I don’t quite understand what you mean by your question but I am guessing you are asking for sentences for each word. Hope this helps.
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Valid- There is not a valid excuse for the stunt she pulled.
Formulate- The two boys went on their way, trying to formulate an apology for the other, so that when they see each other the next day they could make amends.
Logical- It is in your best interest to think like a logical human being in these types of situations.