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Monday, July 30, 2007 10:30 AM Predicate Logic Jay and Kay are sophomores. Jay and Kay are cousins. The second implies a relationship between Jay and Kay. We grammatically analyze the second sentence as having a subjectpredicate structure. The two place predicate ' __ is a cousin of__' . The one place predicate ' __ is a sophomore' expresses the property of being a sophomore. Some one place predicates ___ is clever ___ sleeps soundly ___ is very happy. 2 place __ is taller than ___ ___ loves _____ ___ admires ____ 3 place ___ is between ___ and ___ ___ is the sum of ___ and ___ Predicates work like connectives in that they take in one or multiple inputs and spit out an output. Singular terms. 1 2 3 Different kinds of expressions that function as singular terms in english. Proper nouns Definite description president of the USA Demonstrative noun phrases e.g. that guy, that thing A useful test is to ask: can this expression be used with the singular verb form is Intro to Logic Page 1 John is Jenny and Fred is X The happiest drunkard is She is The two unfriendliest ogres is X We symbolize simple statements with an uppercase letter and singular terms as lower case letters __is Tall T __ is insane I __is a cousin of __ C ___lent___ to __ L The king of France k John Lennon j He h Mongolia m Cjk Sometimes we want the predicate to symbolize a property and not a relation such as Jay and Kay are married but not to each other Mj&Mk As opposed to Mjk ~Mkj Quantifiers and variables Some dogs are pets. All people are crazy. There are no unicorns. Everyone who is married is purple. A quantifier is an expression denoting the quantity of something. All, some, none In predicate logic we only use two quantifiers. 1 2 1 2 All, every Some, at least one Universal quantifier: everything is such and such Existential quantifier: there is at least one thing that exists that is such and such C1 Everything is blue C2 Something is blue F1 xBx Intro to Logic Page 2 F2 xBx Intro to Logic Page 3 ...
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This note was uploaded on 04/07/2008 for the course PHILOSOPHY 201 taught by Professor Morgan during the Spring '08 term at Rutgers.
- Spring '08