Probabilistic Reasoning in Terminological Logics

Jaeger, Manfred

doi:10.1016/b978-1-4832-1452-8.50124-x

Cited by 97 publications

(56 citation statements)

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“…The probabilistic information can either be embedded as part of the terminological axiom (Giugno & Lukasiewicz, 2002;Heinsohn, 1994;Jaeger, 1994) or be stored in Bayesian networks (Koller, Levy, & Pfeffer, 1997;Staker, 2002). For lack of space, we describe only the first approach here.…”

Section: Probabilistic Knowledge Basementioning

confidence: 99%

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Semantic Web Uncertainty Management

Haarslev

Pai

Shiri

2009

Encyclopedia of Information Science and Technology, Second Edition

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Since the introduction of the Semantic Web vision (Berners- Lee, Hendler, & Lassila, 2001), attempts have been made for making Web resources more machine interpretable by giving them a well-defined meaning through semantic markups. One way to encode such semantic markups is to use ontologies. An ontology is “an explicit specification of a conceptualization” (Gruber, 1993, p. 199). Informally, an ontology consists of a set of terms in a domain, relationships between the terms, and a set of constraints on the way in which those terms can be combined. By explicitly defining the relationships and constraints among the terms, the semantics of the terms can be better defined and understood. Over the last few years, a number of ontology languages have been developed, most of which use Description Logics (DLs) (Baader, McGuinness, Nardi, & Schneider, 2003) as the foundation. The family of DLs is a subset of first-order logic (FOL) and is considered to be attractive as it keeps a good compromise between expressive power and computational tractability. Uncertainty is a form of deficiency or imperfection in the information/data, where the truth of information is not established definitely. Uncertainty modeling and reasoning have been challenging issues for over two decades in many disciplines, such as database and artificial intelligence. Most of the information in the real world is uncertain or imprecise, for example, classifications of genes in bioinformatics, schema matching in information integration, finding best matches in a Web search, and so forth. Therefore, uncertainty management is essential for the success of many such applications and in particular DLs and the Semantic Web. Despite its popularity, it has been realized that classical DLs are inadequate to model uncertainty. For example, in the medical domain, one might want to express that: “It is very likely that an obese person would have heart disease,” where “obese” is a vague concept that may vary across regions and “likely” shows the uncertain nature of this information. Such an expression cannot be expressed using classical DLs. The importance of incorporating uncertainty in DLs has been recognized by the knowledge representation community: “modeling primitives such as … fuzzy/probabilistic definitions” could be the next step for extension (Horrocks et al., 2000, p. 3). For this, a number of frameworks have been proposed to incorporate uncertainty in DLs. This paper provides a survey of these proposals. The rest of this paper is organized as follows. We first provide the background on the classical DL framework. We then study representative extensions of DLs with uncertainty. This follows by some possible research directions for incorporating uncertainty in the Semantic Web. We conclude with a summary and some remarks.

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Section: Probabilistic Knowledge Basementioning

confidence: 99%

“…A probabilistic ABox (Giugno & Lukasiewicz, 2002;Jaeger, 1994) contains assertions of the form P(a:C)∈ [l,u], where C is a concept, a is an individual, and l, u∈ [0,1]. Intuitively, this asserts that "the probability that an individual a belongs to concept C lies in [l,u]."…”

Section: Probabilistic Knowledge Basementioning

confidence: 99%

Semantic Web Uncertainty Management

Haarslev

Pai

Shiri

2009

Encyclopedia of Information Science and Technology, Second Edition

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“…For practical applications and implementations one should consider suitable fragments of this logic, e.g. the probabilistic description logics described in (Jaeger 1994b). Such fragments can reduce the complexities of reasoning in L ip in several ways: they can enforce the closure of the sets ∆ F (φ, M), so that some of the difficulties described in section 3.3 are avoided; they can further reduce the discrepancy between realvalued and lrc-field valued probabilities, and thereby become complete also for real-valued probabilities; finally, and most importantly, fragments will give rise to specialized inference techniques that can make automated reasoning more effective.…”

Section: Resultsmentioning

confidence: 99%

A Logic for Inductive Probabilistic Reasoning

Jaeger

2005

Uncertainty, Rationality, and Agency

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Inductive probabilistic reasoning is understood as the application of inference patterns that use statistical background information to assign (subjective) probabilities to single events. The simplest such inference pattern is direct inference: from "70% of As are Bs" and "a is an A" infer that a is a B with probability 0.7. Direct inference is generalized by Jeffrey's rule and the principle of cross-entropy minimization. To adequately formalize inductive probabilistic reasoning is an interesting topic for artificial intelligence, as an autonomous system acting in a complex environment may have to base its actions on a probabilistic model of its environment, and the probabilities needed to form this model can often be obtained by combining statistical background information with particular observations made, i.e. by inductive probabilistic reasoning.In this paper a formal framework for inductive probabilistic reasoning is developed: syntactically it consists of an extension of the language of firstorder predicate logic that allows to express statements about both statistical and subjective probabilities. Semantics for this representation language are developed that give rise to two distinct entailment relations: a relation |= that models strict, probabilistically valid, inferences, and a relation |≈ that models inductive probabilistic inferences. The inductive entailment relation is obtained by implementing cross-entropy minimization in a preferred model semantics. A main objective of our approach is to ensure that for both entailment relations complete proof systems exist. This is achieved by allowing probability distributions in our semantic models that use non-standard probability values. A number of results are presented that show that in several important aspects the resulting logic behaves just like a logic based on realvalued probabilities alone.

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“…Another early approach to probabilistic description logics is due to Jaeger [61], who also proposes a probabilistic extension of the description logic ALC, which allows for terminological probabilistic knowledge about concepts and roles, and assertional probabilistic knowledge about concept instances, but does not support assertional probabilistic knowledge about role instances (but he mentions a possible extension in this direction). The entailment of terminological probabilistic knowledge from terminological probabilistic knowledge is based on the notion of logical entailment in probabilistic logic, while the entailment of assertional probabilistic knowledge from terminological and assertional probabilistic knowledge is based on a cross-entropy minimization relative to terminological probabilistic knowledge.…”

Section: Probabilistic Description Logicsmentioning

confidence: 99%

Managing uncertainty and vagueness in description logics for the Semantic Web

Lukasiewicz

Straccia

2008

Journal of Web Semantics

328

101

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a b s t r a c tOntologies play a crucial role in the development of the Semantic Web as a means for defining shared terms in web resources. They are formulated in web ontology languages, which are based on expressive description logics. Significant research efforts in the semantic web community are recently directed towards representing and reasoning with uncertainty and vagueness in ontologies for the Semantic Web. In this paper, we give an overview of approaches in this context to managing probabilistic uncertainty, possibilistic uncertainty, and vagueness in expressive description logics for the Semantic Web.

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Probabilistic Reasoning in Terminological Logics

Cited by 97 publications

References 10 publications

Semantic Web Uncertainty Management

Semantic Web Uncertainty Management

A Logic for Inductive Probabilistic Reasoning

Managing uncertainty and vagueness in description logics for the Semantic Web

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