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<p>utrecht</p> <p><b>New page</b></p><div>&#039;&#039;&#039;Left [[upward monotonicity]]&#039;&#039;&#039; is a property of a [[determiner]] D in [[Generalized Quantifier Theory]]. A determiner D has the property of being left upward monotone if and only if in a domain of entities E condition (i) holds.<br /> <br /> (i) for all A,B,A&#039; subset E: if D(A,B) and A subset A&#039;, then D(A&#039;,B)<br /> <br /> Left upward monotonicity can be tested as in (ii); as shown &#039;&#039;there&#039;&#039;, &#039;&#039;some&#039;&#039; and &#039;&#039;at least two&#039;&#039; are left upward monotone, but &#039;&#039;all&#039;&#039; and &#039;&#039;exactly two&#039;&#039; are not.<br /> <br /> (ii) a If some/at least two dogs walked, then<br /> some/at least two animals walked.<br /> b If all/exactly two dogs walked, then<br /> all/exactly two animals walked.<br /> <br /> Other terms are &#039;&#039;persistent&#039;&#039; and &#039;&#039;left monotone increasing&#039;&#039;.<br /> <br /> === Link ===<br /> <br /> [http://www2.let.uu.nl/UiL-OTS/Lexicon/zoek.pl?lemma=Left+upward+monotonicity&amp;lemmacode=594 Utrecht Lexicon of Linguistics]<br /> <br /> === References ===<br /> <br /> * Gamut, L.T.F. 1991. &#039;&#039;Logic, language, and meaning,&#039;&#039; Univ. of Chicago Press, Chicago.<br /> <br /> {{dc}}<br /> [[Category:Semantics]]</div>

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