Conditional quantifier
In logic, a conditional quantifier is a kind of Lindström quantifier (or generalized quantifier) QA that, relative to a classical model 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 ∀A, which can be viewed as set-theoretic inclusion, satisfies all of the above except [symmetry].