L3predicatelogic(ch2)

L3predicatelogic(ch2) - Predicate Logic (part 1) (Chapter...

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Predicate Logic (part 1) (Chapter 2) CSE 352 Artificial Intelligence Professor Anita Wasilewska Lecture Notes (3)
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Predicate Logic Language Symbols: 1. P, Q, R… predicates symbols , denote relations in “real life”, countably infinite set 2. x,y,z…. variables, countably infinite set 3. c1, c2, … constants , countably infinite set 4. f, g, h functional symbols , may be empty, denote functions in “real life” 5. Propositional connectives : , , , ¬, 6 . Symbols for quantifiers x – universal quantifier reads: For all x… x – existential quantifier reads: There is x…
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Formulas of Predicate Logic We use symbols 1 - 6 to build formulas of predicate logic as follows 1. P(x), Q(x,y), R(x)… R(c1), Q(x, c3), P(c), … are called atomic formulas for any variables x, y,… and constants c, c1, c2, … 2. All atomic formulas are formulas ; 3. If A,B are formulas then (like in propositional logic): (A B) , (A B), (A B), (A B), ¬A are formulas 4. x A, y A are formulas, for any variables x, y 5. The set F of all formulas is the smallest set that fulfills the conditions 1 -4.
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