[sigmoid10]

I wouldn't resort to language examples, as the other comments show how this gets imprecise and lost in semantic details quickly. Instead think of a basic logic example: Consider an OR gate with inputs A and B and output X. If B=1 that means X=1. But if X=1 you can't infer that B=1, because there is an alternative (i.e. A=1,B=0). So from B=1→X=1, the inverse simply does not follow. This extends to all statements where a relation is not symmetric. Of course you can also go beyond and find cases where the relationship is not transitive or not even reflexive. There's a whole branch of language based IQ test puzzles (e.g. "all X are Y, some Y are Z" kind of stuff) that exploit this rabbit hole. Any LLM that does good on these will not jump to conclusions about reverse equalities quickly.

[Dylan16807]

Except the researchers are not asking about the inverse of arbitrary logic statements.