. In Proceedings of the 8th International Workshop on Non-Monotonic Reasoning, Breckenridge, CO, USA, April 2000.

....in probabilistic logic does not follow the principle of inheritance with overriding. It is thus a natural idea to strengthen logical entailment by adding inheritance with overriding. In this paper, we realize this idea by using recent ap proaches to probabilistic default reasoning from [21, 22]. The main contributions of this paper are as follows: We present probabilistic logic programming under inheritance with overriding, which is based on recent approaches to probabilistic default reasoning from [21, 22] We describe some general nonmontonic properties of entailment under ....

.... idea by using recent ap proaches to probabilistic default reasoning from [21, 22] The main contributions of this paper are as follows: We present probabilistic logic programming under inheritance with overriding, which is based on recent approaches to probabilistic default reasoning from [21, 22]. We describe some general nonmontonic properties of entailment under inheritance with overriding. We present algorithms for probabilistic logic programming under inheritance with overriding. We analyze the propositional complexity of probabilistic logic programming under inheritance ....

[Article contains additional citation context not shown here]

T. Lukasiewicz. Probabilistic default reasoning with conditional constraints. In Proceedings of the 8th International Workshop on Non-Monotonic Reasoning, Breckenridge, CO, USA, April 2000.

....is to explore how other notions of coherence are related to model theoretic probabilistic logic and to default reasoning. It would also be very interesting to develop coherence based probabilistic extensions of notions of default reasoning different from system P (for example, in the spirit of [21]) Acknowledgments. This work has been partially supported by a DFG grant and the Austrian Science Fund under project N Z29 INF. We are very grateful to the anonymous reviewers for their useful comments. ....

T. Lukasiewicz. Probabilistic default reasoning with conditional constraints. In Proceedings of the 8th International Workshop on Non-monotonic Reasoning, 2000.

....entailment in probabilistic logic does not follow the principle of inheritance with overriding. It is thus a natural idea to strengthen logical entailment by adding inheritance with overriding. In this paper, we realize this idea by using recent approaches to probabilistic default reasoning from [22, 23]. INFSYS RR 1843 01 05 3 The main contributions of this paper can be summarized as follows: We present probabilistic logic programming under inheritance with overriding, which is based on recent approaches to probabilistic default reasoning from [22, 23] We describe general nonmontonic ....

.... to probabilistic default reasoning from [22, 23] INFSYS RR 1843 01 05 3 The main contributions of this paper can be summarized as follows: We present probabilistic logic programming under inheritance with overriding, which is based on recent approaches to probabilistic default reasoning from [22, 23]. We describe general nonmontonic properties of entailment under inheritance with overriding. We present algorithms for probabilistic logic programming under inheritance with overriding. We analyze the computational complexity of probabilistic logic programming under inheritance with ....

[Article contains additional citation context not shown here]

T. Lukasiewicz. Probabilistic default reasoning with conditional constraints. In Proceedings of the 8th International Workshop on Non-Monotonic Reasoning, Breckenridge, CO, USA, April 2000.

No context found.

T. Lukasiewicz. Probabilistic default reasoning with conditional constraints. In Proc. 8th International Workshop on Non-monotonic Reasoning, Breckenridge, CO, USA, 2000.

....several incompatible probabilistic rules might be applicable to the same concrete scenario. Then, we have to remove all those probabilistic rules that should not be applied anymore, which can be done by a probabilistic generalization of classical default reasoning from conditional knowledge bases [49]. Finally, depending on our application, we can also use the stronger 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 ....

T. Lukasiewicz. Probabilistic default reasoning with conditional constraints. In Proceedings of the 8th International Workshop on Non-Monotonic Reasoning, Special Session on Uncertainty Frameworks in NMR, 2000.

.... 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 = a 2 j ) 0:3; 0:8] 0:5] C = c 1 j A= a 1 ) 0:3; 0:4] 0:4] C = c 2 j A= a 1 ) 0:6; 0:7] 0:6] C = c 1 j A= a 2 ) 0:3; 0:5] 0:5] C = c 2 j A= a 2 ) 0:5; 0:7] 0:5] F ....

T. Lukasiewicz. Probabilistic default reasoning with conditional constraints. In Proceedings of the 8th International Workshop on Non-Monotonic Reasoning, Special Session on Uncertainty Frameworks in NMR, 2000.

.... 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 their useful comments on an earlier version of this paper. Many thanks also to the referees for their useful suggestions. This work has been partially supported by a DFG grant and ....

T. Lukasiewicz. Probabilistic default reasoning with conditional constraints. In Proceedings of the 8th International Workshop on Non-Monotonic Reasoning, Special Session on Uncertainty Frameworks in NMR, 2000.

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