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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“Plot, rules, nor even poetry, are not half so great beauties in tragedy or comedy as a just imitation of nature, of character, of the passions and their operations in diversified situations.”
—Horace Walpole (1717–1797)
“In frames as large as rooms that face all ways
And block the ends of streets with giant loaves,
Screen graves with custard, cover slums with praise
Of motor-oil and cuts of salmon, shine
Perpetually these sharply-pictured groves
Of how life should be.”
—Philip Larkin (1922–1986)