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Reasoning in expressive description logics with fixpoints based on automata on infinite trees
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In this paper we formalize UML class diagrams in terms of a logic belonging to Description Logics, which are subsets of First-Order Logic that have been thoroughly investigated in Knowledge Representation. The logic we have devised is specifically tailored towards the high expressiveness of UML information structuring mechanisms, and allows one to formally model important properties which typically can only be specified by means of qualifiers. The logic is equipped with decidable reasoning procedures which can be profitably exploited in reasoning on UML class diagrams. This makes it possible to provide computer aided support during the application design phase in order to automatically detect relevant properties, such as inconsistencies and redundancies.