querying procedure (Alferes et al. 2009), making the approach amenable to practical applications that need to deal with large ontologies.

But this only addresses part of the problem. The highly dynamic character of the Semantic Web calls for the development of ways to deal with updates **of these hybrid**
knowledge bases composed of both rules and ontologies, and the inconsistencies that may arise. The dynamics of hybrid knowledge bases, to the best of our knowledge, has never been addressed before.

However, the problems associated with knowledge evolution have been extensively studied, over the years, by researchers in different research communities, namely in the context of Classical Logic, and in the context of Logic Programming. They proved to be extremely difficult to solve, and existing solutions, even **within each** community, are still subject of active debate as they do not seem adequate in all kinds of situations in which their application is desirable.

In the context of Classical Logic, the seminal work by Alchourr´on, G¨ardenfors and Makinson (AGM) (Alchourr´on et al. 1985) proposed a set of desirable properties of belief change operators, now called AGM postulates**. Subsequently, in**
(Katsuno and Mendelzon 1991), update and revision **have been distinguished as**
two very related but ultimately different belief change operations. While revision deals with incorporating new information about a static world, update takes place when changes occurring in a dynamic world are recorded. The authors of (Katsuno and Mendelzon 1991) formulated a separate set of postulates for updates. One of the specific update operators that satisfies these postulates is Winslett's minimal change update operator (Winslett 1990). Though we believe that revision operators for hybrid knowledge bases pose an interesting and important research topic, in this paper we focus on update operators and do not tackle **revision any** further.

Further research showed that, in most cases, belief update operators cannot be directly applied to Description Logic ontologies. The existing work considers only ABox updates, allowing only for static acyclic TBoxes which are "expanded" before the update takes place (Liu et al. 2006), or static general TBoxes in the form of integrity constraints (Giacomo et al. 2007). The main reasons for these restrictions were expressibility and computability of the updated ontology. But we believe there is a more fundamental problem with using belief update operators to **update TBoxes**
because it frequently yields counterintuitive results, as illustrated **here:**

## Example 1.1 (**Counterintuitive Tbox Update**)

Suppose we want to update the description logic TBox T = { B ⊑ A } **and we want** to update it with the new information U = { C ⊑ B }**. In other words, we introduce**
a new subconcept C of concept B**. Using Winslett's update operator we obtain**
the updated knowledge base { C ⊑ B, B ⊓ ¬C ⊑ A }**. Thus, the subconcept axiom**
from T **is severely weakened. Using other operators (see (Herzig and Rifi 1999) for**
a survey) it may even get completely forgotten. Such a forgetful **behaviour cannot** be explained by the sole fact that we are recording a change that occurred in the modelled environment - new subconcepts may arise without disturbing other relations the target concept may have.