IEEE - Aerospace and Electronic Systems - May 2023 - 84

Formal Verification of Safety-Critical Aerospace Systems
where the conditional probability of stall given x
follows Bayes Theorem:
Pðstall ¼ true jX ¼ xÞ
¼ PðX¼x j stall¼trueÞPðstall¼trueÞ
PðX¼xÞ
:
A classification function CcondðMstall ; t;xÞ¼ k is
t-confident iffk 6¼ uncertain:
Two mechanically verified Agda theorems about
safety envelopes for stall classification are given below.
Theorem 8 (z-predictability within Safety Envelope).
If an energy signal x belongs to safety envelope
SEcondðMstall;z;xÞ,
9 u 2 Qstates :
q
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðmu xÞS1
then
u ðmu xÞ 


IEEE - Aerospace and Electronic Systems - May 2023

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