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Update: Removed ancillary wording. My question was how to represent sometimes in propositional logic in the sentence:

 I sometimes pet bunnies.
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  • Note that the English sentence you give as an example (I pet bunnies.) is a generic sentence, which refers to a variable number of occasions of your petting bunnies, resulting in characterization of this activity as a documented trait of yours. I don't think that Pet (I, bunnies) really explicates this kind of sentence. Generic verb phrases like this are, if anything, a good example of 2nd-order quantification.
    – jlawler
    Aug 23 '15 at 22:52
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There seem to be three issues here. (1) Why is "I sometimes pet bunnies" second order, in view of the fact that it seems to mean about the same as "I pet bunnies"? What is the second order logical form?

(2) Reichenbach's idea about second order logic is that it involves quantifying over predicates. His example was "Napoleon had all the properties of a great general", which he gave a translation roughly like (For all properties P)(For all great generals G)(if P(G) then P(Napoleon)). This doesn't seem much like "I sometimes pet bunnies".

(3) Dragging in non-binary truth values seems gratuitous.

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You should look at intensional logic. This is the study of how to represent things like sometimes, maybe, taller etc. You would represent your example sentence with something along the lines of "There exists an infinite set of possible worlds. There exists at least one world where I pet a bunny. However, I do not pet a bunny in every world."

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