Verifying Logical Arguments with Extensible Truth Tables

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Presentation transcript:

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 February 15, 2019

Breaking Tradition Traditional Truth Table: Extensible 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. February 15, 2019

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. February 15, 2019

Translating to Logic Legend: s = the Steelers win; p = the Packers win; d = I go to Disneyland; a = I go to Adventureland. Argument: February 15, 2019

Verifying with Extensible Truth Table February 15, 2019

Method Premises must be true Extensible Truth Table 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 February 15, 2019

Conclusion Breaking tradition Can introduce any number of variables Cross off the impossible Creates efficiency Sometimes statement reason still better February 15, 2019

February 15, 2019