bwk@mbunix.mitre.org (Barry W. Kort) (01/24/89)
Having spent most of our professional lives with von Neumann machines, Boolean Logic, Crisp Sets, and Aristotle's Law of the Excluded Middle, we have difficulty breaking out of our conceptual prison. Let us gently walk through the Gateless Gate... A proposition may represent a hunch, opinion, belief, hypothesis, or theory. Consider a few: Fermat's Last Theorem is provable. Black holes are connected to white holes by worm holes. Kort's Theory of Theories is vague. It is convenient (and even useful) to assign numerical "degrees of belief" to such assertions. We can then apply the calculus of Fuzzy Logic, or Bayesian Inference, or Confidence Values to collections of unproven assertions. As evidence accumulates, we attempt to push the numerical degree of belief toward one (provably true) or zero (provably false). As in traditional calculii and algebras, the truth values are symbolized by "x", the Unknown. Our language is rich with expressions denoting degrees of belief: probably, surely, uncertain, likely, doubtful, maybe. By admitting a continuum in the void between True and False, we invent a more powerful logic than that of Aristotle. Kripke's Intuitionist Logic is an example of trans-Boolean symbolic logic. Lofti Zadeh's Fuzzy Logic is a poor man's implementation of continuous-valued logic, with a simple, if technically flawed calculus. Rather than quibble over the paradoxes in bivalent logic, would we not be better served if we perfected our theory and understanding of continuous-valued logic? Or is the theory too vague to be believable? --Barry Kort