Logic1014 - First-order logic jq 1. 2. 3. All and some...

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Midterm Monday 19th 9pm, Room 403 (this build- ing) Covers Smullyan, pp.1 – 119 (up to today’s lecture) Format True-false questions Problem-solving questions F Similar to Problems in Smullyan Proof questions F Similar to HW questions requiring proofs
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Symbols for all and some All: a universal quantifier ∀ (inverted A for “All”). Some: an existential quantifier ∃ (inverted E for “Exist”). These quantifiers are followed by variables x, y, z – standing for arbitrary objects in the domain. The domain is simply the set of objects we are interested in – set of people, set of natural numbers, etc.
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“x has property P” is symbolized by Px. “All x has the property P”: ∀xPx. Ex. everyone is special: ∀xSx. “Some x has the property P”: ∃xPx. Meaning “at least one” or “there ∃xists” Ex. Some people are good: ∃xGx. “No one is good”: ~∃xGx or ∀x(~Gx).
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“All good(G) people go to heaven(H).” ∀x is obvious. But what comes next? F “For every x, if x is good, then x goes to heaven.” ∀x (Gx => Hx). “Only good people go to heaven.” F “ All those who go to heaven are good.” ∀x (Hx => Gx).
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“Some good people go to heaven.” ∃x is obvious. But what comes next?
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This note was uploaded on 02/04/2010 for the course HSS Hss105 taught by Professor Yeelee during the Fall '09 term at Korea Advanced Institute of Science and Technology.

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Logic1014 - First-order logic jq 1. 2. 3. All and some...

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