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Having read this over, fwiw I am definitively siding with @[email protected] on this. Here is an illustration that I think will help:
Child 1: Hey, let's grab some cookies!
Child 2: Okay! (reaches for cookie but before they can grab one...)
Mother: Hey, what are you doing - you two are not eating cookies are you, hrm!?
Child 1: No mummy dearest (choose appropriate slang of choice here:-), we two are not eating cookies...
Question: did child 1 lie? Technically their statement is accurate according to the narrowest possible interpretation - they both were not eating cookies, yet, even though the intentions of them both were fairly blatantly obvious.
Communication among humans is not math - the meaning of a message requires interpretation from the multiple parties involved. And in particular the recipient is usually in possession of additional data than the sender - at the very least, once the sender chooses to send the message packet, then the receiver has obtained +1 message that prior to the sending did not yet exist between them (and which may contain additional data, such as "a sender exists" and "the sender was located in this direction, at the time of the sending").
Anyway the child KNOWS what the mother intended to ask, but deliberately and blatantly told an extremely skewed version of the truth that is SO distorted, SO unwieldy, SO twisted, that there is no doubt that the intention was to deceive. In a normal situation anyway - though ofc exceptions always exist e.g. an autistic child, or one who has suffered some form of brain damage that causes them to struggle with over-literal statements might somehow literally be confused what the intention of the mother was. But in a normal situation, the meaning is clear: the child lied.
Any judgement about that is ofc up to interpretation - maybe the mother is actually pleased at having taught her children to lie so well? :-P