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Kripke model

Kripke model noun: a Kripke frame together with any one of the following: (1) a function associating each of the frame's worlds to a set of prime formulae which are "true" for the given world, (2) a function associating each prime formula to a set of worlds for which the prime formula is "true", (3) a forcing relation between worlds and prime formulae. Additionally, there is a set of rules for deducing (from the given function or relation) what formulae are forced to be true by a given world. (The set of rules depends on which logic the Kripke model is being applied to, whether one of several modal logics or intuitionistic logic). For intuitionistic logic the forcing relation satisfies a persistence relation, namely, if world w forces proposition p, then all worlds accessible from w also force p.

Noun

Kripke model (plural Kripke models)

  1. A Kripke frame together with any one of the following: (1) a function associating each of the frame's worlds to a set of prime formulae which are "true" for the given world, (2) a function associating each prime formula to a set of worlds for which the prime formula is "true", (3) a forcing relation between worlds and prime formulae. Additionally, there is a set of rules for deducing (from the given function or relation) what formulae are forced to be true by a given world. (The set of rules depends on which logic the Kripke model is being applied to, whether one of several modal logics or intuitionistic logic). For intuitionistic logic the forcing relation satisfies a persistence relation, namely, if world w forces proposition p, then all worlds accessible from w also force p.
    • A formula is intuitionistically valid iff it is forced true by every world of every Kripke model.
    • A terminal world of a Kripke model (for intuitionistic logic) has a forcing relation equivalent to a classical model/interpretation.

Forms of Kripke model

pluralKripke models

Origin of Kripke model

Named after Saul Kripke.

Questions about Kripke model

What does Kripke model mean?
Kripke model means a Kripke frame together with any one of the following: (1) a function associating each of the frame's worlds to a set of prime formulae which are "true" for the given world, (2) a function associating each prime formula to a set of worlds for which the prime formula is "true", (3) a forcing relation between worlds and prime formulae. Additionally, there is a set of rules for deducing (from the given function or relation) what formulae are forced to be true by a given world. (The set of rules depends on which logic the Kripke model is being applied to, whether one of several modal logics or intuitionistic logic). For intuitionistic logic the forcing relation satisfies a persistence relation, namely, if world w forces proposition p, then all worlds accessible from w also force p.
What part of speech is Kripke model?
Kripke model is a noun.
What is the plural of Kripke model?
The plural of Kripke model is Kripke models.

Words near Kripke model in the dictionary

  1. Kripacharya
  2. Kripi
  3. Kripke
  4. Kripke frame
  5. Kripke frames
  6. Kripke model
  7. Kripke models
  8. Kripkean
  9. Kripkenstein
  10. Kripkensteinian
  11. kris

Source and license

Adapted from Wiktionary: Kripke model (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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