|From:||Ali Hashemi <ali.hashemi+ontolog@xxxxxxxxxxx>|
|Date:||Mon, 22 Feb 2010 19:12:50 -0500|
Thanks for the feedback. Comments below.
On Mon, Feb 22, 2010 at 5:53 PM, Christopher Menzel <cmenzel@xxxxxxxx> wrote:
Hmm, my phrasing was awkward. All I meant to say here is that associated with any set of axioms are a set of permissible models... I wasn't aiming to define satisfiabilty. Just pointing out something that is perhaps trivial, mainly because I don't know what the background of the general reader on this forum is.
Yes, the wiki article is a mess, thanks for the link.
Also true. One way of addressing this concern re the introduction of new "orthogonal" vocabulary (i.e. conservative extensions) is to organize theories / modules in a repository according to something we term "core-hierarchies."
A core hierarchy consists of theories which are non-conservative extensions of a particular intuition. Note you can still introduce new terms, but they will be extending previous ones. Slide 5 of Michael Gruninger's presentation at the Feb 19 conference call ( http://ontolog.cim3.net/file/work/OpenOntologyRepository/2010-02-19_OOR-Developers-Panel/COLORE--MichaelGruninger_20100219.pdf ) includes the definition for core hierarchies:
A core hierarchy is a set of core theories T1, ..., Tn such that:
L(Ti) = L(Tj) for all i,j
(Heh, it just occurred to me that organizing theories in such a way could inadvertently lead to and is possibly very similar to the quest for primitives.)
Alternatively, if you lift this restriction, you must accommodate what I awkwardly and tentatively phrased as the n-dimensional interactions between sets of models with different vocabularies. Instead of simply slicing out models in a single plane, you have an n-dimensional space corresponding to the different vocabularies... However, there is no way I am going to start trying to explicate what this entails or how it would work via email :D.
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