# [DL] From DL to FOL

Enrico Franconi franconi at inf.unibz.it
Thu Nov 25 16:31:34 CET 2010

On 21 Nov 2010, at 20:16, Rodolfo Rieckhof wrote:

> Hello,
> I am new to this so this question maybe fairly trivial.  I want to transform the DL Formulas that represent Domain and Range in Fist order Logic. What i have:
> The two DL sentences
>  isManufacteredBy.T  Product            (Domain)
> T   isManufacteredBy.Manufaterer   (Range)
>
> In FOL ?
> x(  y. isManufacteredBy(x,y) -> Product (x))                             (Domain)
> x ( T -> y( isManufacteredBy(x,y)  Manufacterer(y) ) )      (Range)
>
> I am not really sure about the transformation in FOL beacause i dont know how to translate the T to FOL. Could any tell me how this should be done.

the \top class contains all possible objects in the universe, so you can neglect it in the context of a universal quantification.

\forall x( \exists y. isManufacteredBy(x,y) -> Product (x))                             (Domain)
\forall x ( \forall y ( isManufacteredBy(x,y) -> Manufacterer(y) ) )      (Range)

--e.
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