Symbolic Logic Definition of an Opposite

Logic & Philosophy of Mathematics
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Is it possible to give a logical/mathematical definition of what makes a something an opposite of something else?

Hot is considered the opposite of cold, light the opposite of darkness. But is upstairs the opposite of downstairs? Is cool the opposite of warm? And can “oppositeness” be described by a definition in symbolic logic?

Or is it just vibes?

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That’s a very good question, indeed.

I don’t know because when I see symbolic logic as this, ¬𝑃 or this, 𝑃→¬𝑄, I think it may be representing contradiction and not oppositeness.

@Banno and @Michael may know.