[DL] question about the distinction between transitive roles and transitive closure

[Yvonne Violet Shashoua]

   I have been reading through the appendix in the Description Logic
Handbook.  On page 527, they mention that AL extended with transitive roles
is denoted by AL_R+.  That's in the section entitled Restrictions on Role
Interpretations.  But in the paragraph right above it, they use R^c instead
of R+.  Then, in a separate section, entitled Role Constructors, on page
529, they use the same symbol, R+, to denote the transitive closure role
constructor.  I assume that there's a difference between extending a
description logic with transitive roles, and making a description logic that
includes the transitive closure role constructor.  But could someone clarify
the distinction?  And is the only difference in the notation used for the
name of the language just whether you make R+ a subscript or superscript?  I
could use some help understanding this.  Thanks.
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