Linkless Normal Form for ALC Concepts and TBoxes

@inproceedings{Schon2011LinklessNF,
  title={Linkless Normal Form for ALC Concepts and TBoxes},
  author={Claudia Schon},
  booktitle={KI},
  year={2011}
}
  • C. Schon
  • Published in KI 4 October 2011
  • Computer Science
In this paper we introduce a normal form for \(\mathcal{ALC}\) concepts and TBoxes called linkless normal form. We investigate properties of concepts given in this normal form such as an efficient satisfiability test and the calculation of uniform interpolants. We further show a way to approximate a TBox by a concept in linkless normal form, which allows us to check certain subsumptions efficiently. This makes the linkless normal form interesting from the viewpoint of knowledge compilation… 

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References

SHOWING 1-10 OF 24 REFERENCES

Linkless normal form for ALC concepts

TLDR
A normal form called linkless normal form for ALC concepts is introduced and an ecient satisability test for concepts given in this normal form is discussed and it is shown how to eciently calculate uniform interpolants of precompiled concepts w.r.t. a given signature.

Precompiling ALC TBoxes and Query Answering

TLDR
An efficient satisfiability test as well as a subsumption test for pr ecompiled concept descriptions are discussed and an algorithm, based on path dis solution, which can be used for this precompilation step is presented.

Tableaux, Path Dissolution, and Decomposable Negation Normal Form for Knowledge Compilation

TLDR
A class of formulae is presented on which earlier DNNF conversion techniques are necessarily exponential; path dissolution and semantic factoring handle these formulAE in linear time.

Knowledge compilation and theory approximation

TLDR
It is shown how propositional logical theories can be compiled into Horn theories that approximate the original information, and the approximations bound the original theory from below and above in terms of logical strength.

Computing Least Common Subsumers in Description Logics with Existential Restrictions

TLDR
The main new contribution of this paper is the treatment of description logics with existential restrictions, based on an appropriate representation of concept descriptions by certain trees, and a characterization of subsumption by homomorphisins between these trees.

A Knowledge Compilation Technique for ALC Tboxes

TLDR
An efficient satisfiability test as well as a subsumption test for precompiled concepts and Tboxes and the precompiling Tboxes are used for efficient Tbox reasoning.

Definitorially Complete Description Logics

TLDR
The topic of this paper is the effect of the available operations in a DL on the length and the syntactic shape of definitions in a Terminology Box, and the following property of DL's: every new conceptdefined in the implicit way can also be defined in the explicit manner.

Dissolution: making paths vanish

TLDR
A rule of inference that operates on formulas in negation normal form and that employs a representation called semantic graphs is introduced, which has several advantages in comparison with many other reference technologies.

Decomposable negation normal form

TLDR
It is shown that DNNF is universal; supports a rich set of polynomial--time logical operations; is more space-efficient than OBDDs; and is very simple as far as its structure and algorithms are concerned.

Prime Implicates and Prime Implicants in Modal Logic

TLDR
This paper considers a number of different potential definitions of clauses and terms for κ with respect to their syntactic, semantic, and complexity-theoretic properties and provides algorithms and complexity results for the prime implicate generation and recognition tasks.