Operations and Morphisms On Frames
Every Kripke model induces the general frame, where V is defined as
The fundamental truth-preserving operations of generated subframes, p-morphic images, and disjoint unions of Kripke frames have analogues on general frames. A frame is a generated subframe of a frame, if the Kripke frame is a generated subframe of the Kripke frame (i.e., G is a subset of F closed upwards under R, and S is the restriction of R to G), and
A p-morphism (or bounded morphism) is a function from F to G which is a p-morphism of the Kripke frames and, and satisfies the additional constraint
- for every .
The disjoint union of an indexed set of frames, is the frame, where F is the disjoint union of, R is the union of, and
The refinement of a frame is a refined frame defined as follows. We consider the equivalence relation
and let be the set of equivalence classes of . Then we put
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