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September 6, 2022, Problem 9. Translation between different logics

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Can you please explain the rule that led to the step where I placed a Question mark in the image below?

Same with the below question as well.

 

in * TF "Emb. Sys. and Rob." by (410 points)

1 Answer

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That rule is explained in detail on slides 45-46 of the temporal logic chapter. There are the following important equivalences that allow us to remove conjunctions of temporal operations by a temporal operator which is sometimes required for a translation to CTL:

  • [a1 SU b1] & [a2 SU b2] = [(a1 & a2) SU (b1 & [a2 SU b2] | b2 & [a1 SU b1])]
  • [a1 SU b1] & [a2 WU b2] = [(a1 & a2) SU (b1 & [a2 WU b2] | b2 & [a1 SU b1])]
  • [a1 WU b1] & [a2 WU b2] = [(a1 & a2) WU (b1 & [a2 WU b2] | b2 & [a1 WU b1])]
Slides 47-49 consider conjunctions with all other temporal operators which are reduced to the above three basic laws.

by (166k points)
Thank you, Professor
by (410 points)

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