Towards mechanical metamathematics
Journal of Automated Reasoning
Systematic software development using VDM (2nd ed.)
Systematic software development using VDM (2nd ed.)
Proving termination with multiset orderings
Communications of the ACM
Classical Propositional Decidability via Nuprl Proof Extraction
Proceedings of the 11th International Conference on Theorem Proving in Higher Order Logics
Formalizing Basic First Order Model Theory
Proceedings of the 11th International Conference on Theorem Proving in Higher Order Logics
A Terminological Knowledge Representation System with Complete Inference Algorithms
PDK '91 Proceedings of the International Workshop on Processing Declarative Knowledge
PVS: A Prototype Verification System
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
The description logic handbook: theory, implementation, and applications
The description logic handbook: theory, implementation, and applications
Implementation and optimization techniques
The description logic handbook
A PVS Graph Theory Library
Constructing Formally Verified Reasoners for the ALC Description Logic
Electronic Notes in Theoretical Computer Science (ENTCS)
Formalization and Implementation of Modern SAT Solvers
Journal of Automated Reasoning
A formally verified prover for the ALC description logic
TPHOLs'07 Proceedings of the 20th international conference on Theorem proving in higher order logics
The Mechanical Verification of a DPLL-Based Satisfiability Solver
Electronic Notes in Theoretical Computer Science (ENTCS)
FaCT++ description logic reasoner: system description
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
A mechanically verified, sound and complete theorem prover for first order logic
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
A Proof Theory for Description Logics
A Proof Theory for Description Logics
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Description Logics are a family of logics used to represent and reason about conceptual and terminological knowledge. One of the most basic description logics is ${\mathcal{ALC}}$, used as a basis from which to obtain others. Description logics are particularly important to provide a logical basis for the web ontology languages (such as OWL) used in the Semantic Web. In order to increase the reliability of the Semantic Web, formal methods can be applied, and in particular formal verification of its reasoning services can be carried out. In this paper, we present the formal verification of a tableau-based satisfiability algorithm for the logic ${\mathcal{ALC}}$. The verification has been completed in several stages. First, we develop an abstract formalization of satisfiability-checking of ${\mathcal{ALC}}$-concepts. Secondly, we define and formally verify a tableau-based algorithm in which the order of rule application and branch selection can be flexibly specified, using a methodology of refinements to transfer the main properties from the ${\mathcal{ALC}}$ abstract formalization. Finally, we obtain verified and executable reasoners from the algorithm via a process of instantiation.