http://glottopedia.org/index.php?action=history&feed=atom&title=Dual_%28semantics%29Dual (semantics) - Revision history2026-04-06T12:46:29ZRevision history for this page on the wikiMediaWiki 1.34.2http://glottopedia.org/index.php?title=Dual_(semantics)&diff=7532&oldid=prevWohlgemuth: utrecht2009-02-12T21:10:51Z<p>utrecht</p>
<p><b>New page</b></p><div>'''Dual''' is the dual Q<sup><nowiki>*</nowiki></sup> of a [[generalized quantifier]] Q can be made by taking both the external negation and the internal negation of Q, i.e.:<br />
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(i) Q<sup><nowiki>*</nowiki></sup> = Neg Q Neg<br />
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This can be written out as:<br />
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(ii) Q<sup><nowiki>*</nowiki></sup> = { X subset E : (E - X) not_in Q }<br />
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''All N'' and ''some N'', for instance are pairs of quantifiers which are each other's duals:<br />
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(iii) a All dogs bark &lt;-&gt;<br />
b It is not the case that some dogs do not bark<br />
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''Some dogs'' is the dual of ''all dogs'' because every set X that belongs to the interpretation of ''some dogs'' contains at least one dog; so there is no set (E - X) that belongs to the interpretation of ''all dogs''. If Q = Q<sup><nowiki>*</nowiki></sup>, then Q is called ''self-dual''. Proper names, for instance, are self-dual.<br />
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=== Link ===<br />
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[http://www2.let.uu.nl/UiL-OTS/Lexicon/zoek.pl?lemma=Dual&lemmacode=1101 Utrecht Lexicon of Linguistics]<br />
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=== References ===<br />
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* Gamut, L.T.F. 1991. ''Logic, language, and meaning,'' Univ. of Chicago Press, Chicago.<br />
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[[Category:Semantics]]</div>Wohlgemuth