and for this logic, exactly one KB accomplishes the insertion of a set of ABox assertions minimally. It follows that for instance-level insertion, their bold semantics coincides with ours. On the other hand, the presence of identification assertions in DL-LiteA,id **changes the picture considerably, since with such assertions in the TBox, many KBs may exist accomplishing the insertion minimally.**
In this case, the two approaches are indeed different. Finally, [6] proposes a variant of the bold semantics, called careful semantics**, for instance-level insertion**
in DL-LiteFR**. Intuitively, such a semantics aims at disregarding knowledge that**
is entailed neither by the original KB, nor by the set of newly asserted facts. Although such principle is interesting, we believe that the careful semantics is too drastic, as it tends to eliminate too many information from the original KB as shown in the following example.

Example 3. Consider the KB K of the Example 1, and suppose that we c **is now**
a member of a formula one team, which means changing K **with the insertion of**
TM(c**). Notice that such a new fact does not contradict any information** in K. Therefore, in our approach, the result of the insertion is hT , {OD(s), mf(**s, t**1), T D(b), TM(p), TM(c) }i**. Conversely, one can verify that the result under the**
careful semantics is hT , {OD(s), mf(s, t1), TM(c) }i**, thus loosing both the** information that b is a test driver, and the information that p **is a team member.**
Finally, we point out that, to our knowledge, the evolution operator **presented**
in this work is the first tractable evolution operator based on the WIDTIO
principle.

## 4 Deletion In Dl-Lite**A,Id**

We study deletion under the assumption that the DL language L is DL-Lite**A,id**.

Thus, we refer to a DL-LiteA,id-KB K = hT , Ai**, and we address the problem of**
changing K with the deletion of a finite set F **of ABox assertions. We assume**
that both hT , Ai and hT , Fi **are satisfiable.**
The following theorem specifies when a DL-LiteA,id**-KB accomplishes the**
deletion of F from hT , Ai **minimally.**
Theorem 1. hT , A′i accomplishes the deletion of F from hT , Ai minimally if and only if clT (A′) is a maximal T -closed subset of clT (A) such that F 6⊆
clT (A′).

We now consider the case where the set F **is constituted by just one assertion**
f**. By exploiting Theorem 1, it is easy to conclude that there is exactly one KB** accomplishing the deletion of {f} **from a given KB.**
Theorem 2. Let f be an ABox assertion. Up to logical equivalence, there is exactly one KB of the form hT , A′i that accomplishes the deletion of {f} from hT , Ai minimally, and such KB can be computed in polynomial time with respect to **|T |** and |A|.