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Class expressions

A class-expression is either a class name $ \textsf{CN}$ (some of which have predefined interpretations), an enumerated-class, a slot-constraint, a conjunction of class expressions, written $ C_1 \sqcap \ldots \sqcap C_n$, a disjunction of class expressions, written $ C_1 \sqcup \ldots \sqcup C_n$ or a negated class expression, written $ \neg C$.

The class names top, thing and bottom have pre-defined interpretations: top and thing are interpreted as the most general class (written $ \top$), while bottom is interpreted as the inconsistent class (written $ \bot$). Note that top and bottom can just be considered as abbreviations for the class expressions $ (C~\key{or}~(\key{not}~C))$ and $ (C~\key{and}~(\key{not}~C))$ respectively (for some arbitrary class $ C$).

An enumerated-class consists of a list of individual names (introduced by the one-of key word) written $ i_1,\ldots,i_n$.

Ian Horrocks 2000-09-10