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Canonical formulas for K4. I: Basic results. (English) Zbl 0774.03005
This paper presents a new technique for handling modal logics with transitive frames, i.e. extensions of the modal system K4. In effect, the technique is based on the following fundamental result: given a formula \(\varphi\), the finite frames \({\mathfrak F}_ 1,\dots,{\mathfrak F}_ n\) can be effectively constructed such that they completely characterize the set of all transitive general frames refuting \(\varphi\).
The paper consists of two parts. The first part establishes basic results on the canonical formulas for K4, while the second contains some applications concerning the finite model property, decidability and definability.

MSC:
03B45 Modal logic (including the logic of norms)
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