Most of the work regarding complexity results for concept languages consider subsumption as the prototypical inference. However, when concept languages are used for building knowledge bases including assertions on individuals, the basic deductive service of the knowledge base is the so-called instance checking, which is the problem of checking if an individual is an instance of a given concept. We consider a particular concept language, calledALE, and we address the question of whether instance checking can be really solved by means of subsumption algorithms in this language. Therefore, we indirectly ask whether considering subsumption as the prototypical inference is justified. Our analysis, carried out considering two different measure of complexity, shows that inALE instance checking is strictly harder than subsumption. This result singles out a new source of complexity in concept languages, which does not show up when checking subsumption between concepts.
