A Proof Theory for Description Logics

Description Logics (DLs) is a family of formalisms used to represent knowledge of a domain. They are equipped with a formal logic-based semantics. Knowledge representation systems based on description logics provide various inference capabilities that deduce implicit knowledge from the explicitly represented knowledge.

A Proof Theory for Description Logics introduces Sequent Calculi and Natural Deduction for some DLs (ALC, ALCQ). Cut-elimination and Normalization are proved for the calculi. The author argues that such systems can improve the extraction of computational content from DLs proofs for explanation purposes.

Provides an innovative approach for reasoning with description logic theories Presents future practical applications of description logic proof theories Includes supplementary material: sn.pub/extras

Inhalt

Introduction.- Background.- Sequent Calculus for ALC.- Comparing SCalc with other ALC Deduction Systems.- Natural Deduction for ALC.- A Proof Theory for ALCQI.- Proofs and Explanations.- A Prototype Theorem Prover.- Conclusion.