lecture2 2009

Lecture2 2009 - Names(also called individual constants Names of first order logic(FOL refer to pick out individual objects in the world In FOL we

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Names (also called individual constants). Names of first order logic (FOL) refer to, pick out, individual objects in the world. In FOL, we insist that: A) They must uniquely denote B) The object denoted must exist (i.e. not be fictional, imaginary, etc.) In English, we are laxer. `Bertrand Arthur William Russell’ is a name that satisfies B) and (almost certainly) A). `George Foreman’ is a name that satisfies B) but not A). `Sherlock Holmes’ is a name that satisfies A) but not B). `Agent Smith’ (as used within The Matrix) satisfies neither A) nor B).
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Examples of names in FOL: a,b,c,. ..f, n 1 , n 2, ...... It is acceptable in FOL for a given object to have more than one name. But a single name in FOL cannot pick out more than one object. There can also be objects that have no name. Example: most of the stars have no name, although they could in principle. (Mathematical Fact: It is impossible to name almost all of the real numbers, where `almost all’ means `all but countably many’.)
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Unary Predicate Symbols. Unary predicates apply to single names. They often,
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This note was uploaded on 10/10/2009 for the course CS 2102 taught by Professor Knight during the Spring '08 term at UVA.

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Lecture2 2009 - Names(also called individual constants Names of first order logic(FOL refer to pick out individual objects in the world In FOL we

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