Logical Musings #5

At about this stage in my research, I became interested in the connections with modal logic, the logic of necessity and possibility. Here, my primary source was the symbolic version developed by C. I. Lewis. I adopted his box-and-diamond notation, but I also noted that his versions were developed on an axiomatic basis and did not use truth tables. I took a look at his axioms and tried to fit them with theorems or tautologies of the three valued logic, and they didn’t quit fit. They were close, but didn’t quite match. There was even a mathematical proof that the Lewis systems could not be reduced to a finite number of truth values. There was enough similarity, and I had produced enough theorems to match most of the laws of Boolean Algebra, that I wondered what the difference was. I also took a course in logic at Phoenix College, using “The Logic Book” by Bergmann, Moor, and Nelson, which covered the natural deduction method of logical proof. We only covered propositional logic, but it gave me a better insight into the subject. I also made contact with people who were discussing the possibilities of using three-valued logic in Database programming, particularly as it was implemented in the language SQL. I didn’t quite have the full satisfactory theory yet, but I notice that there was a fierce debate over “Practically Useful” versus “Theoretically Sound” going on in articles and letters of Data Base Programming and Design Journal. The editors called a moratorium and the journal went into electronic publication only, so I lost track of the debate, and the journal has now ceased publication. It did raise some theoretical issues, which bedeviled me for a time.

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