in case B(c) was true before and C(c) was false. Since A **is interpreted under the** closed world assumption, we can now conclude that A(c**) is false:**
P ⊕T(A1, A2) |= { ¬A(c), ¬B(c), ¬A(d) }
Consider now the update A3 = { C(c) ∧ E(d) }**. Given (2), this reinstates** A(c).

Furthermore, rule (6) can now infer P(c, d**) and by (3) we obtain** D(d):
P ⊕T(A1, A2, A3) |= { A(c), ¬B(c), C(c), ¬A(d), E(d), P(c, d), D(d) }
In the next update A4 = { E(c) } **we block the body of rule (6), which also prevents**
D(d**) from being inferred:**
P ⊕T(A1, A2, A3, A4) |= { A(c), ¬B(c), C(c), ¬A(d), E(d), E(c) }
The last update7 A5 = { ¬E(c) ∧ ¬P(c, d) } **illustrates how the conclusion of a rule**
may be overridden through the ABox updates - though the body of **rule (6) is true,**
its head does not become true since it is in direct conflict with A5:
P ⊕T(A1, A2, A3, A4, A5) |= { A(c), ¬B(c), C(c), ¬A(d), E(d), ¬E(c), ¬P(**c, d**) }

## 4 Properties And Relations

In this section we investigate a number of formal properties of the **defined operator.** The first property guarantees that every minimal change dynamic **stable model of**
P⊕T A is a model of A. This is known as the **principle of primacy of new information**
(Dalal 1988). Proposition 4.1 (**Primacy of new information**) Let P be a finite ground program, T a TBox, A an ABox and M **a minimal change**
dynamic stable model of P ⊕T A**. Then** M |= A.

## Proof

See Appendix Appendix D, page 35.

The second property guarantees that our operator is syntax-independent w.r.t.

the TBox and the updating ABox. This is a desirable property as it shows that providing equivalent TBoxes and updating by equivalent ABoxes always produces the same result. It is inherited from the classical minimal change update operator. Proposition 4.2 (**Syntax independence**)
Let P **be a finite ground program,** T , T
′ **be TBoxes such that** mod(T ) = mod(T
′),
A, A′ **be ABoxes such that** mod(A) = mod(A′) and M **be an MKNF interpretation.**
Then M is a minimal change dynamic stable model of P ⊕T A **if and only if** M is a minimal change dynamic stable model of P ⊕T
′

A′.