Intermediate Logic - Relation To Modal Logics

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.

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