<html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><br><div><div>On 21 Nov 2010, at 20:16, Rodolfo Rieckhof wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite">Hello, <br>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:<br>The two DL sentences<br><img class="tex" alt="\exists " src="http://upload.wikimedia.org/math/9/3/e/93ebe8636e1f8d60004fe33d1321674e.png"> isManufacteredBy.T <img class="tex" alt="\sqsubseteq" src="http://upload.wikimedia.org/math/b/1/b/b1be6c28d38e18390ea808e56c4e1d93.png"> Product (Domain)<br>
T <img class="tex" alt="\sqsubseteq" src="http://upload.wikimedia.org/math/b/1/b/b1be6c28d38e18390ea808e56c4e1d93.png"> <img class="tex" alt="\forall " src="http://upload.wikimedia.org/math/d/4/d/d4d49bead125261b226eaa867bd016ce.png"> isManufacteredBy.Manufaterer (Range)<br>
<br>In FOL ? <br><img class="tex" alt="\forall " src="http://upload.wikimedia.org/math/d/4/d/d4d49bead125261b226eaa867bd016ce.png">x( <img class="tex" alt="\exists " src="http://upload.wikimedia.org/math/9/3/e/93ebe8636e1f8d60004fe33d1321674e.png"> y. isManufacteredBy(x,y) -> Product (x)) (Domain)<br>
<img class="tex" alt="\forall " src="http://upload.wikimedia.org/math/d/4/d/d4d49bead125261b226eaa867bd016ce.png">x ( T -> <img class="tex" alt="\forall " src="http://upload.wikimedia.org/math/d/4/d/d4d49bead125261b226eaa867bd016ce.png">y( isManufacteredBy(x,y) <img class="tex" alt="\land" src="http://upload.wikimedia.org/math/9/c/a/9cae4437756a15b8e44ec23e07fb1f65.png"> Manufacterer(y) ) ) (Range) <br>
<br>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.</blockquote><div><br></div>the \top class contains all possible objects in the universe, so you can neglect it in the context of a universal quantification.<br><br></div><div><div><br>\forall x( \exists y. isManufacteredBy(x,y) -> Product (x)) (Domain)<br>\forall x ( \forall y ( isManufacteredBy(x,y) -> Manufacterer(y) ) ) (Range) </div><div><br></div><div>--e.</div></div></body></html>