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=====Concepts===== The set of <math>\mathcal{ALC}</math> ''concepts'' is the smallest set such that: * The following are ''concepts'': ** <math>\top</math> (''top'' is a ''concept'') ** <math>\bot</math> (''bottom'' is a ''concept'') ** Every <math>A \in N_C</math> (all ''atomic concepts'' are ''concepts'') * If <math>C</math> and <math>D</math> are ''concepts'' and <math>R \in N_R</math> then the following are ''concepts'': ** <math>C\sqcap D</math> (the intersection of two ''concepts'' is a ''concept'') ** <math>C\sqcup D</math> (the union of two ''concepts'' is a ''concept'') ** <math>\neg C</math> (the complement of a ''concept'' is a ''concept'') ** <math>\forall R.C</math> (the universal restriction of a ''concept'' by a ''role'' is a ''concept'') ** <math>\exists R.C</math> (the existential restriction of a ''concept'' by a ''role'' is a ''concept'')
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