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
Famous quotes containing the words relation to, relation and/or logics:
“You must realize that I was suffering from love and I knew him as intimately as I knew my own image in a mirror. In other words, I knew him only in relation to myself.”
—Angela Carter (1940–1992)
“You know there are no secrets in America. It’s quite different in England, where people think of a secret as a shared relation between two people.”
—W.H. (Wystan Hugh)
“When logics die,
The secret of the soil grows through the eye,
And blood jumps in the sun;
Above the waste allotments the dawn halts.”
—Dylan Thomas (1914–1953)