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Your formula `(A --> B) ^ (¬A --> C)` expands to `¬(A & B) & (A | ¬C)`. I would propose that `(A & B) ^ (¬A & C)`, which expands to `(¬A | B) & (A | C)`, comes
by tempodox 6y ago
Your formula `(A --> B) ^ (¬A --> C)` expands to `¬(A & B) & (A | ¬C)`. I would propose that `(A & B) ^ (¬A & C)`, which expands to `(¬A | B) & (A | C)`, comes closer to actual `if` semantics.
- hollerith 6y agoThey are equivalent (assuming ^ is the same as &). In particular, A --> B is equivalent to ¬A | B.
- tempodox 6y agoI see. I interpreted `^` as XOR. The implication (`-->`) was clear enough to not be misunderstood.
- chriskanan 6y agoThe "ʌ" symbol (^ due to laziness) is commonly used to mean AND in propositional/formal logic in mathematics: https://en.wikipedia.org/wiki/Propositional_calculus https://en.wikipedia.org/wiki/Propositional_calculus
- tempodox 6y agoI know, but due to the use of “¬” for the negation I would have expected “∧” (‘LOGICAL AND’, U+2227), or at least something less ambiguous, like “&”. C conditioned me into thinking of ASCII caret as XOR.