Graham Priest observed that not all uses of "and" in English commute: (page 15)
...according to the truth table for &, 'a and b' always has the same value as 'b and a', namely, they are both true if a and b are both true, and false otherwise. But consider the sentences:
- John hit his head and fell down.
- John fell down and hit his head.
The first says that John hit his head and then fell down. The second says that John fell down and then hit his head. Clearly, the first could be true whilst the second is false, and vice versa. Thus, it is not just the truth values of the conjuncts that are important, but which conjunct caused which.
I am not sure how one would symbolize such sentences where "and" means "and then" nor which logic to use to best represent them, hence the question: How should one symbolize "and then" in logic?
Priest, G. (2017). Logic: a very short introduction (Vol. 29). Oxford University Press.