for all the other rules, their negative bodies are discarded. Then PM **is updated by**
A using the above definition for definite logic programs and if the result **is identical**
to M, then M is given the status of a minimal change dynamic stable model**. Hence,**
the resulting operator can be used to update an arbitrary normal **logic program by** a sequence of ABoxes. Definition 3.4 (**Minimal change dynamic stable model**) Let P be a finite ground program, T a TBox, A **a sequence of ABoxes and** M an MKNF interpretation. We say M is a **minimal change dynamic stable model of**
P ⊕T A if M is a minimal change dynamic stable model of PM ⊕T A **where**

## P M =H(R) ⊂ B +(R) R **∈ P ∧** M |= B −(R)	.

The minimal change dynamic stable models can be used to define a consequence relation from P ⊕T A where P is a finite ground program, T **is a TBox and** A
a sequence of ABoxes. We offer a definition which adopts a skeptical **approach to**
inference, credulous and other definitions may be obtained similarly.

Definition 3.5 (**Consequence relation**) Let P be a finite ground program, T a TBox, A **a sequence of ABoxes and** φ an MKNF sentence. We say that P ⊕T A entails φ, written P ⊕T A |= φ**, if and only**
if M |= φ for all minimal change dynamic stable models M of P ⊕T A.

We now demonstrate the defined update semantics on a simple example:
Example 3.6 Consider the following TBox T **and program** P:

$\mathcal{T}:\quad A\equiv B\sqcup C$  $\quad$Neg$A\equiv\neg A$  $\quad$D$\equiv\neg A\sqcap\exists P^{-}.A$  $\mathcal{P}:\quad$Neg$A(X)\gets not\,A(X)$.  $\quad$P(X,Y)\gets A(X),E(Y),not\,E(X)$.  
$$\left(2\right)$$

TBox assertions (2) and (3) together with rule (5) define the concept A **as a union** of concepts B and C **and they make this concept interpreted under CWA instead of**
OWA, i.e. whenever for some constant c we cannot conclude that A(c**) is true, the**
rule (5) infers NegA(c) and by (3) we obtain ¬A(c**). Assertion (4) defines concept**
D as those members d of ¬A for which there exists some c from A with P(**c, d**).

Rule (6) infers the relation P(c, d) whenever c is in A but not in E and d **is in** E.

Given the initial definitions, an update by A1 = { A(c) } **now yields**6 P ⊕T A1 |= { A(c), ¬A(d) } .

A further update by A2 = { ¬B(c) } introduces a possibility of A(c**) not being true**
6 In the example we assume that the rules are grounded using all **constants explicitly mentioned**
in the knowledge base. In this case there are only two: c and d.