T. Lukasiewicz. Probabilistic logic programming with conditional constraints. ACM Trans. Comput. Log. 2(3): 289-339 (2001).  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... comes especially from philosophy and logic, and whose roots go back to Boole s book of 1854 The Laws of Thought [11] There is a wide spectrum of formal languages that have been explored in model theoretic probabilistic logic, ranging from constraints for unconditional and conditional events [16, 20, 2, 52, 19, 23, 33, 44, 39, 40, 42, 45] to rich languages that specify linear inequalities over events [22] The main problems related to model theoretic probabilistic logic are checking satisfiability, deciding logical consequence, and computing tight logically entailed intervals. Another important approach to probabilistic reasoning ....

....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 classical notion of model theoretic entailment is too weak, for example, in probabilistic logic programming [42, 41]. Other applications are deriving degrees of belief from statistical knowledge and degrees of belief, handling inconsistencies in probabilistic knowledge bases, and probabilistic belief revision. The main contributions of this paper are as follows: We show that the notions of g coherence and ....

T. Lukasiewicz. Probabilistic logic programming with conditional constraints. ACM Trans. Computat. Logic, 2(3):289--339, 2001.

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Lukasiewicz, T.: 2001, `Probabilistic logic programming with conditional constraints'. ACM Transactions on Computational Logic 2(3), 289--339.

.... especially from philosophy and logic, and whose roots go back to Boole s book of 1854 The Laws of Thought [11] There is a wide spectrum of formal languages that have been explored in model theoretic probabilistic logic, ranging from constraints for unconditional and conditional events [16, 20, 2, 53, 19, 23, 33, 45, 39, 40, 42, 46] to rich languages that specify linear inequalities over events [22] The main problems related to model theoretic probabilistic logic are checking satisfiability, deciding logical consequence, and computing tight logically entailed intervals. Another important approach to probabilistic reasoning ....

....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 classical notion of modeltheoretic entailment is too weak, for example, in probabilistic logic programming [42, 41]. Other applications are deriving degrees of belief from statistical knowledge and degrees of belief, handling inconsistencies in probabilistic knowledge bases, and probabilistic belief revision. The main contributions of this paper are as follows: We show that the notions of g coherence and of ....

T. Lukasiewicz. Probabilistic logic programming with conditional constraints. ACM Trans. Computat. Logic, 2(3):289--339, 2001.

.... probabilistic logic, whose roots go back to Boole s book of 1854 The Laws of Thought [BOO 54] There is a wide spectrum of formal languages that have been explored in probabilistic logic, which ranges from constraints for unconditional and conditional events [AMA 91, FRI 94, LUK 99a, LUK 99b, LUK 01, NIL 86] to rich languages that specify linear inequalities over events [FAG 90] The main problems related to model theoretic probabilistic logic are checking satisfiability, deciding logical consequence, and computing tight logically entailed intervals. Coherence based and model theoretic ....

LUKASIEWICZ T., "Probabilistic logic programming with conditional constraints", ACM Trans. Computat. Logic, vol. 2, num. 3, 2001, p. 289--339.

....linear optimization techniques (see especially [31, 30] on the issue of local versus global approaches) As shown by Georgakopoulos et al. 21] deciding satisfiability and logical consequence in probabilistic logic is NP and coNP complete, and thus intractable. Moreover, as recently shown in [28], deciding and computing tight logical consequences is complete for the classes , respectively. Substantial research efforts were directed towards efficient techniques for reasoning in probabilistic logic. In particular, column generation techniques from the area of linear optimization have ....

.... optimization have been successfully used to solve large problem instances (see the work by Jaumard et al. 27] and Hansen et al. 26] Other techniques, which may be described as problem transformations on the language level, have been successfully applied in probabilistic logic programming [28]. Moreover, a global approach for the conjunctive case, which characterizes a reduced set of variables, has been presented in [29] We point out that in model theoretic probabilistic logic, for every conditional constraint in the given probabilistic knowledge base, the conditional ....

[Article contains additional citation context not shown here]

T. Lukasiewicz. Probabilistic logic programming with conditional constraints. ACM Transactions on Computational Logic, 2001. To appear.

....different from the various notions of causality that we have considered here. Other less related work concerns reasoning about conditional probability statements in probabilistic logic. Here, the results by Fagin et al. 7] imply that y8) M[Q,JI T 6Z complete, while Lukasiewicz [26] has shown that computing the tightest interval T 6Z y8) FJ,JI[ 6Z i.e. complete for the class of functions computable in polynomial time with an oracle. 6.3 Applications of results Our complexity results show that, similar to independencies [31] deterministic and ....

T. Lukasiewicz. Probabilistic logic programming with conditional constraints. ACM Transactions on Computational Logic, 2(3):289--339, 2001. INFSYS RR 1843-01-01

.... probabilistic logic, ranging from constraints for unconditional and conditional events to rich languages that specify linear inequalities over events (see especially the work by Nilsson [52] Fagin et al. 24] Dubois and Prade et al. 18, 22, 2, 21] Frisch and Haddawy [25] and the author [46, 47, 49]; see also the survey on sentential probability logic by Hailperin [38] The main decision and optimization problems in model theoretic probabilistic reasoning are deciding satisfiability, deciding logical consequence, and computing tight logically entailed intervals. Example 1.2 (Eagles ....

....probabilistic logic. For this reason, they are generally much stronger than entailment in model theoretic probabilistic logic. Thus, they are especially useful where the classical notion of model theoretic logical entailment is too weak, for example, in probabilistic logic programming [49, 48]. Other applications are deriving degrees of belief from statistical knowledge and degrees of belief, handling inconsistencies in probabilistic knowledge bases, and probabilistic belief revision. The main contributions of this paper can be summarized as follows: We show that the notions of ....

[Article contains additional citation context not shown here]

T. Lukasiewicz. Probabilistic logic programming with conditional constraints. ACM Transactions on Computational Logic (TOCL), 2(3):289--339, 2001.

.... for handling conditional constraints is model theoretic probabilistic logic, which can be traced back to Boole [10] There is a wide spectrum of formal languages that have been explored in model theoretic probabilistic logic, ranging from constraints for unconditional and conditional events [15, 19, 2, 18, 23, 33, 47, 41, 42, 44, 48] to rich languages that specify linear inequalities over events [21] The main algorithmic tasks related to model theoretic probabilistic logic are deciding satisfiability, deciding logical consequence, and computing tight logically entailed intervals. In model theoretic probabilistic logic, we ....

....to entailment in model theoretic probabilistic logic. This is why they are generally much stronger than entailment in model theoretic probabilistic logic. Thus, they are especially useful where the notion of model theoretic entailment is too weak, for example, in probabilistic logic programming [44, 43]. Other applications are deriving degrees of belief from statistical knowledge and degrees of belief, handling inconsistencies in probabilistic knowledge bases, and probabilistic belief revision. In the present paper, we define a general approach to nonmonotonic probabilistic reasoning, which ....

[Article contains additional citation context not shown here]

T. Lukasiewicz. Probabilistic logic programming with conditional constraints. ACM Transactions on Computational Logic (TOCL), 2(3):289--339, 2001.

....and from the drowning problem. They both also satisfy the property of rational monotonicity and several irrelevance properties. We finally present algorithms for both approaches, which are based on generalizations of techniques from probabilistic logic programming under logical entailment in [45]. The algorithm for the first approach still produces quite large weighted entropy maximization problems, while the one for the second approach generates optimization problems of the same size as the ones produced by probabilistic logic programming under logical entailment in [45] Fachbereich ....

.... entailment in [45] The algorithm for the first approach still produces quite large weighted entropy maximization problems, while the one for the second approach generates optimization problems of the same size as the ones produced by probabilistic logic programming under logical entailment in [45]. Fachbereich Informatik, FernUniversitat Hagen, P.O. Box 940, D 58084 Hagen, Germany; e mail: gabriele.kernisberner fernuni hagen.de. Dipartimento di Informatica e Sistemistica, Universita di Roma La Sapienza , Via Salaria 113, 00198 Rome, Italy; e mail: lukasiewicz dis.uniroma1.it. ....

[Article contains additional citation context not shown here]

T. Lukasiewicz. Probabilistic logic programming with conditional constraints. ACM Transactions on Computational Logic (TOCL), 2(3):264--312, 2001.

.... constraints is model theoretic probabilistic logic, whose roots go back to Boole s book of 1854 The Laws of Thought [7] There is a wide spectrum of formal languages that have been explored in probabilistic logic, which ranges from constraints for unconditional and conditional events [2, 15, 27, 28, 29, 32] to rich languages that specify linear inequalities over events [14] The main problems related to model theoretic probabilistic logic are checking satisfiability, deciding logical consequence, and computing tight logically entailed intervals. Coherence based and model theoretic probabilistic ....

T. Lukasiewicz. Probabilistic logic programming with conditional constraints. ACM Trans. Computat. Logic, 2(3):289--339, 2001.

.... constraints is model theoretic probabilistic logic, whose roots go back to Boole s book of 1854 The Laws of Thought [7] There is a wide spectrum of formal languages that have been explored in probabilistic logic, which ranges from constraints for unconditional and conditional events [2, 15, 25, 26, 27, 29] to rich languages that specify linear inequalities over events [14] The main problems related to model theoretic probabilistic logic are checking satisfiability, deciding logical consequence, and computing tight logically entailed intervals. Coherence based and model theoretic probabilistic ....

T. Lukasiewicz. Probabilistic logic programming with conditional constraints. ACM Trans. Computat. Logic, 2(3):289--339, 2001.

....in probabilistic logic: The new notions of entailment are generally much stronger than the classical notion of logical entailment based on conditioning. Thus, they may especially be useful where the classical notion of logical entailment is too weak, for example, in probabilistic logic programming [64, 63]. Handling probabilistic inconsistencies: The new formalisms can be used for resolving inconsistencies in probabilistic knowledge bases. Belief revision: The new formalisms can also be used for belief revision with sets of probabilistic formulas as belief sets. The main contributions of ....

....V VII. Roughly speaking, the complexity of probabilistic default reasoning with conditional constraints is a combination of the complexity of classical default reasoning from conditional knowledge bases [26] and with the complexity of classical probabilistic reasoning with conditional constraints [64]. Table V. Complexity of CONSISTENCY. general case literal Horn case consistency NP complete NP complete Table VI. Complexity of CONSEQUENCE. general case literal Horn case L;M N OQPSR G complete NP hard, in LAM N O PSR G u M complete L M complete T ....

[Article contains additional citation context not shown here]

Lukasiewicz, T.: 2001b, `Probabilistic logic programming with conditional constraints'. ACM Transactions on Computational Logic 2(3), 289--339.

....linear optimization techniques (see especially [31, 30] on the issue of local versus global approaches) As shown by Georgakopoulos et al. 21] deciding satisfiability and logical consequence in probabilistic logic is NP and coNP complete, and thus intractable. Moreover, as recently shown in [28], deciding and computing tight logical consequences is complete for the classes D P and F P 2 , respectively. Substantial research efforts were directed towards efficient techniques for reasoning in probabilistic logic. In particular, column generation techniques from the area of linear ....

.... optimization have been successfully used to solve large problem instances (see the work by Jaumard et al. 27] and Hansen et al. 26] Other techniques, which may be described as problem transformations on the language level, have been successfully applied in probabilistic logic programming [28]. Moreover, a global approach for the conjunctive case, which characterizes a reduced set of variables, has been presented in [29] We point out that in model theoretic probabilistic logic, for every conditional constraint P ( j ) in the given probabilistic knowledge base, the conditional ....

[Article contains additional citation context not shown here]

T. Lukasiewicz. Probabilistic logic programming with conditional constraints. ACM Transactions on Computational Logic, 2001. To appear.

No context found.

T. Lukasiewicz. Probabilistic logic programming with conditional constraints. ACM Trans. Computat. Logic, 2(3):289--337, 2001.

....A number of recent research efforts are directed towards integrating logic oriented and probabilitybased representation and reasoning formalisms. In particular, there are approaches to probabilistic logic programming that combine logic programming techniques with probabilities over possible worlds [25, 26, 4, 5, 20]. They are based on the model theoretic notion of logical entailment, which is well known from probabilistic propositional logics [28, 7, 6] The notion of logical entailment, however, has often been criticized in the literature for its inferential weakness. For this reason, many recent approaches ....

....CONSISTENCY and TIGHT S CONSEQUENCE are NP and complete, respectively, in the general and the 1 conjunctive propositional case. That is, they have the same complexity as the problems SATISFIABILITY and TIGHT LOGI CAL CONSEQUENCE, respectively, in the respective propositional cases [20]. Intuitively, adding inheritance with overriding to probabilistic logic programming does not increase its complexity. Table 1: Propositional Complexity of CONSISTENCY general case 1 conjunctive case consistency NP complete NP complete Table 2: Propositional Complexity of TIGHT S CONSEQUENCE ....

[Article contains additional citation context not shown here]

T. Lukasiewicz. Probabilistic logic programming with conditional constraints. ACM Trans. Computat. Logic. 2(3):289--337, July 2001. To appear. INFSYS RR 1843-01-05

....number of recent research efforts are directed towards integrating logic oriented and probability based representation and reasoning formalisms. In particular, there are approaches to probabilistic logic programming that combine logic programming techniques with probabilities over possible worlds [25, 26, 4, 5, 19]. They are based on the model theoretic notion of logical entailment, which is wellknown from probabilistic propositional logics [28, 7, 6] The notion of logical entailment, however, has often been criticized in the literature for its inferential weakness. For this reason, many recent approaches ....

....detail, CONSISTENCY and TIGHT S CONSE QUENCE are NP and Q complete, respectively, in the general and the 1 conjunctive propositional case. That is, they have the same complexity as the problems SATISFIABILITY and TIGHT LOGICAL CONSEQUENCE, respectively, in the respective propositional cases [19]. Intuitively, adding inheritance with overriding to probabilistic logic programming does not increase its complexity. Table 1: Prop. Complexity of CONSISTENCY general case 1 conjunctive case consistency NP complete NP complete Table 2: Prop. Complexity of TIGHT S CONSEQUENCE general case ....

T. Lukasiewicz. Probabilistic logic programming with conditional constraints. ACM Trans. Computat. Logic. 2(3):289--337, July 2001. To appear.

No context found.

T. Lukasiewicz. Probabilistic logic programming with conditional constraints. ACM Trans. Computat. Logic, 2(3):289--337, 2001. 20 INFSYS RR 1843-01-06

.... constraints is model theoretic probabilistic logic, whose roots go back to Boole s book of 1854 The Laws of Thought [8] There is a wide spectrum of formal languages that have been explored in probabilistic logic, which ranges from constraints for unconditional and conditional events [2, 13, 19, 20, 22, 23] to rich languages that specify linear inequalities over events [12] The main problems related to model theoretic probabilistic logic are checking satisfiability, deciding logical entailment, and computing tight logically entailed intervals. Coherence based and model theoretic probabilistic ....

T. Lukasiewicz. Probabilistic logic programming with conditional constraints. ACM Trans. Computat. Logic, 2(3):289--337, July 2001. To appear.

No context found.

T. Lukasiewicz. Probabilistic logic programming with conditional constraints. ACM Trans. Computat. Logic, 2(3):289--337, 2001. INFSYS RR 1843-01-06

....A number of recent research efforts are directed towards integrating logic oriented and probabilitybased representation and reasoning formalisms. In particular, there are approaches to probabilistic logic programming that combine logic programming techniques with probabilities over possible worlds [25, 26, 4, 5, 20]. They are based on the model theoretic notion of logical entailment, which is well known from probabilistic propositional logics [28, 7, 6] The notion of logical entailment, however, has often been criticized in the literature for its inferential weakness. For this reason, many recent approaches ....

....CONSISTENCY and TIGHT S CONSEQUENCE are NP and F P 2 complete, respectively, in the general and the 1 conjunctive propositional case. That is, they have the same complexity as the problems SATISFIABILITY and TIGHT LOGI CAL CONSEQUENCE, respectively, in the respective propositional cases [20]. Intuitively, adding inheritance with overriding to probabilistic logic programming does not increase its complexity. Table 1: Propositional Complexity of CONSISTENCY general case 1 conjunctive case consistency NP complete NP complete Table 2: Propositional Complexity of TIGHT S CONSEQUENCE ....

[Article contains additional citation context not shown here]

T. Lukasiewicz. Probabilistic logic programming with conditional constraints. ACM Trans. Computat. Logic. 2(3):289--337, July 2001. To appear. INFSYS RR 1843-01-05

....linear optimization techniques (see especially [30, 29] on the issue of local versus global approaches) As shown by Georgakopoulos et al. 20] deciding satisfiability and logical consequence in probabilistic logic is NP and co NP complete, and thus intractable. Moreover, as recently shown in [27], deciding and computing tight logical consequences is complete for the classes D P and F P 2 , respectively. Substantial research efforts were directed towards efficient techniques for reasoning in probabilistic logic. In particular, column generation techniques from the area of linear ....

.... optimization have been successfully used to solve large problem instances (see the work by Jaumard et al. 26] and Hansen et al. 25] Other techniques, which may be described as problem transformations on the language level, have been successfully applied in probabilistic logic programming [27]. Moreover, a global approach for the conjunctive case, which characterizes a reduced set of variables, has been presented in [28] We point out that in model theoretic probabilistic logic, for every conditional constraint P ( j ) in the given probabilistic knowledge base, the conditional ....

[Article contains additional citation context not shown here]

T. Lukasiewicz. Probabilistic logic programming with conditional constraints. ACM Transactions on Computational Logic, 2001. To appear.

.... constraints is model theoretic probabilistic logic, whose roots go back to Boole s book of 1854 The Laws of Thought [7] There is a wide spectrum of formal languages that have been explored in probabilistic logic, which ranges from constraints for unconditional and conditional events [2, 15, 24, 25, 27, 28] to rich languages that specify linear inequalities over events [14] The main problems related to model theoretic probabilistic logic are checking satisfiability, deciding logical entailment, and computing tight logically entailed intervals. Coherence based and model theoretic probabilistic ....

T. Lukasiewicz. Probabilistic logic programming with conditional constraints. ACM Trans. Computat. Logic, 2001. To appear.

....edge bases (see Section 9) Moreover, the new notions of entailment are generally much stronger than the classical notion of logical entailment based on conditioning. Thus, they may especially be useful where classical logical entailment is too weak, for example, in probabilistic logic programming [54, 55]. The main contributions of this paper can be briefly summarized as follows: We show that neither the classical notion of logical entailment for conditional constraints nor the classical notion of entailment under coherence have the properties that are desired in reasoning from statistical and ....

....results are summarized in Tables 5 7. Roughly speaking, the complexity of probabilistic default reasoning with conditional constraints combines the complexity of classical default reasoning from conditional knowledge bases [22] and of classical probabilistic reasoning with conditional constraints [54]. It turns out that deciding consistency and z consequence in the literal Horn case is NP hard, while the counterparts in classical default reasoning are both tractable. The other decision problems for consistency and z , lex , and c consequence have the same complexity as their counterparts ....

[Article contains additional citation context not shown here]

T. Lukasiewicz. Probabilistic logic programming with conditional constraints. ACM Transactions on Computational Logic. To appear.

....results are summarized in Tables 3 5. Roughly speaking, the complexity of probabilistic default reasoning with conditional constraints combines the complexity of classical default reasoning from conditional knowledge bases [13] and classical probabilistic reasoning with conditional constraints [38]. We remark that deciding consistency and z consequence in the literal Horn case is NP hard, while their classical counterparts are tractable. The other decision problems for consistency and z , lexicographic, and conditional consequence have the same complexity as their classical ....

....Pr and Pr 0 of P [ fKBg that satisfy D are incomparable to each other. Hence, for every priority ordering , the set of all minimal models of P [ fKBg coincides with the set of all models of P [ D[ fKBg. 2 D Proofs for Section 7 We first recall some results that have been proved in [38]. The following theorem shows that deciding satisfiability and logical consequence for strict conditional constraints is in NP and co NP, respectively. Theorem D.1 a) Given a finite set of strict conditional constraints F , deciding whether F is satisfiable is in NP. b) Given a finite set of ....

[Article contains additional citation context not shown here]

T. Lukasiewicz. Probabilistic logic programming with conditional constraints. Technical Report 1843-00-01, Institut fur Informationssysteme, Technische Universitat Wien, 2000.

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T. Lukasiewicz. Probabilistic logic programming with conditional constraints. ACM Trans. Comput. Log. 2(3): 289-339 (2001).

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T. Lukasiewicz. Probabilistic logic programming with conditional constraints. ACM Trans. Comput. Logic, 2(3):289--339, 2001.

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