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:
“We must get back into relation, vivid and nourishing relation to the cosmos and the universe. The way is through daily ritual, and is an affair of the individual and the household, a ritual of dawn and noon and sunset, the ritual of the kindling fire and pouring water, the ritual of the first breath, and the last.”
—D.H. (David Herbert)
“Among the most valuable but least appreciated experiences parenthood can provide are the opportunities it offers for exploring, reliving, and resolving one’s own childhood problems in the context of one’s relation to one’s child.”
—Bruno Bettelheim (20th century)
“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)