Universal #1210

Legacy number: 1210

 Number  1206
 Original  Constraint on negating self-dual and monotone decreasing quantifiers:
If a language has a syntactic construction whose semantic function is to negate a quantifier, then this construction will not be used with NPs expressing monotone decreasing or self-dual quantifiers.
 Standardized  Constraint on negating self-dual and monotone decreasing quantifiers:
IF there is a syntactic construction whose semantic function is to negate a quantifier, THEN this construction will not be used with NPs expressing monotone decreasing or self-dual quantifiers.
 Keywords  quantification, monotonicity, negation, NP
 Domain  semantics, syntax
 Type  no genuine implication; rather: provided that
 Status  achronic
 Quality  absolute
 Basis  unspecified
 Source  Barwise & Cooper 1981: 198, U9

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Discussion
Counterexamples
Notes
1. For technical reasons, the following logical relations are abbreviated as follows: A is a subset of E = A $ E ; X is a member of set Q = X % Q; X is not a member of set Q = X ¬% Q . 2. The dual of a quantifier Q on E is the quantifier q defined by q = {X $ E | (E - X) ¬% Q}, i.e., q = ~ (Q~) = (~Q)~. If Q = q then Q is called ‘self-dual’. The dual of ||some man|| is ||every man|| and vice versa. On a finite set A $ E of odd cardinality, {X $ E | X contains more than half A} is self-dual. For any A % E, {X $ E | a % X} is self-dual.3. Cf. also with #1211.
Comment
Frans Plank · 3 Aug 2006
1. For technical reasons, the following logical relations are abbreviated as follows:
<table class = "textTable">
<tr>
<td> </td>
<td>A is a subset of E</td>
<td> = </td>
<td>A $ E ;</td>
</tr>
<td> </td>
<td>X is a member of set Q </td>
<td> = </td>
<td>X % Q;</td>
</tr>
<tr>
<td> </td>
<td>X is not a member of set Q</td>
<td> = </td>
<td>X ¬% Q.</td>
</tr>
</table>


2. The dual of a quantifier Q on E is the quantifier q defined by q = {X $ E | (E - X) ¬% Q}, i.e., q = ~ (Q~) = (~Q)~. If Q = q then Q is called 'self-dual'. The dual of ||some man|| is ||every man|| and vice versa. On a finite set A $ E of odd cardinality, {X $ E | X contains more than half A} is self-dual. For any A % E, {X $ E | a % X} is self-dual.

3. Cf. also with <a class="innerLink" href="browse.php?entry_id=1211"><img src="../img/entry.gif" border="0">.