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ai-lect8 - Last time Logic and Reasoning Knowledge Base(KB...

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1 Last time: Logic and Reasoning Knowledge Base (KB): contains a set of sentences  expressed using a  knowledge representation language TELL: operator to add a sentence to the KB ASK: to query the KB  Logics are KRLs where conclusions can be drawn Syntax Semantics Entailment: KB |= a iff a is true in all worlds where KB is true Inference: KB |– i   a  = sentence a can be derived from KB using procedure  i Sound: whenever KB |– i   a then KB |= a is true Complete: whenever KB |= a then KB |– i  
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2 Last Time: Syntax of propositional logic
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3 Last Time: Semantics of Propositional logic
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4 Last Time: Inference rules for propositional logic
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5 This time First-order logic Syntax Semantics Wumpus world example
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6 Why first-order logic? We saw that propositional logic is limited because it only makes the  ontological commitment that the world consists of  facts . Difficult to represent even simple worlds like the Wumpus world; e.g.,  “don’t go forward if the Wumpus is in front of you” takes 64 rules
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7 First-order logic (FOL) Ontological commitments: Objects :  wheel, door, body, engine, seat, car, passenger, driver Relations :  Inside(car, passenger), Beside(driver, passenger) Functions :  ColorOf(car) Properties :  Color(car), IsOpen(door), IsOn(engine) Functions are relations with single value for each object
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8 Examples: “One plus two equals three” Objects: Relations: Properties: Functions: “Squares neighboring the Wumpus are smelly” Objects: Relations: Properties: Functions:
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9 Examples: “One plus two equals three” Objects: one, two, three, one plus two Relations: equals Properties: --
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