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Understanding Knowledge Representation and Propositional Logic

This recitation provides insights into knowledge representation through various logic forms, focusing on propositional logic and clause forms. Exploring key concepts like terms, predicates, and propositions, the recitation references Aristotle's thoughts on self-acting tools to highlight the importance of structured reasoning. Practical exercises and resources are suggested to reinforce learning, including the use of resolution refutation techniques. Students can find additional practice problems online to enhance their understanding of logical reasoning and representation.

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Understanding Knowledge Representation and Propositional Logic

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  1. CSE4/563: Knowledge RepresentationRecitation October 6, 2010 “If every tool, when ordered, or even of its own accord, could do the work that befits it, just as the creations of Daedalus moved of themselves . . . If the weavers' shuttles were to weave of themselves, then there would be no need either of apprentices for the master workers or of slaves for the lords” --Aristotle

  2. HW3/Proj1 Questions/Concerns? http://www.cse.buffalo.edu/~shapiro/Courses/CSE563/2010/Homeworks/hw3.pdf http://www.cse.buffalo.edu/~shapiro/Courses/CSE563/2010/Projects/proj1.pdf

  3. Recitation Website • http://danielschlegel.org/pages/teaching.htm

  4. Fitch Example From Last Time…

  5. Clause Form Propositional Logic • P <=> q |- (p=>q) ^ (q=>p) • Convert to clause form • Do resolution refutation (trivial)

  6. Resolution Refutation • ((p->q) ^ (r->s) ^ (p v r)) |- q v s • Known as the “Constructive Dilemma” We can think of this in our Dorothy world as: • (DorothyHasToFindToto->InOz)^ MakesToCellar->TakesAWalkWithTotoInKansas ^ (DorothyHasToFindToto v MakesToCellar)) |- (InOz v TakesAWalkWithTotoInKansas)

  7. Resources • If you’re looking for more problems to practice with, one place to look is: • http://en.wikipedia.org/wiki/Propositional_calculus

  8. Terminology Review • Term • Predicate • Proposition • Formula • Open • Closed • Ground

  9. Terminology Practice • Drives(Betty, y) • Is this a term, predicate, proposition, or formula? • Is “Drives” a term, predicate, proposition, or formula? • Is “Betty” a term, predicate, proposition, or formula? • Is “y” a term, predicate, proposition, or formula?

  10. Terminology Practice • Drives(Betty, y) • Is this a term, predicate, proposition, or formula? • Is “Drives” a term, predicate, proposition, or formula? • Is “Betty” a term, predicate, proposition, or formula? • Is “y” a term, predicate, proposition, or formula? • TomDrivesBetty • Is this a term, predicate, proposition, or formula?

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