alt Hacker NewsGranted all that, but we're not really talking about normal everyday English, but a hypothetical conversation with some mythical entity who can only lie, which is not really a capability of humans; even the most pathological liar among us can and will tell the truth.
So I'd put all that theory in a drawer somewhere and acknowledge that, when we're talking about logic puzzles, the rules of logic are paramount, not grammar.
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As I said in a previous part of this thread, the rules of logic are as arbitrary (by definition) as they are paramount, and often diverge from natural language logic: https://news.ycombinator.com/item?id=42365222#42368661
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I mean, it's important to remember that the axioms of first-order logic are arbitrary. We could easily argue that the truth value of an empty group is undecidable, and that would better correlate to natural language logic.
The fact that we compact these edge cases into arbitrary truth values is just for ease of computing.
This is also relevant to the arbitrary choice of the 'inclusive or' as a default over an 'exclusive or', which most people use in natural language.
Sure, if your main use of formal logic is to while away the time doing vacuous puzzles.