[DL] Monotonicity and Conservative extension Of OWL 2 DL

Uli Sattler Ulrike.Sattler at manchester.ac.uk
Thu Aug 20 12:49:35 CEST 2015

Hi Leila, 

On 19 Aug 2015, at 22:41, Leila Bayoudhi <bayoudhileila at yahoo.fr> wrote:

> Hi,
> Since OWL 2 is based on description Logics, let me know please more about the two notions
> 	• Conservative extension: this concept means that we should not infere axioms that where were not entailed before an information addition? Is it true what I am saying?

sorry, no: this is a mechanism to compare 2 ontologies, say O1 and  a superset O2, with respect to a set of (concept and role) names S: we say that O2 is a conservative extension of O1 wrt S if they have the same entailments over S. This means that, for any axiom alpha built with terms from S, O1 entails alpha if and only if O2 entails alpha. In other words, the extension O2 of O1 is a *conservative* extension wrt S if the axioms in O2\O1 do not add further information/constraints regarding the terms in S.  

> 	• Monotonicity: additional information to an ontology should not make loose old entailments. Is it true?

sort of: a logic (like ALC, SHIQ, etc) is called monotonic if, whenever you add more axioms to a set of axioms, you will only *gain* entailments, but never loose them. Most Description Logics and OWL are monotonic, but there are a number of non-monotonic variants of DLs. 

Monotonicity is a property of a logic, determined by its semantics. 

conservative extension is a relation between two sets of axioms (plus a set of terms S)

Cheers, Uli   

> m I saying true things? Can you correct for me the two concepts in the context of adding knowldge to an an OWL 2 DL ontology? Does this addition should respect these two principles? Are they related in a some way to ontology consistency?
> Thks.
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