Topics: Deductive reasoning (linear temporal logic aka LTL)
Given
If the server detects an error, it will eventually enter recovery mode. [1]
The server remains in recovery mode until the error is resolved. [2]
If the error is resolved, the server will eventually return to normal operation. [3]
The server has detected an error now. [4]
Find
Will the server eventually return to normal operation?
Solution
Definition:
E: The server has detected an error.
R: The server is in recovery mode.
N: The server is operating normally.
(X: Next — Xφ means that φ is true at the next moment.)
F: Eventually — Fφ means that φ will be true at some future point.
G: Always — Gφ means that φ is true at all future points.
U: Until — φUψ means that φ remains true until ψ becomes true.
Representation:
[1]: G(E→FR)
[2]: G(R→(RU¬E))
[3]: G(¬E→FN)
[4]: E
Deduction:
E —[1]—> FR —[2]—> RU¬E —[3]—> FN
Answer
Yes, the server will eventually return to normal operation.