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Introduction to Predicate Logic: Key Concepts and Techniques

Explore predicate logic concepts, including propositional logic, induction, and formal proof techniques. Discover how to reason without knowing specific variable values. Dive into puzzles to apply your new logic skills.

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Introduction to Predicate Logic: Key Concepts and Techniques

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  1. CS1001 Lecture 21

  2. Overview • Projects • Predicate Logic

  3. Goals • Learn some predicate logic

  4. Assignments • Brookshear: Chapter 11 • Read linked documents on these slides (slides will be posted in courseworks)

  5. Induction • A formal proof technique • Prove a ground case • Prove every case “one more” than some case is also true (prove n+1 assuming n)

  6. Propositional Logic • Symbols (variables holding true/false) • Operators • Key Point: The logic system does not rely on the actual values inside the variables. You can reason without knowing the actual values (like an algorithm) • A and B -> A

  7. Logic Rules • There are a number of rules for introducing/removing • Core operators: And, Or, Not, Implies

  8. A Puzzle Introduction (Smullyan) • There are two casket makers, Bellini and Cellini • All Bellini caskets have true inscriptions • All Cellini caskets have false inscriptions

  9. A Puzzle (Smullyan)

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