Complexity and expressive power of logic programming

Dantsin, Evgeny; Eiter, Thomas; Gottlob, Georg; Воронков, Андрей

doi:10.1145/502807.502810

Cited by 478 publications

(207 citation statements)

References 261 publications

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“…When comparing ILP (first order predicate logic rules) and feature-value learning techniques (propositional logic rules), there is a trade-off between expressive power and efficiency (Dantsin et al 2001). ILP techniques are typically more expressive (see Fig.…”

Section: Inductive Logic Programmingmentioning

confidence: 99%

Machine learning: a review of classification and combining techniques

2006

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Supervised classification is one of the tasks most frequently carried out by socalled Intelligent Systems. Thus, a large number of techniques have been developed based on Artificial Intelligence (Logic-based techniques, Perceptron-based techniques) and Statistics (Bayesian Networks, Instance-based techniques). The goal of supervised learning is to build a concise model of the distribution of class labels in terms of predictor features. The resulting classifier is then used to assign class labels to the testing instances where the values of the predictor features are known, but the value of the class label is unknown. This paper describes various classification algorithms and the recent attempt for improving classification accuracy-ensembles of classifiers.

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Section: Inductive Logic Programmingmentioning

confidence: 99%

Machine learning: a review of classification and combining techniques

2006

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“…The bounds follow from a similar argumentation as in the case of data complexity, except that now, deciding, given an ordinary positive program P and a ground atom a, whether P logically entails a is hard for EXP in general [10], and computing the well-founded semantics of ordinary normal programs is in EXP in general. Notice that, by a similar line of argumentation, tight query processing in probabilistic dl-programs under the well-founded semantics can also be done in exponential time in general.…”

Section: Complexitymentioning

confidence: 97%

“…Recall that the complexity class P contains all decision problems that can be solved in polynomial time on a deterministic Turing machine, and that the data complexity for probabilistic dlprograms KB = (L, P, C, μ) describes the case where all of KB but the facts in P and the concept, role, and attribute membership axioms in L are fixed. Hardness for P follows from the hardness for P of deciding, given an ordinary positive program P and a ground atom a, whether P logically entails a in the data complexity [10]. Membership in P follows from Theorem 9 and that (a) computing the well-founded semantics of ordinary normal programs can be done in polynomial time in the data complexity, and (b) instance checking and knowledge base satisfiability in DL-Lite A can be done in polynomial time.…”

Section: Complexitymentioning

confidence: 99%

“…Thus, deciding w-consistency and correct query processing in probabilistic dlprograms under the well-founded semantics have a lower complexity than their counterparts under the answer set semantics, which are hard for NP and co-NP in the data and for NEXP and co-NEXP in general, as they generalize deciding consistency and brave consequences of ground atoms under the answer set semantics in ordinary normal programs, which are complete for NP and co-NP in the data and for NEXP and co-NEXP in general [10].…”

Section: Complexitymentioning

confidence: 99%

“…Proof of Theorem 11 Hardness for P in both (a) and (b) follows from the P-hardness of deciding, given an ordinary positive program P and a ground atom a, whether P logically entails a in the data complexity [10]. Membership in P in both (a) and (b) follows from Theorem 9 and the fact that the fixpoint iterations for computing WFS(L, P ∪ {p ← | p ∈ B}) for each total choice B of C with μ(B) > 0 can be done in polynomial time in the data complexity, since instance checking and knowledge base satisfiability in DL-Lite A can be done in polynomial time.…”

Section: Appendix: Proofsmentioning

confidence: 99%

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Tightly integrated probabilistic description logic programs for representing ontology mappings

Lukasiewicz

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Stuckenschmidt

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Creating mappings between ontologies is a common way of approaching the semantic heterogeneity problem on the Semantic Web. To fit into the landscape of Semantic Web languages, a suitable, logic-based representation formalism for mappings is needed. We argue that such a formalism has to be able to deal with uncertainty and inconsistencies in automatically created mappings. We analyze the requirements for such a formalism, and we propose a novel approach to probabilistic description logic programs as such a formalism, which tightly combines normal logic programs under the well-founded semantics with both tractable ontology languages and Bayesian probabilities. We define the language, and we show that it can be used to resolve inconsistencies and merge mappings from different matchers based on the level of confidence assigned to different rules. Furthermore, we explore the semantic and computational aspects of probabilistic description logic programs under the well-founded semantics. In particular, we show that the well-founded semantics approximates the answer set semantics. We also describe algorithms for consistency checking and tight query processing, and we analyze the data and general complexity of these two central computational problems. As a crucial property, the novel tightly integrated probabilistic description logic programs under the well-founded This article is a significantly extended and revised version of two papers that appeared in Proc. URSW-2007 [2] and Proc. FoIKS-2008 [3]. 386T. Lukasiewicz et al.semantics allow for tractable consistency checking and for tractable tight query processing in the data complexity, and they even have a first-order rewritable (and thus LogSpace data complexity) special case, which is especially interesting for representing ontology mappings.

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Computational Complexity in Natural Language

Pratt-Hartmann

2010

The Handbook of Computational Linguistics and Natural Language Processing

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We have become so used to viewing natural language in computational terms that we need occasionally to remind ourselves of the methodological commitment this view entails. That commitment is this: we assume that to understand linguistic tasks-tasks such as recognizing sentences, determining their structure, extracting their meaning, and manipulating the information they contain-is to discover the algorithms required to perform those tasks, and to investigate their computational properties. To be sure, the physical realization of the corresponding processes in humans is a legitimate study too, but one from which the computational investigation of language may be pursued in Splendid Isolation. Complexity Theory is the mathematical study of the resources-both in time and space-required to perform computational tasks. What bounds can we place-from above or below-on the number of steps taken to compute such-and-such a function, or a function belonging to such-and-such a class? What bounds can we place on the amount of memory required? It is not surprising, therefore, that in the study of natural language, complexity-theoretic issues abound.Since any computational task can be the object of complexity-theoretic investigation, it would be hopeless even to attempt a complete survey of Complexity Theory in the study of natural language. We focus therefore on a selection of topics in natural language where there has been a particular accumulation of complexity-theoretic results. Section 2 discusses parsing and recognition; Section 3 discusses the computation of logical form; and Section 4 discusses the problem of determining logical relationships between sentences in natural language. But we begin with a brief review of the Complexity Theory itself.

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Complexity and expressive power of logic programming

Cited by 478 publications

References 261 publications

Machine learning: a review of classification and combining techniques

Machine learning: a review of classification and combining techniques

Tightly integrated probabilistic description logic programs for representing ontology mappings

Computational Complexity in Natural Language

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