After checking some publications I am convinced that the multivalued logic
definitions for AND and INCLUSIVE OR are the same as that for fuzzy logic.
Lukasiewicz used the following definitions (> is the IMPLICATION operation):
INCLUSIVE OR = ((p>q)>q)
AND = -(-p OR -q).
Which are equivalent to the fuzzy logic minimum and maximum definitions (see
proofs in Robert Ackermann (1967) An Introduction to Many-valued Logics).
The definitions you gave come from the following definitions which while
associated with Lukasiewicz logic were not the ones chosen by him:
INCLUSIVE OR = -p>q
AND = -(p>-q)
Sincerely,
David Olmsted
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