Axiomatization of General Concept Inclusions in Probabilistic Description Logics

Logic-based knowledge representation is one of the main building blocks of (logic-based) artificial intelligence. While most successful knowledge representation languages are based on classical logic, realistic intelligent applications need to handle uncertainty in an adequate manner. Over the years, many different languages for representing uncertain knowledge—often extensions of classical knowledge representation languages—have been proposed. We briefly present some of the defining properties of these languages as they pertain to the family of probabilistic description logics. This limited view is intended to help pave the way for the interested researcher to find the most adequate language for their needs, and potentially identify the remaining gaps.

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Hybrid Unification in the Description Logic EL

10.29007/h59c ◽

2018 ◽

Author(s):

Franz Baader ◽

Oliver Fernandez Gil ◽

Barbara Morawska

Keyword(s):

Description Logic ◽

Description Logics ◽

General Concept ◽

Biomedical Ontologies ◽

Declarative Semantics ◽

Np Complete ◽

Unification Algorithms

Unification in Description Logics (DLs) has been proposed as an inferenceservice that can, for example, be used to detect redundancies in ontologies.For the DL EL, which is used to define several largebiomedical ontologies, unification is NP-complete. However, the unification algorithms for EL developeduntil recently could not deal with ontologies containing general concept inclusions (GCIs).In a series of recent papers we have made some progress towards addressing this problem, but the ontologies thedeveloped unification algorithms can deal with need to satisfy a certain cycle restriction.In the present paper, we follow a different approach. Instead of restricting the input ontologies,we generalize the notion of unifiers to so-called hybrid unifiers. Whereas classical unifiers can be viewed as acyclic TBoxes,hybrid unifiers are cyclic TBoxes, which are interpreted together with the ontology of the input using a hybrid semantics thatcombines fixpoint and declarative semantics. We show that hybrid unification in EL is NP-complete

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Probabilistic Description Logics for Subjective Uncertainty

Journal of Artificial Intelligence Research ◽

10.1613/jair.5222 ◽

2017 ◽

Vol 58 ◽

pp. 1-66 ◽

Cited By ~ 6

Author(s):

Victor Gutierrez-Basulto ◽

Jean Christoph Jung ◽

Carsten Lutz ◽

Lutz Schröder

Keyword(s):

Description Logics ◽

Order Logic ◽

First Order Logic ◽

Two Dimensional ◽

Subjective Probabilities ◽

Subjective Uncertainty ◽

First Order ◽

New Family ◽

Probabilistic Description

We propose a family of probabilistic description logics (DLs) that are derived in a principled way from Halpern's probabilistic first-order logic. The resulting probabilistic DLs have a two-dimensional semantics similar to temporal DLs and are well-suited for representing subjective probabilities. We carry out a detailed study of reasoning in the new family of logics, concentrating on probabilistic extensions of the DLs ALC and EL, and showing that the complexity ranges from PTime via ExpTime and 2ExpTime to undecidable.

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The Probabilistic Description Logic

Theory and Practice of Logic Programming ◽

10.1017/s1471068420000460 ◽

2020 ◽

pp. 1-24

Author(s):

LEONARD BOTHA ◽

THOMAS MEYER ◽

RAFAEL PEÑALOZA

Keyword(s):

Knowledge Representation ◽

Description Logic ◽

Description Logics ◽

Light Weight ◽

Classical Form ◽

First Order ◽

Probabilistic Description

Abstract Description logics (DLs) are well-known knowledge representation formalisms focused on the representation of terminological knowledge. Due to their first-order semantics, these languages (in their classical form) are not suitable for representing and handling uncertainty. 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 of the propositionally closed DL . 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 .

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A Modular Inference System for Probabilistic Description Logics

Lecture Notes in Computer Science - Scalable Uncertainty Management ◽

10.1007/978-3-030-00461-3_6 ◽

2018 ◽

pp. 78-92

Author(s):

Giuseppe Cota ◽

Fabrizio Riguzzi ◽

Riccardo Zese ◽

Elena Bellodi ◽

Evelina Lamma

Keyword(s):

Description Logics ◽

Inference System ◽

Probabilistic Description

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Probabilistic Description Logics

Uncertainty Proceedings 1994 ◽

10.1016/b978-1-55860-332-5.50044-4 ◽

1994 ◽

pp. 311-318 ◽

Cited By ~ 47

Author(s):

Jochen Heinsohn

Keyword(s):

Description Logics ◽

Probabilistic Description

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Assessment of Uncertainties in Mechanical Models

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.378.13 ◽

2013 ◽

Vol 378 ◽

pp. 13-18 ◽

Cited By ~ 9

Author(s):

Miroslav Sýkora ◽

Milan Holicky

Keyword(s):

Model Uncertainty ◽

Mechanical Model ◽

General Concept ◽

Present Contribution ◽

Factors Affecting ◽

Uncertainty Factors ◽

Probabilistic Description ◽

Resistance Model ◽

Mechanical Models ◽

The Mean

Resistances of mechanical systems are primarily dependent on material properties, geometry and uncertainties associated to an applied resistance model. While materials and geometry can be relatively well described, the resistance model uncertainty is not yet well understood. The present contribution proposes a general concept of the model uncertainty. Factors affecting results obtained by tests and models and influences of actual structural conditions are overviewed. Application of theoretical principles is illustrated by an example of historic iron columns considering a simple mechanical model. Proposed probabilistic description of the model uncertainty consists of the lognormal distribution having the mean 1.35 and coefficient of variation of 0.12.

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