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1.1 No 45
😃: The truth value of the negation of a proposition in fuzzy
logic is 1 minus the truth value of the proposition. What
are the truth values of the statements “Fred is not happy”
and “John is not happy?”
🤖: In classical logic, the negation of a proposition p is denoted by "not p" or "p → false". The truth value of the negation of a proposition is indeed 1 minus the truth value of the proposition.
However, in fuzzy logic, things work differently. In fuzzy logic, the negation of a proposition is often represented using the operator "-", which gives a fuzziness value between 0 (completely false) and 1 (completely true).
Using this convention, we can calculate the truth values of the statements "Fred is not happy" and "John is not happy":
- Statement: Fred is not happy
Truth Value: -(Fred is happy) = 0.5 (fuzzily between completely false and completely true) - Statement: John is not happy
Truth Value: -(John is happy) = 0.5 (fuzzily between completely false and completely true)
So, both statements have a truth value of approximately 0.5, indicating that they are neither entirely true nor entirely false. This makes sense since happiness is a subjective feeling that can vary from person to person, so it's difficult to make absolute claims about someone else's emotional state without direct evidence.