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Unlocking the Power of Logical Thinking: Understanding Knowledge Representation

Explore how our minds surpass computers in non-logical tasks. Dive into logical entailment, well-formed propositions, and semantic properties of WFPs.

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Unlocking the Power of Logical Thinking: Understanding Knowledge Representation

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  1. CSE4/563: Knowledge RepresentationRecitation September 15, 2010 “In activities other than purely logical thought, our minds function much faster than any computer yet devised.” --Daniel Crevier

  2. Brief Unix Tutorial

  3. Questions/Concerns? • http://www.cse.buffalo.edu/~shapiro/Courses/CSE563/2010/Homeworks/hw0.pdf

  4. Logical Entailment • A1,…, An ╞L B

  5. Logical Entailment • A1,…, An ╞L B • Example: • A1 = Tom drives  Betty is the passenger • A2= Tom drives • A1, A2 ╞ Betty is the passenger

  6. Logical Entailment • A1,…, An ╞L B • Example: • A1 = Tom drives  Betty is the passenger • A2= Tom drives • A1, A2 ╞ Betty is the passenger • ╞ B

  7. Well Formed Propositions • Every atomic proposition is a wfp. • 2. If P is a wfp, then so is (~P). • 3. If P and Q are wfps, then so are • (a) (P ^ Q) (b) (P v Q) • (c) (P => Q) (d) (P <=> Q) • 4. Nothing else is a wfp.

  8. Semantic Properties of WFPs • Satisfiable? • Contingent? • Valid? • Unsatisfiable? • Contradictory?

  9. Denotation Example from Notes • Notes p. 48

  10. Logical Entailment • A1,…, An ╞L B • Example: • A1 = Tom drives  Betty is the passenger • A2= Tom drives • A1, A2 ╞ Betty is the passenger • ╞ B • Example: ╞ (P or ~P)

  11. Semantic Tableau • http://www.cse.buffalo.edu/~shapiro/Courses/CSE563/Slides/chap2.pdf p51

  12. Model-Finding Refutation • TDB=>TD, TD=>BP, ~(TP^BP) ╞ ~(TDB ^ TP)

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