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Verifying Logical Arguments with Extensible Truth Tables. David B. Sher Dept. of Math, Computer Science and Information Technology Nassau Community College Garden City NY 11530 David. Sher @ncc.edu. Breaking Tradition. Traditional Truth Table: Mysterious Memorized Extensible Truth Table:
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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
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.
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.
Translating to Logic • Legend: s = the Steelers win; p = the Packers win; d = I go to Disneyland; a = I go to Adventureland. • Argument:
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
Conclusion • Breaking tradition • Can introduce any number of variables • Cross off the impossible • Creates efficiency • Sometimes statement reason still better