Formal verification of a proof procedure for the description logic ALC

@inproceedings{Chaabani2013FormalVO,
  title={Formal verification of a proof procedure for the description logic ALC},
  author={Mohamed Chaabani and Mohamed Mezghiche and Martin Strecker},
  booktitle={International Symposium on Symbolic Computation in Software Science},
  year={2013}
}
Description Logics (DLs) are a family of languages used for the representation and reasoning on the knowledge of an application domain, in a structured and formal manner. In order to achieve this objective, several provers, such as RACER and FaCT++, have been implemented, but these provers themselves have not been yet certified. In order to ensure the soundness of derivations in these DLs, it is necessary to formally verify the deductions applied by these reasoners. Formal methods offer… 
1 Citations

Tables from this paper

Axiomatic and dual systems for constructive necessity, a formally verified equivalence

ABSTRACT We present a proof of the equivalence between two deductive systems for constructive necessity, namely an axiomatic characterisation inspired by Hakli and Negri's system of derivations from

References

SHOWING 1-10 OF 23 REFERENCES

A Formally Verified Prover for the ALC Description Logic

The PVS specification of a prover for \(\mathcal{ALC\,}\) is presented, as well as the proofs of its termination, soundness and completeness, and the formalization of the well-foundedness of the multiset relation induced by a well–founded relation.

A Mechanically Verified, Sound and Complete Theorem Prover for First Order Logic

We present a system of first order logic, together with soundness and completeness proofs wrt. standard first order semantics. Proofs are mechanised in Isabelle/HOL. Our definitions are computable,

The Description Logic Handbook

This introduction presents the main motivations for the development of Description Logics (DLs) as a formalism for representing knowledge, as well as some important basic notions underlying all

Construction of Büchi Automata for LTL Model Checking Verified in Isabelle/HOL

The correctness and termination of the implementation of a translation of LTL formulae into Buchi automata are proven in Isabelle/HOL, and executable code is generated using the Isabelle /HOL code generator.

On Expressive Number Restrictions in Description Logics

  • F. Grandi
  • Computer Science
    Description Logics
  • 2001
It is shown by reduction of a domino problem that A LC N(+ ; t) and ALC N( + ; u) are undecidable, which represents very expressive description languages and can be shown very useful for applications.

A Scheme for Integrating Concrete Domains into Concept Languages

This paper shall define a terminological and an assertional language, and consider the important inference problems such as subsumption, instantiation, and consistency, and proposes a scheme for integrating such concrete domains into concept languages.

Isabelle/HOL: A Proof Assistant for Higher-Order Logic

This presentation discusses Functional Programming in HOL, which aims to provide students with an understanding of the programming language through the lens of Haskell.

Reasoning on UML Class Diagrams using Description Logic Based Systems

It is shown that UML class diagrams can be formalized as knowledge bases expressed in the DL DLR, and some experiments indicating that state-of-the-art systems have still difficulty in dealing with the resulting knowledge bases.

Reasoning on UML Class Diagrams using Description Logic Based Systems

The primary focus of this workshop was on applications of description logics, and Ian Horrocks gives a tutorial-style talk about latest developments in description logic research.

The Complexity of Concept Languages

A complexity analysis of concept satisfiability and subsumption for a wide class of concept languages and algorithms for these inferences that comply with the worst-case complexity of the reasoning task they perform.