Converting ALC Connection Proofs into ALC Sequents

Eunice Palmeira
(Federal Institute of Alagoas)
Fred Freitas
(Federal University of Pernambuco)
Jens Otten
(University of Oslo)

The connection method has earned good reputation in the area of automated theorem proving, due to its simplicity, efficiency and rational use of memory. This method has been applied recently in automatic provers that reason over ontologies written in the description logic ALC. However, proofs generated by connection calculi are difficult to understand. Proof readability is largely lost by the transformations to disjunctive normal form applied over the formulae to be proven. Such a proof model, albeit efficient, prevents inference systems based on it from effectively providing justifications and/or descriptions of the steps used in inferences. To address this problem, in this paper we propose a method for converting matricial proofs generated by the ALC connection method to ALC sequent proofs, which are much easier to understand, and whose translation to natural language is more straightforward. We also describe a calculus that accepts the input formula in a non-clausal ALC format, what simplifies the translation.

In Giselle Reis and Haniel Barbosa: Proceedings Sixth Workshop on Proof eXchange for Theorem Proving (PxTP 2019), Natal, Brazil, August 26, 2019, Electronic Proceedings in Theoretical Computer Science 301, pp. 3–17.
Thanks to CAPES: Coordination for the Improvement of Higher Level Personnel.
Published: 23rd August 2019.

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