Tight Complexity Bounds for Reasoning in the Description Logic $\mathcal{BE{\kern-.1em}L}$

Ceylan, İsmail İlkan; Peñaloza, Rafael

doi:10.1007/978-3-319-11558-0_6

Cited by 3 publications

(5 citation statements)

References 14 publications

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“…Using this idea, we also obtain tight complexity bounds for many expressive DLs, and good upper bounds for others. This paper collects, extends, and improves on the results previously published in two international conferences and a workshop [14][15][16]; see also [13]. In particular, in this paper we show how to handle also conditional probabilistic inferences, as opposed to the material implication used in previous work; we provide a simpler and smaller construction of the proof structure; and provide full proofs for our results.…”

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confidence: 63%

The Bayesian Ontology Language $$\mathcal {BEL}$$ BEL

Ceylan¹,

Peñaloza²

2016

J Autom Reasoning

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We introduce the new probabilistic description logic (DL) BEL, which extends the light-weight DL EL with the possibility of expressing uncertainty about the validity of some knowledge. Contrary to other probabilistic DLs, BEL is designed to represent classical knowledge that depends on an uncertain context; that is, some of the knowledge may hold or not depending on the current situation. The probability distribution of these contexts is expressed by a Bayesian network (BN).We study different reasoning problems in BEL, providing tight complexity bounds for all of them. One particularly interesting property of our framework is that reasoning can be decoupled between the logical (i.e., EL), and the probabilistic (i.e., the BN) components. We later generalize all the notions presented to introduce Bayesian extensions of arbitrary ontology languages. Using the decoupling property, we are able to provide tight complexity bounds for reasoning in the Bayesian extensions of many other DLs. We provide a detailed analysis of our formalism w.r.t. the assumptions made and compare it with the existing approaches.

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confidence: 63%

The Bayesian Ontology Language $$\mathcal {BEL}$$ BEL

Ceylan¹,

Peñaloza²

2016

J Autom Reasoning

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“…In previous work, the standard reasoning problems for EL have been extended to their probabilistic variant in BEL, leading to tight complexity bounds for several problems [11,12]. Particularly, it has been shown that the complexity of these tasks is bounded by the complexity of reasoning in EL and in the BN.…”

Section: Preliminariesmentioning

confidence: 99%

“…For the combined complexity, coNP PP -hardness is immediate since deciding one most likely context for simple queries is already coNP PP -hard w.r.t. KB complexity [12]. We prove that top-k mlc is in coNP PP : If a tuple is not a top-k mlc, then guess a new context κ and show using a PP oracle that K κ |= q and P B (κ) > P B (κ k ).…”

Section: Most Likely Contexts For a Querymentioning

confidence: 99%

“…As is in BEL, BDL-Lite only allows probabilities over axioms and conditional dependencies are represented faithfully. However, as it has been pointed before [12], the authors use a closed world assumption, which easily leads to inconsistencies.…”

Section: Related Workmentioning

confidence: 99%

“…the size of the logical component of the input, although intractable w.r.t. the BN [11,12]. These analysis have also shown their impact in practice, we refer the reader to the recent prototypical reasoner BORN [8] for such details (available at http://lat.inf.tu-dresden.de/systems/born).…”

Section: Introductionmentioning

confidence: 99%

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Probabilistic Query Answering in the Bayesian Description Logic $$\mathcal {BE{}L}$$

Ceylan

Peñaloza

2015

Lecture Notes in Computer Science

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BEL is a probabilistic description logic (DL) that extends the lightweight DL EL with a joint probability distribution over the axioms, expressed with the help of a Bayesian network (BN). In recent work it has been shown that the complexity of standard logical reasoning in BEL is the same as performing probabilistic inferences over the BN. In this paper we consider conjunctive query answering in BEL. We study the complexity of the three main problems associated to this setting: computing the probability of a query entailment, computing the most probable answers to a query, and computing the most probable context in which a query is entailed. In particular, we show that all these problems are tractable w.r.t. data and ontology complexity.

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A Bayesian Extension of the Description Logic $$\mathcal {ALC}$$

Botha

Meyer

Peñaloza

2019

Logics in Artificial Intelligence

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Description logics (DLs) are well-known knowledge representation formalisms focused on the representation of terminological knowledge. A probabilistic extension of a light-weight DL was recently proposed for dealing with certain knowledge occurring in uncertain contexts. In this paper, we continue that line of research by introducing the Bayesian extension BALC of the DL ALC. We present a tableau-based procedure for deciding consistency, and adapt it to solve other probabilistic, contextual, and general inferences in this logic. We also show that all these problems remain ExpTime-complete, the same as reasoning in the underlying classical ALC.

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Tight Complexity Bounds for Reasoning in the Description Logic $\mathcal{BE{\kern-.1em}L}$

Cited by 3 publications

References 14 publications

The Bayesian Ontology Language $$\mathcal {BEL}$$ BEL

The Bayesian Ontology Language $$\mathcal {BEL}$$ BEL

Probabilistic Query Answering in the Bayesian Description Logic $$\mathcal {BE{}L}$$

A Bayesian Extension of the Description Logic $$\mathcal {ALC}$$

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