An Intuitionisticaly based Description Logic
Abstract
This article presents iALC, an intuitionistic version of the classical description logic ALC, based on the framework for constructive modal logics presented by Simpson simpson95 and related to description languages, via hybrid logics, by dePaiva depaiva2003. This article correcta and extends the presentation of iALC appearing in PHR:2010. It points out the difference between iALC and the intuitionistic hybrid logic presented in 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 HPR:2010a,HPR:2010ab,Jurix, HPR:2011, and in fact, was specifically designed to this goal.
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