Lecture 6 - Limitation of propositional logic Propositional...

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Limitation of propositional logic Propositional logic has very limited expressive power (unlike natural language) E.g., cannot say "pits cause breezes in adjacent squares“ • except by writing one sentence for each square
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First-order logic Whereas propositional logic assumes the world contains facts , first-order logic (like natural language) assumes the world contains Objects : people, houses, numbers, colors, baseball games, wars, … Relations : red, round, prime, brother of, bigger than, part of, comes between, … Functions : father of, best friend, one more than, plus, … Much more expressive than propositional
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Models for FOL: Example
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Syntax of FOL: Basic Elements Constants KingJohn, 2, NUS,. .. Predicates Brother, >,. .. Functions Sqrt, LeftLegOf,. .. Variables x, y, a, b,. .. Connectives ¬ , , , , Equality = Quantifiers 2200 , 5
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Atomic sentences Atomic sentence = predicate ( term 1 ,..., term n ) or term 1 = term 2 Term = function ( term 1 ,..., term n ) or constant or variable E.g., Brother(KingJohn,RichardTheLionheart) (Length(LeftLegOf(Richard)) > Length(LeftLegOf(KingJohn)))
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Complex sentences Complex sentences are made from atomic
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Lecture 6 - Limitation of propositional logic Propositional...

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