# Conditional quantifier

In logic, a conditional quantifier is a kind of Lindström quantifier (or generalized quantifier) ${\displaystyle Q_{A}}$ that, relative to a classical model ${\displaystyle A}$, satisfies some or all of the following conditions ('X' and 'Y' range over arbitrary formulas in one free variable):
(The implication arrow denotes material implication in the metalanguage.) The minimal conditional logic M is characterized by the first six properties, and stronger conditional logics include some of the other ones. For example, the quantifier ${\displaystyle \forall _{A}}$, which can be viewed as set-theoretic inclusion, satisfies all of the above except [symmetry]. Clearly [symmetry] holds for ${\displaystyle \exists _{A}}$ while e.g. [contraposition] fails.