http://glottopedia.org/index.php?title=Generalized_quantifier&feed=atom&action=historyGeneralized quantifier - Revision history2024-03-28T10:03:50ZRevision history for this page on the wikiMediaWiki 1.34.2http://glottopedia.org/index.php?title=Generalized_quantifier&diff=7733&oldid=prevWohlgemuth: utrecht link2009-02-15T15:29:09Z<p>utrecht link</p>
<table class="diff diff-contentalign-left" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 15:29, 15 February 2009</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l19" >Line 19:</td>
<td colspan="2" class="diff-lineno">Line 19:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Montague, R. (1974)</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Montague, R. (1974)</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Partee, B.H., A. ter Meulen, and R. Wall (1990)</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Partee, B.H., A. ter Meulen, and R. Wall (1990)</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">=== Link ===</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[http://www2.let.uu.nl/UiL-OTS/Lexicon/zoek.pl?lemma=Generalized+Quantifier&lemmacode=717 Utrecht Lexicon of Linguistics]</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{dc}}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{dc}}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Semantics]]</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Semantics]]</div></td></tr>
</table>Wohlgemuthhttp://glottopedia.org/index.php?title=Generalized_quantifier&diff=4845&oldid=prevHaspelmath at 10:09, 3 December 20072007-12-03T10:09:00Z<p></p>
<table class="diff diff-contentalign-left" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 10:09, 3 December 2007</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l3" >Line 3:</td>
<td colspan="2" class="diff-lineno">Line 3:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*(i) Every boy walks</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*(i) Every boy walks</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*(ii) All(x) [ boy(x) -> walk(x) ]</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*(ii) All(x) [ boy(x) -> walk(x) ]</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*(iii) Walk translates into walk</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*(iii) Walk translates into walk<ins class="diffchange diffchange-inline">, </ins>every boy translates as lambda P [ All(x) [ boy(x) -> P(x) ]]</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline"> </del>every boy translates as lambda P [ All(x) [ boy(x) -> P(x) ]]</div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The noun phrase ''every boy'' denotes a set of properties (or sets), namely the set of properties that every boy has and sentence (i) is true when the property of walking is in this set. Barwise and Cooper showed that this treatment of NPs as sets of sets can be used to assign denotations to those NPs that cannot be represented in first-order logic, like most, or only very cumbersomely, like three. They did not use Montague's intermediate logical language, but a direct interpretation in set-theoretic terms (|| || is the interpretation function):</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The noun phrase ''every boy'' denotes a set of properties (or sets), namely the set of properties that every boy has and sentence (i) is true when the property of walking is in this set. Barwise and Cooper showed that this treatment of NPs as sets of sets can be used to assign denotations to those NPs that cannot be represented in first-order logic, like most, or only very cumbersomely, like three. They did not use Montague's intermediate logical language, but a direct interpretation in set-theoretic terms (|| || is the interpretation function):</div></td></tr>
</table>Haspelmathhttp://glottopedia.org/index.php?title=Generalized_quantifier&diff=4844&oldid=prevHaspelmath: from Utrecht Lexicon of Linguistics2007-12-03T10:08:31Z<p>from Utrecht Lexicon of Linguistics</p>
<p><b>New page</b></p><div>A '''generalized quantifier''' is a generalization of the [[universal quantifier|universal]] and [[existential quantifier]] of [[predicate logic]] to a higher-order concept of a quantifier as a set of sets. This generalization was already implicit in Montague (1974) but made explicit in Barwise & Cooper (1981). Montague (1974) proposed a compositional translation of quantified sentences making use of [[lambda-abstraction]]. He showed that a compositional translation of (i) into (ii) is possible if the subject ''every boy'' takes the predicate ''walks'', as in (iii):<br />
<br />
*(i) Every boy walks<br />
*(ii) All(x) [ boy(x) -> walk(x) ]<br />
*(iii) Walk translates into walk<br />
every boy translates as lambda P [ All(x) [ boy(x) -> P(x) ]]<br />
<br />
The noun phrase ''every boy'' denotes a set of properties (or sets), namely the set of properties that every boy has and sentence (i) is true when the property of walking is in this set. Barwise and Cooper showed that this treatment of NPs as sets of sets can be used to assign denotations to those NPs that cannot be represented in first-order logic, like most, or only very cumbersomely, like three. They did not use Montague's intermediate logical language, but a direct interpretation in set-theoretic terms (|| || is the interpretation function):<br />
<br />
(iv) || most boys || = { X subset E : | X intersect || boys || > <br />
| || boys || - X | <br />
|| two boys || = { X subset E : | X intersect || boys || | >= 2 <br />
<br />
The interpretation of most boys is the set of sets such that there are more boys that they do contain than don't, and the interpretation of two boys is the set of sets which contain at least two boys.<br />
<br />
===References===<br />
<br />
*Barwise, J. & R. Cooper (1981)<br />
*Gamut, L.T.F. (1991)<br />
*Montague, R. (1974)<br />
*Partee, B.H., A. ter Meulen, and R. Wall (1990)<br />
<br />
{{dc}}<br />
[[Category:Semantics]]</div>Haspelmath