"... In PAGE 4: ... The constructors determine the expressive power of the DL. In this work, we consider concept descriptions built from the constructors shown in Table1 . In the description logic EL, concept descriptions are formed using the constructors top-concept ( gt;), conjunction (C u D) and existential restriction (9r:C).... ..."

"... In PAGE 6: ... The constructors determine the expressive power of the DL. In this work, we consider concept descriptions built from the constructors shown in Table1 . In the description logic EL, concept descriptions are formed using the constructors top-concept ( gt;), conjunction (C u D) and existential restriction (9r:C).... In PAGE 6: ... In the description logic EL, concept descriptions are formed using the constructors top-concept ( gt;), conjunction (C u D) and existential restriction (9r:C). The description logic ALE allows for all the constructors shown in Table1 . In the following, we refer to concept descriptions in the languages EL or ALE by EL- and ALE-concept descriptions, respectively.... ..."

"... In PAGE 2: ...echnical report [Baader et al., 2005]. 2 The Description Logic EL++ In DLs, concept descriptions are inductively defined with the help of a set of constructors, starting with a set NC of concept names, a set NR of role names, and (possibly) a set NI of individual names. In this section, we introduce the extension EL++ of EL, whose concept descriptions are formed using the constructors shown in the upper part of Table1 . There and in general, we use a and b to denote individual names, r and s to denote role names, and C; D to denote concept descriptions.... In PAGE 2: ... To provide a link between the DL and the concrete domain, we introduce a set of feature names NF. In Table1 , p denotes a predicate of some concrete domain D and f1; : : : ; fk are feature names. The DL EL++ may be equipped with a number of concrete domains D1; : : : ; Dn such that Di \ Dj = ; for 1 i lt; j n.... In PAGE 2: ... The extension of I to arbitrary concept descriptions is inductively defined as shown in the third column of Table 1. An EL++ constraint box (CBox) is a finite set of general concept inclusions (GCIs) and role inclusions (RIs), whose syntax can be found in the lower part of Table1 . Note that a finite set of GCIs would commonly be called a general TBox.... In PAGE 2: ... We use the term CBox due to the presence of RIs. An inter- pretation I is a model of a CBox C if, for each GCI and RI in C, the conditions given in the third column of Table1 are satisfied. In the definition of the semantics of RIs, the symbol denotes composition of binary relations.... ..."

"... In PAGE 5: ... The constructors determine the expressive power of the DL. In this work, we consider concept descriptions built from the constructors shown in Table1 . In the description logic EL, concept descriptions are formed using the constructors top-concept ( gt;), conjunction (C u D) and existential restriction (9r:C); FLE extends EL by value restrictions (8r:C); the description logic ALE allows for all the constructors shown in Table 1.... ..."

"... In PAGE 5: ... The constructors determine the expressive power of the DL. In this work, we consider concept descriptions built from the constructors shown in Table1 . In the description logic EL, concept descriptions are formed using the constructors top-concept ( gt;), conjunction (C u D) and existential restriction (9r:C).... In PAGE 5: ... In the description logic EL, concept descriptions are formed using the constructors top-concept ( gt;), conjunction (C u D) and existential restriction (9r:C). The description logic EL: additionally provides us with primitive negation (:P, P 2 NC), and ALE allows for all the constructors shown in Table1 except of number restrictions. Finally, ALN allows for the top- and bottom-concept, concept conjunction, primitive negation, value restrictions, and number restric- tions.... ..."

"... In PAGE 2: ... With this LISP-like syntax, it is easy to port existing ontologies that have been used with well-known DL reasoners like FaCT and RACER. Table1 shows the concept constructors available in EL+ that can be used to form concept descriptions. For building up ontologies, the expressive means shown in Table 2 can be used, where conventionally A, B denotes a named concept, C, D concept descriptions, and r, s named roles.... ..."

"... In PAGE 2: ... We use the notation of DLs, focusing on the well-known DL ALC, corresponding to the standard PDL with atomic programs only. Table1 summarizes the syntax and the semantics of ALC and the corresponding PDL. In addition, weusethetwo nonmonotonic modal operators: a minimal knowledge operator K and a default assumption operator A.... ..."