Kripke model
（ plural ）
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(logic) A Kripke frame together with either 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).
Kripke model
The Kripke model consists of a frame together with either a valuation assigning each world the set of atomic formulas true there, a valuation assigning each atomic formula the set of worlds where it is true, or a forcing relation between worlds and atomic formulas, together with deduction rules (which depend on the chosen logic, such as a modal logic or intuitionistic logic) that determine which formulas are forced at a given world.
The Kripke model consists of a frame together with either a valuation assigning each world the set of atomic formulas true there, a valuation assigning each atomic formula the set of worlds where it is true, or a forcing relation between worlds and atomic formulas, together with deduction rules (which depend on the chosen logic, such as a modal logic or intuitionistic logic) that determine which formulas are forced at a given world.
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