An Intuitionisticaly based Description Logic

This article presents iALC, an intuitionistic version of the classical description logic ALC, based on the framework for constructive modal logics presented by Simpson \cite{simpson95} and related to description languages, via hybrid logics, by dePaiva \cite{depaiva2003}. This article correcta and extends the presentation of iALC appearing in \cite{PHR:2010}. It points out the difference between iALC and the intuitionistic hybrid logic presented in \cite{depaiva2003}. Completeness and soundness proofs are provided. A brief discussion on the computacional complexity of iALC provability is taken. It is worth mentioning that iALC is used to formalize legal knowledge \cite{HPR:2010a,HPR:2010ab,Jurix, HPR:2011}, and in fact, was specifically designed to this goal.