[DL] can you find minimal models from the open and complete situation using Tableaux?

[Jun Fang]

Hi All,

Given an consistent ontology O, applying the tableaux algorithm till it is
in the final open and complete situation. There may be many models which can
be constructed from it.

A minimal model is a model that removing any element from the concept
interpretation or role interpretation in it can make it is not a model.

I have two question about the canonical model and the minimality:

1) Is there a method to find its minimal canonical models? If exists, what's
the method? just need pick one from the disjunctive branches? (soundness)

For instance, if the ontology is (C\unionD)(a), then model1: \domian ={a},
 a \in C^I; model2: \domian ={a},  a \in D^I; model3: \domian ={a},  a \in
C^I, a \in D^I are all its models, while model1 and model2 are its minimal
models. For this simple example, it is easy to find the minimal models by
just select one from the disjunctive branches each time. Is it also true in
more complex situation.

2) Furthermore, Is there a method to find all its minimal canonical models?
If exists, what's it? (completeness)

Thanks for any comments!

If it is too complicated, we can just discuss it in simper DL language, such
as ALC.

-- 
Best Regards!

Jun Fang
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