Knowledge Base Revision in Description Logics

This paper offers an approach to extensible knowledge representation and reasoning for a family of formalisms known as Description Logics. The approach is based on the notion of adding new concept constructors, and includes a heuristic methodology for specifying the desired extensions, as well as a modularized software architecture that supports implementing extensions. The architecture detailed here falls in the normalize-compared paradigm, and supports both intentional reasoning (subsumption) involving concepts, and extensional reasoning involving individuals after incremental updates to the knowledge base. The resulting approach can be used to extend the reasoner with specialized notions that are motivated by specific problems or application areas, such as reasoning about dates, plans, etc. In addition, it provides an opportunity to implement constructors that are not currently yet sufficiently well understood theoretically, but are needed in practice. Also, for constructors that are provably hard to reason with (e.g., ones whose presence would lead to undecidability), it allows the implementation of incomplete reasoners where the incompleteness is tailored to be acceptable for the application at hand.

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Reasoning About Typicality and Probabilities in Preferential Description Logics

Applications and Practices in Ontology Design, Extraction, and Reasoning - Studies on the Semantic Web ◽

10.3233/ssw200041 ◽

2020 ◽

Author(s):

Laura Giordano ◽

Valentina Gliozzi ◽

Antonio Lieto ◽

Nicola Olivetti ◽

Gian Luca Pozzato

Keyword(s):

Knowledge Base ◽

Minimal Model ◽

Description Logics ◽

The Other ◽

Rational Closure ◽

Preferential Semantics ◽

Concept Combination ◽

Basic Concepts ◽

The One ◽

Property Inheritance

In this work we describe preferential Description Logics of typicality, a nonmonotonic extension of standard Description Logics by means of a typicality operator T allowing to extend a knowledge base with inclusions of the form T(C) ⊑ D, whose intuitive meaning is that “normally/typically Cs are also Ds”. This extension is based on a minimal model semantics corresponding to a notion of rational closure, built upon preferential models. We recall the basic concepts underlying preferential Description Logics. We also present two extensions of the preferential semantics: on the one hand, we consider probabilistic extensions, based on a distributed semantics that is suitable for tackling the problem of commonsense concept combination, on the other hand, we consider other strengthening of the rational closure semantics and construction to avoid the so called “blocking of property inheritance problem”.

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A Framework for Reasoning about Dynamic Axioms in Description Logics

Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2020/233 ◽

2020 ◽

Author(s):

Bartosz Bednarczyk ◽

Stephane Demri ◽

Alessio Mansutti

Keyword(s):

Knowledge Representation ◽

Knowledge Base ◽

Data Structures ◽

Description Logics ◽

Knowledge Bases ◽

Dynamic Data Structures ◽

Dynamic Data ◽

Logical Connectives ◽

Consistency Problem ◽

Natural Means

Description logics are well-known logical formalisms for knowledge representation. We propose to enrich knowledge bases (KBs) with dynamic axioms that specify how the satisfaction of statements from the KBs evolves when the interpretation is decomposed or recomposed, providing a natural means to predict the evolution of interpretations. Our dynamic axioms borrow logical connectives from separation logics, well-known specification languages to verify programs with dynamic data structures. In the paper, we focus on ALC and EL augmented with dynamic axioms, or to their subclass of positive dynamic axioms. The knowledge base consistency problem in the presence of dynamic axioms is investigated, leading to interesting complexity results, among which the problem for EL with positive dynamic axioms is tractable, whereas EL with dynamic axioms is undecidable.

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Research on Consistency Checking of OntoUML Model

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.433-440.2862 ◽

2012 ◽

Vol 433-440 ◽

pp. 2862-2867

Author(s):

Bin Yang ◽

Yu Dong Qi ◽

Xiu We Wang ◽

Ya Ning Wang

Keyword(s):

Knowledge Base ◽

Conceptual Model ◽

Description Logics ◽

Conceptual Modeling ◽

Modeling Language ◽

Consistency Checking ◽

Model Based ◽

Reasoning System ◽

Uml Metamodel

OntoUML is a conceptual modeling language which is built with a lightweight expansion of UML metamodel, but it doesn’t provide mechanism of consistency checking on conceptual model. The correctness of the syntax and semantics of the model still need artificial check. The paper introduced OntoUML briefly and put forward a scheme of consistency checking of OntoUML model based on description logics. By transforming into knowledge base of description logics, the detection of consistencies at the OntoUML model can be realized using existing mature reasoning system.

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