Lecture 5

Lecture 5 - Lecture 5 Logic is a Game II Limitations of...

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Lecture 5 Logic is a Game II
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Limitations of Propositional Logic How does propositional logic express a statement like: All men are mortal. If there are finitely many of those men, then we can say: (Man 1 is mortal) (Man 2 is mortal) Notes: The above sentence could be very long. What if there are infinitely many men?
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Predicate (First Order) Logic For the statement: All men are mortal. We use the predicates: Man(x), which means: “x is a man”. Mortal(x), which means: “x is mortal”. We then write: ( 2200 x)(Man(x) Mortal(x)) to mean: “For every x, if x is a man, then x is mortal” Note: (A B) is an abbreviation for ( ¬ A B), i.e. the above sentence reads: “For every x, either x is not man, or (if x is indeed a man) x is mortal”
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Syntax of Predicate Logic Formed from atomic formulas like: Man(x), Mortal(x): unary predicates, Friend(x,y): a binary predicate, which means: “x is a friend of y”. Addition(x,y,z): a ternary predicate, which
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Lecture 5 - Lecture 5 Logic is a Game II Limitations of...

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