In logic a branching quantifier, also called a Henkin quantifier, finite partially ordered quantifier or even nonlinear quantifier, is a partial ordering
of quantifiers for Q∈{∀,∃}. It is a special case of generalized quantifier. In classical logic, quantifier prefixes are linearly ordered such that the value of a variable ym bound by a quantifier Qm depends on the value of the variables
- y1,...,ym-1
bound by quantifiers
- Qy1,...,Qym-1
preceding Qm. In a logic with (finite) partially ordered quantification this is not in general the case.
Branching quantification first appeared in a 1959 conference paper of Leon Henkin. Systems of partially ordered quantification are intermediate in strength between first-order logic and second-order logic. They are being used as a basis for Hintikka's and Gabriel Sandu's independence-friendly logic.
Read more about Branching Quantifier: Definition and Properties, Relation To Natural Languages
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