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.
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.
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.