<div class="gmail_quote">2010/12/4 Norbert E. Fuchs <span dir="ltr"><<a href="mailto:fuchs@ifi.uzh.ch">fuchs@ifi.uzh.ch</a>></span><br><blockquote class="gmail_quote" style="margin: 0pt 0pt 0pt 0.8ex; border-left: 1px solid rgb(204, 204, 204); padding-left: 1ex;">
<div class="im"><br>
On 4 Dec 2010, at 14:11, Jean-Marc Vanel wrote:<br>
<br>
> 2010/12/4 Norbert E. Fuchs <<a href="mailto:fuchs@ifi.uzh.ch">fuchs@ifi.uzh.ch</a>>:<br>
</div>> ...<br>
<div class="im">> ><br>
> > If the number of the parts of a product X is N then the number of the workers of X is N.<br>
> ><br>
</div>> ...<br>
<div class="im">> In order to capture the semantics of the sentence, what is desirable is that a DRS variable binds the cardinality of the "part" object to that of the "worker" object.<br>
</div>> ...<br>
<br>
Why? From your example it seems that you want the "number of the parts" to equal "the number of the workers". The cardinality "geq 2" of "parts" and "workers" reflects simply that these words are plural.<br>
</blockquote><div><br>On the surface the ACE interpretation of the sentence makes sense, but it misses the common sense ( and also set theoretic sense ) about the cardinaty of 2 sets being equal.<br>The word "number" applied to object "part" is indeed equal to the word "number" applied to object "worker". But number is just a word in the user's vocabulary; it does not have the meaning of a set's cardinality.<br>
<br>I acknowledge that a software application can leverage on that and exploit the DRS, but this is not satisfying because this relies on a private semantics shared by the author of the ACE sentences and the software.<br>
<br>What I want to explore is the possibility extend ACE and DRS to capture such meaning.<br>Let 's take again our ACE sentence :<br> <br><i>If the number of the parts of a product X is N then the number of the workers of X is N.</i><br>
<br>If now "<i>the number of</i>" is interpreted as "the cardinality of the set of", we could have this (extended ) DRS , where the new variable CD stands for the cardinality of the set of the D's .<br>
<br><span style="font-family: courier new,monospace;">[]</span><br style="font-family: courier new,monospace;">
<span style="font-family: courier new,monospace;"> [D,E,CD]</span><span style="font-family: courier new,monospace;"></span><br style="font-family: courier new,monospace;">
<span style="font-family: courier new,monospace;"> relation(D,of,E)-1/7</span><br style="font-family: courier new,monospace;"><span style="font-family: courier new,monospace;"> object(E,product,countable,na,eq,1)-1/9</span><br style="font-family: courier new,monospace;">
<span style="font-family: courier new,monospace;"> <b>object(D,part,countable,na,eq, CD )-1/6</b></span><span style="font-family: courier new,monospace;"></span><br style="font-family: courier new,monospace;">
<span style="font-family: courier new,monospace;"> =></span><br style="font-family: courier new,monospace;"><span style="font-family: courier new,monospace;"> [H]</span><span style="font-family: courier new,monospace;"></span><br style="font-family: courier new,monospace;">
<span style="font-family: courier new,monospace;"> relation(H,of,E)-1/19</span><br style="font-family: courier new,monospace;">
<span style="font-family: courier new,monospace;"> <b>object(H,worker,countable,na,eq, CD )-1/18</b></span><br></div></div><br clear="all"><br>-- <br>Jean-Marc Vanel<br>Consulting, services, training,<br>Rule-based programming, Semantic Web<br>
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