16_FirstOrderLogic

16_FirstOrderLogic - Beyond Propositional logic...

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11/16/2009 1 First Order Logic Beyond Propositional logic Propositional logic not expressive enough In Wumpus world we needed to explicitly write every case of Breeze & Pit relation “All squares next to pits are breezy” “Regular” programming languages mix facts (data) and procedures (algorithms) World[2,2]=Pit Cannot deduce/compose facts automatically Declarative vs. Procedural Natural Language Natural language probably not used for representation Used for communication “Look!” Look! Visual Thinking One time, we were discussing something – we must have been eleven or twelve at the time – and I said, “But thinking is nothing but talking to yourself.” – “Oh, yeah?”, Bennie said, “Do you know the crazy shape of the crankshaft in a car?” – “Yeah, what of it?” – “Good. Now tell me: how did you describe it when you were talking to yourself?” (Feynman, 1988) First Order Logic Idea: Don’t treat propositions as “atomic” entities. First Order Logic: Objects: cs4701, fred, ph219, emptylist … Relations/Predicates: is_Man(fred), Located(cs4701, ph219) … Note: Relations typically correspond to verbs Functions: Best_friend(), beginning_of() Connectives: , , , , Quantifiers: Universal: x: ( is_Man(x) ) is_Mortal(x) ) Existential: y: ( is_Father(y, fred) )
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11/16/2009 2 Wumpus Squares neighboring the wumpus are smelly Objects: Wumpus, squares Property: Smelly Relation: neighboring Evil king john rules England in 1200 Objects: John, England, 1200 Property: evil, king Relation: ruled Example: Representing Facts in First Order Logic 1. Lucy* is a professor 2. All professors are people. 3. Ober is the dean. 4. Deans are professors. 5. All professors consider the dean a friend or don’t know him. 6. Everyone is a friend of someone. 7. People only criticize people that are not their friends. 8. Lucy criticized Ober. * Name changed for privacy reasons. Example: Proof Knowledge base: is prof(lucy) x ( is prof(x) is person(x) ) is dean(Ober) x (is dean(x) is prof(x)) x ( y ( is prof(x) is dean(y) is friend of(y,x)   knows(x, y) ) ) x ( y ( is friend of (y, x) ) ) x ( y (is person(x) is person(y) criticize (x,y) is friend of (y,x))) criticize(lucy, Ober) Question: Is Ober no friend of Lucy? is friend of(Ober ,lucy) Other logics Temporal logic Truths and relationships change and depend on time Fuzzy logic Uncertainty contradictions Uncertainty, contradictions High order logic Where relationships are themselves objects Knowledge Engineering 1. Identify the task.
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