Relation To Modal Logics
Let A be a propositional formula. The Gödel–Tarski translation of A is defined recursively as follows:
If M is a modal logic extending S4 then ρM = {A | T(A) ∈ M} is a superintuitionistic logic, and M is called a modal companion of ρM. In particular:
- IPC = ρS4
- KC = ρS4.2
- LC = ρS4.3
- CPC = ρS5
For every intermediate logic L there are many modal logics M such that L = ρM.
Read more about this topic: Intermediate Logic
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