[FOM] Logical Correctness
pratt at cs.stanford.edu
Fri Nov 23 17:23:01 EST 2012
While I don't know whether Zadeh would agree with this, I would think
that to answer his question without first reading Peter Hajek's
excellent article at
one would basically have to re-invent Hajek's wheel. The two references
Zadeh offered along with his question,
both assume it as a prerequisite.
The former reference should be of particular interest to fans of Belnap
and Anderson's relevant logic, Girard's linear logic, and Dunn's gaggle
(for "generalized galois logics") theory because of the role played in
it by Ward and Dilworth's much earlier (1939) residuated lattices in a
nonclassical modal setting.
Zadeh's question seems to me somewhere between motivation and
advertisement for these papers, which address a considerably wider range
of questions about modal fuzzy logic and suitable implications.
Birkhoff and von Neumann's quantum logic based on orthocomplemented
lattices is another logic with perfectly fine laws for conjunction,
disjunction and (involutory) negation for which implication presents
problems, e.g. the nice-in-some-respects Sasaki hook lacks a Deduction
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