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S5 (modal logic) : ウィキペディア英語版
S5 (modal logic)
In logic and philosophy, S5 is one of five systems of modal logic proposed by
Clarence Irving Lewis and Cooper Harold Langford in their 1932 book ''Symbolic Logic''.
It is a normal modal logic, and one of the oldest systems of modal logic of any kind.
==Axiomatics==
The following makes use of the modal operators \Box ("necessarily") and \Diamond ("possibly").
S5 is characterized by the axioms:
*K: \Box(A\to B)\to(\Box A\to\Box B);
*T: \Box A \to A,
and either:
* 5: \Diamond A\to \Box\Diamond A;
* or both of the following:
:
* 4: \Box A\to\Box\Box A, and
:
* B: A\to\Box\Diamond A.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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