(May 29, 2014 at 2:11 pm)Tea Earl Grey Hot Wrote: In propositional logic, you actually have to write "(a or b) and not (a and b)" to mean exclusive or. There's no symbol for it.
Quote:“(P v Q)” claims that at least one part is true. So “I went to Paris or I went to Quebec” is true just if I went to one or both places. Our “v” symbolizes the inclusive sense of “or”; English also can use “or” in an exclusive sense, which claims that at least one part is true but not both. Both senses of “or” can translate into our symbolism:
• Inclusive “or”: A or B or both = (A v B)
• Exclusive “or”: A or B but not both = ((A v B) · ~(A · B))”
Excerpt From: Harry J. Gensler. “Introduction to Logic: Second Edition.” iBooks. https://itunes.apple.com/WebObjects/MZSt...=495640131
Formal propositional logic isn't my thing, but programming is - the above is precisely why I'm glad we have separate operators for the two classes of OR in programming languages.
It is inconvenient that the meaning is different from ordinary English usage, but that's not all that unexpected - it's not uncommon to find that words take more specific meanings in specialized disciplines (compare the common and scientific use of "theory", for example).
