lecture26

lecture26 - CS245 - Winter 2010, Lecture of Feb. 24th Shai...

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Unformatted text preview: CS245 - Winter 2010, Lecture of Feb. 24th Shai Ben-David first Order Logic (FOL) is, in fact, a family of languages, all sharing the same structure. To determine the specific language in first order logic, we have to choose a vocabulary for that language, which will consist of three types of objects: 1. Constant symbols eg. a,b,... 2. Relation symbols eg. R 1 ,R 2 ,... 3. Function symbols eg. F 1 ,F 2 ,... Examples: 1. A language for discussing orders L = h ,R ( , ) , i where R ( x,y ) expresses x < y . For example, in this language, the formula x y R ( x,y ) expresses the state- ment there is no largest element. 2. A language to express statements about numbers L = h ( a,b ) ,R ( , ) , ( F ( , ) ,G ( , ) i where a may denote the number 0, b may denote 1, R ( x,y ) expresses x < y , F ( x,y ) expresses x + y , and G ( x,y ) expresses the multiplication. Under this interpretation, x y z F ( x,G ( y,z )) = G ( F ( x,y ) ,F ( x,z )) ex- presses the equality...
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This note was uploaded on 04/07/2010 for the course CS 245 taught by Professor A during the Spring '08 term at Waterloo.

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lecture26 - CS245 - Winter 2010, Lecture of Feb. 24th Shai...

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