FOM: Branching quantifiers
JoeShipman@aol.com
JoeShipman at aol.com
Thu Mar 15 10:18:55 EST 2001
M. Mostowski writes:
<<You take the following composition rules
1. for each variable x, the following are prefixes: Ex, Ax;
2. if Q and Q' are prefixes then the following are prefixes: (QQ') - horizontal composition, (Q/Q') - vertical composition, and Q^d - the dualization of Q.
The dualization means that Q^d is equivalent to ~Q~, which trivially is first-order definable, but not in a context of vertical compositions.
Without dualization you will get the logic with Henkin quantifiers, but with dualization you will obtain just the logic equivalent to the second order logic.>>
Can someone please give an ordinary-language semantic interpretation of these quantifiers? I don't understand what they're supposed to mean.
-- Joe Shipman
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