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Efficient Logic Verification with Extensible Truth Tables

Learn how to break traditional truth tables with extensible ones, identifying logical arguments efficiently by eliminating impossible premises and verifying with Extensible Truth Table Method. This method, developed based on Sherlock Holmes' logic, simplifies the process and enhances understanding of arguments through the introduction of new variables.

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Efficient Logic Verification with Extensible Truth Tables

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  1. Verifying Logical Arguments with Extensible Truth Tables David B. SherDept. of Math, Computer Science and Information Technology Nassau Community College Garden City NY 11530 David. Sher @ncc.edu

  2. Breaking Tradition • Traditional Truth Table: • Mysterious • Memorized • Extensible Truth Table: • Any number of new variables • Process not tradition • Explains rows of truth tables as possibilities • New variable doubles possibilities.

  3. Logical Arguments • Developed by L. Sher based on Sherlock Homes. • “when you have eliminated the impossible, whatever remains, however improbable, must be the truth” • Logical arguments apply logic. Either the Steelers will win or the Packers will win. If the Steelers win I go to Disneyland. If the Packers win I go to Adventureland. I don’t go to Disneyland. Therefore I go to Adventure land.

  4. Translating to Logic • Legend: s = the Steelers win; p = the Packers win; d = I go to Disneyland; a = I go to Adventureland. • Argument:

  5. Verifying with Extensible Truth Table

  6. Method • Premises must be true • Eliminate the impossible: cross off lines with premise false • Pick premises that generate large percentage of falses first. • Extensible Truth Table • New variable only copy possible lines • Crossed off lines don’t copy

  7. Conclusion • Breaking tradition • Can introduce any number of variables • Cross off the impossible • Creates efficiency • Sometimes statement reason still better

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