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Problem 9 (φ4): Translation between different logics [ Exam: 2018, February 14th]

https://es.cs.uni-kl.de/teaching/vrs/exams/2018.02.14.vrs/2018.02.14.vrs.solutions.pdf

φ4 = EF([¬U Gb]FG(b))

Solution
EF([¬U Gb∧ FG(b))
=
EF[¬a SUGb]  //Since [U Gb]∧ FG(bIs equivalent to [¬a SU Gb]

EFE[¬a SU Gb]
EFE[¬a SU EGb]

EFE[¬a SU EGb]

My doubt is : as per the comment in the solutions: [U Gb]∧ FG(b) is equivalent to [¬a SU Gb] but  [¬U Gb] ≠ [U Gb] (As the former says ¬a holds until always b holds OR ¬a holds forever and the latter says: a holds until always b holds OR a holds forever).

 Then how did the substitution happen?

in * TF "Emb. Sys. and Rob." by (370 points)

1 Answer

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Best answer

In the comment, a negation symbol is missing. It should be [¬U Gb]∧ FG(bIs equivalent to [¬a SU Gb]

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