Forgetting Concept and Role Symbols in $\mathcal{ALCH}$ -Ontologies

Koopmann, Patrick; Schmidt, Renate A.

doi:10.1007/978-3-642-45221-5_37

Cited by 15 publications

(19 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Fixpoint operators are not supported by the web ontology standard OWL, which is why Lethe offers two ways to eliminating them when producing the result: by either approximation, or by using auxiliary concept names, so-called definers, that simulate the behaviour of greatest fixpoints and make sure all logical entailments of the uniform interpolant are kept. (For details, see [9]. )…”

Section: Uniform Interpolation and Related Tasksmentioning

confidence: 99%

“…Lethe is a tool that can be used to compute uniform interpolants in different expressive DLs. 1 Internally, it uses a resolution method presented in [9] for ALCH TBoxes, and later extended to SHQ [10] and knowledge bases consisting of both a TBox and an ABox [11]. Since those publications, a few bugfixes, optimisations and new features have been implemented.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

LETHE: Forgetting and Uniform Interpolation for Expressive Description Logics

Koopmann

2020

Künstl Intell

Self Cite

View full text Add to dashboard Cite

Uniform interpolation and forgetting describe the task of projecting a given ontology into a user-specified vocabulary, that is, of computing a new ontology that only uses names from a specified set of names, while preserving all logical entailments that can be expressed with those names. This is useful for ontology analysis, ontology reuse and privacy. Lethe is a tool for performing uniform interpolation on ontologies in expressive description logics, and it can be used from the command line, using a graphical interface, and as a Java library. It furthermore implements methods for computing logical difference and performing abduction using uniform interpolation. We present the tool together with an evaluation on a varied corpus of realistic ontologies.

show abstract

Section: Uniform Interpolation and Related Tasksmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

LETHE: Forgetting and Uniform Interpolation for Expressive Description Logics

Koopmann

2020

Künstl Intell

Self Cite

View full text Add to dashboard Cite

show abstract

“…Koopmann and Schmidt presented another resolution-based method exploiting structural transformation to compute uniform interpolants of ALC-TBoxes, which uses fixpoint operators to make uniform interpolants finitely representable [14]. The method has been further extended to handle ALCH [12], SIF [17], SHQ [15], and ALC with ABoxes [18].…”

Section: Related Workmentioning

confidence: 99%

“…Forgetting can be viewed as the problem that is dual to uniform interpolation. A lot of recent work has been focussed on uniform interpolation of mainly TBoxes represented in several description logics, ranging from ones with more limited expressivity, such as DL-Lite [31] and EL [20,22] and EL-extensions [11], to more expressive ones, such as ALC [21,30,19,14,13], ALCH [12], SIF [17] and SHQ [15].…”

Section: Introductionmentioning

confidence: 99%

Concept Forgetting in $$\mathcal {ALCOI}$$-Ontologies Using an Ackermann Approach

Zhao

Schmidt

2015

The Semantic Web - ISWC 2015

Self Cite

View full text Add to dashboard Cite

Abstract. We present a method for forgetting concept symbols in ontologies specified in the description logic ALCOI. The method is an adaptation and improvement of a second-order quantifier elimination method developed for modal logics and used for computing correspondence properties for modal axioms. It follows an approach exploiting a result of Ackermann adapted to description logics. An important feature inherited from the modal approach is that the inference rules are guided by an ordering compatible with the elimination order of the concept symbols. This provides more control over the inference process and reduces non-determinism, resulting in a smaller search space. The method is extended with a new case splitting inference rule, and several simplification rules. Compared to related forgetting and uniform interpolation methods for description logics, the method can handle inverse roles, nominals and ABoxes. Compared to the modal approach on which it is based, it is more efficient in time and improves the success rates. The method has been implemented in Java using the OWL API. Experimental results show that the order in which the concept symbols are eliminated significantly affects the success rate and efficiency.

show abstract

“…Lutz and Wolter [18] propose an approach to uniform interpolation in expressive description logics such as ALC featuring general terminologies showing a tight triple-exponential bound on the size of uniform interpolants. Koopmann and Schmidt [19] and Ludwig and Konev [20] propose practical approaches to computing uniform interpolants in expressive description logics. For the lightweight description logic EL, the problem of uniform interpolation has, however, not been solved.…”

Section: Introductionmentioning

confidence: 99%

(Non-)Succinctness of uniform interpolants of general terminologies in the description logic EL

Nikitina

Rudolph

2014

Artificial Intelligence

View full text Add to dashboard Cite

EL is a popular description logic, used as a core formalism in large existing knowledge bases. Uniform interpolants of knowledge bases are of high interest, e.g. in scenarios where a knowledge base is supposed to be partially reused. However, to the best of our knowledge no procedure has yet been proposed that computes uniform EL interpolants of general EL terminologies. Up to now, also the bound on the size of uniform EL interpolants has remained unknown. In this article, we propose an approach to computing a finite uniform interpolant for a general EL terminology if it exists. To this end, we develop a quadratic representation of EL TBoxes as regular tree grammars. Further, we show that, if a finite uniform EL interpolant exists, then there exists one that is at most triple exponential in the size of the original TBox, and that, in the worst case, no smaller interpolants exist, thereby establishing tight worst-case bounds on their size. Beyond showing these bounds, the notions and results established in this paper also provide useful insights for designing efficient ontology reformulation algorithms, for instance, within the context of module extraction.

show abstract

Forgetting Concept and Role Symbols in $\mathcal{ALCH}$ -Ontologies

Cited by 15 publications

References 8 publications

LETHE: Forgetting and Uniform Interpolation for Expressive Description Logics

LETHE: Forgetting and Uniform Interpolation for Expressive Description Logics

Concept Forgetting in $$\mathcal {ALCOI}$$-Ontologies Using an Ackermann Approach

(Non-)Succinctness of uniform interpolants of general terminologies in the description logic EL

Contact Info

Product

Resources

About