Logic

Note: A username and password may be required for some online papers. Please contact Bill Rapaport.

1. Logic & Automated Theorem Proving
   1. Propositional & First-Order Logic
      • Translating from English to a First-Order Language
        • Representing English Sentences in FOL
        • Suber, Peter (2002), "Translation Tips"
          • Note: The above documents use different symbols for the logical connectives;
            please ask me if you can't figure them out.

   2. Automated Theorem Proving
   3. Syntax vs. Semantics

2. Are there as many true propositions as false ones?

3. Lewis Carroll, Logican
   Lewis Carroll, most well known as the author of "Alice in Wonderland" (more properly known as Alice's Adventures in Wonderland and Through the Looking-Glass), was also a professional logician. You might find the following of interest:
   1. "Lewis Carroll: Logican and Mathematician"

   2. "Lewis Carroll Puzzles"

   3. "Carroll's Paradox"
      • Original version:
        Carroll, Lewis (1895), "What the Tortoise Said to Achilles", Mind 4(14) (April): 278-280.

      • This cute story by the author of Alice in Wonderland, who was a professor of logic at Oxford University(!), has been interpreted in many ways. My understanding of it is that it clarifies the nature of rules of inference.

4. Tropp, Henry S. (1984), "Origin of the Term Bit", [IEEE] Annals of the History of Computing 6(2) (April): 152-155. [PDF]

5. Tymoczko, Thomas (1979), "The Four-Color Problem and Its Philosophical Significance", Journal of Philosophy 76(2) (February): 57-83.
   • Has some interesting ideas on the nature of mathematical proofs by computer, and whether mathematics is an empirical science.

   • Also see:
     Gardner, Martin (1966), Martin Gardner's New Mathematical Diversions from Scientific American (New York: Simon & Schuster), Ch. 10: "The Four-Color Map Theorem", pp. 113-123, 250-251.

6. Logical Equivalences (from Rosen)
   • PowerPoint slides (from Rosen)

7. Rules of Inference (from Rosen)

8. 
   Understanding & Creating Proofs
   • [PPT]
   • [html slide show]
   • [html text]

9. John McCarthy's research on knowledge representation using FOL:
   • McCarthy, John (1959), "Programs with Common Sense", in D.V. Blake & A.M. Uttley (eds.), Proceedings of the ["Teddington"] Symposium on Mechanisation of Thought Processes (London: HM Stationary Office).