In logic a branching quantifier is a partial ordering <math>\langle Qx_1\dots Qx_n\rangle</math> of quantifiers for Q∈{∀,∃}. 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.

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  • In logic a branching quantifier is a partial ordering <math>\langle Qx_1\dots Qx_n\rangle</math> of quantifiers for Q∈{∀,∃}. 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 Leon Henkin's "Some Remarks on Infinitely Long Formulas", Infinitistic Methods, Proceedings of the Symposium on Foundations of Mathematics, Warsaw, 1959. 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 (also known as informational-independence logic) which are claimed to be the most natural logics as a foundations for mathematics (e.g. set theory) or for capturing certain features of natural language and epistemology.
  • Kwantyfikator rozgałęziony (inaczej kwantyfikator Henkina) to zbiór częściowo uporządkowany <math>\{Q_1x_1, Q_2x_2,\dots Q_nx_n\}</math> gdzie <math>Q_i\in {\{ \forall,\exists \}}</math> dla <math>i\in\{1,2,3,.. ,n\}</math>. W rachunku predykatów prefiks kwantyfikatorowy jest liniowym porządkiem tzn. w formule <math>Q_1x_1Q_2x_2\dots Q_nx_n \phi(x_1, x_2, ... , x_n)</math> wartość zmiennej <math>x_i</math> wiązanej przez kwantyfikator <math>Q_i</math> zależy od wartości zmiennych <math>x_1,... ,x_{i-1}</math> wiązanych przez kwantyfikatory <math>Q_1, Q_2,... ,Q_{i-1}</math>. W formule z kwantyfikatorem rozgałęzionym może być inaczej.
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  • In logic a branching quantifier is a partial ordering <math>\langle Qx_1\dots Qx_n\rangle</math> of quantifiers for Q∈{∀,∃}. 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.
  • Kwantyfikator rozgałęziony (inaczej kwantyfikator Henkina) to zbiór częściowo uporządkowany <math>\{Q_1x_1, Q_2x_2,\dots Q_nx_n\}</math> gdzie <math>Q_i\in {\{ \forall,\exists \}}</math> dla <math>i\in\{1,2,3,.. ,n\}</math>. W rachunku predykatów prefiks kwantyfikatorowy jest liniowym porządkiem tzn. w formule <math>Q_1x_1Q_2x_2\dots Q_nx_n \phi(x_1, x_2, ...
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  • Branching quantifier
  • Kwantyfikator rozgałęziony
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