
| Constru t            | Syntax   | Semanti s                            |
|----------------------|----------|--------------------------------------|
| ept                  | A        | AI  I                                      |
| atomi   on  negation | :A       | I n AI                                      |
| atomi tion           | C1 u C2  | CI 1 \ CI                            |
| onjun                | 2        |                                      |
| tion                 | C1 t C2  | CI 1 [ CI                            |
| disjun               | 2        |                                      |
| ation                | 8R.C     | fo j 8o . (o; o0 ) 2 RI ! o 2 CI 0 0 |
| universal quanti     | g        |                                      |
| tions                | 9nR          | fo j ℄fo0 j (o; o0 ) 2 RI g  ng1                                      |
| number restri        | 9nR          | fo j ℄fo0 j (o; o0 ) 2 RI g  ng                                      |
| role                 | P        | P I  I  I                                      |
| atomi inverse role   | P        | ; o) 2 P I g                         |
| f(o; o0 ) j (o 0     |          |                                      |

symbols and by applying suitable onstru tors. It is the set of allowed onstru ts that hara terizes the des ription language.

 A know ledge spe i ation me hanism, whi h spe ies how to onstru t a DL knowledge base, in whi h properties of on epts and roles are asserted.

 A set of basi reasoning tasks provided by the DL.

In the rest of the se tion we des ribe the spe i form that these three omponents assume in aluni.

## 2.1 The Des Ription Language Of Aluni

In the des ription language of aluni, alled ALUN I, 
on epts and roles are formed a
-

ording to the syntax shown in Table 1, where A denotes an atomi
 
on ept, P an atomi role, C an arbitrary on ept expression, R an arbitrary role expression, and n a nonnegative integer. To in rease readability of on ept expressions, we also introdu e the following abbreviations:

$$\begin{array}{r l}{\equiv}&{{}A\sqcup\neg A,\quad{\mathrm{for~some~atomic~concept~}}A}\\ {\equiv}&{{}A\sqcap\neg A,\quad{\mathrm{for~some~atomic~concept~}}A}\\ {\equiv}&{{}\exists^{\geq1}R}\\ {\equiv}&{{}\exists^{\leq n}R\sqcap\exists^{\geq n}R}\end{array}$$
$\huge\color{blue}{\dashv}$  . 
$$\begin{array}{c}{{\bot}}\\ {{\exists R}}\\ {{\exists^{=n}R}}\end{array}$$

Con epts are interpreted as subsets of a domain and roles as binary relations over that domain. Intuitively, :A represents the negation of an atomi
 
on ept, and is interpreted as the omplement with respe t to the domain of interpretation. C1 u C2 represents the onjun tion of two on epts and is interpreted as set interse tion, while C1 t C2 represents disjun tion and is interpreted as set union. Consequently, > represents the whole domain, 1. ℄S denotes the ardinality of a set S.

