  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.
