Converting ALC Connection Proofs into ALC Sequents

TL;DR

This paper introduces a method to convert connection proofs in ALC into sequent proofs, enhancing understandability and facilitating natural language explanations, addressing the complexity caused by previous transformations.

Contribution

It presents a novel conversion technique from connection proofs to sequent proofs in ALC, improving proof readability and interpretability in description logic reasoning.

Findings

Conversion method successfully produces more understandable proofs.

Enhanced proof interpretability aids in explanation and justification.

The approach simplifies translation to natural language.

Abstract

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.