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:
“Science is the language of the temporal world; love is that of the spiritual world. Man, indeed, describes more than he explains; while the angelic spirit sees and understands. Science saddens man; love enraptures the angel; science is still seeking, love has found. Man judges of nature in relation to itself; the angelic spirit judges of it in relation to heaven. In short to the spirits everything speaks.”
—Honoré De Balzac (1799–1850)
“Hesitation increases in relation to risk in equal proportion to age.”
—Ernest Hemingway (1899–1961)
“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)