ln3 - Unit 3 Notes Predicate Logic Quantifiers Translations...

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Unformatted text preview: Unit 3 Notes Predicate Logic Quantifiers Translations in Monadic Predicate Logic Translations in Polyadic Predicate Logic Restrictive Clauses Review Introduction to Logic, Unit 3 Kevin C. Klement UMassAmherst Unit 3 Notes Predicate Logic Quantifiers Translations in Monadic Predicate Logic Translations in Polyadic Predicate Logic Restrictive Clauses Review The Limitations of Sentential Logic In sentential logic, a letter represents an entire atomic statement. It cannot represent common features between atomic statements. Examples of Common Features in Atomic Statements 1 Kanye West is an egotist. shares features in common with: 2 Kanye West is a musician. (Same subject, different predicate.) 3 Lindsay Lohan is an egotist. (Same predicate, different subject.) 4 Everyone is an egotist. (Same predicate, general subject.) 5 Someone is an egotist. (Same predicate, indefinite subject.) Unit 3 Notes Predicate Logic Quantifiers Translations in Monadic Predicate Logic Translations in Polyadic Predicate Logic Restrictive Clauses Review The Limitations of Sentential Logic, continued Sentential logic treats these all as simple statements ( K , M , T , E , S , etc.), and so loses any connection between them. A Valid Argument not captured by Sentential Logic Kanye West is an egotist. Therefore, someone is an egotist. However the argument: K S is obviously invalid in sentential logic. We now introduce a new style of symbolic logic, called predicate logic . Unit 3 Notes Predicate Logic Quantifiers Translations in Monadic Predicate Logic Translations in Polyadic Predicate Logic Restrictive Clauses Review Subjects and Predicates In predicate logic . . . Lowercase letters (except x , y and z ) represent specific individual persons, places or things. (Subjects) Uppercase letters represent things that can be said about the things above. (Predicates) Example subjects English becomes Amsterdam a Kevin k Britney Spears b the Pope p five (or 5) f Example predicates English becomes is hungry H plays tennis T has driven drunk D is prime P loves . . . L Unit 3 Notes Predicate Logic Quantifiers Translations in Monadic Predicate Logic Translations in Polyadic Predicate Logic Restrictive Clauses Review Predicate Logic Statements We put these together, capital letters first , to form statements. Example Statements 1 Kevin is hungry. Becomes: Hk 2 Britney Spears is hungry. Becomes: Hb 3 Britney Spears plays tennis. Becomes: Tb 4 5 is prime. Becomes: Pf 5 The pope loves Britney Spears. Becomes: Lpb Unit 3 Notes Predicate Logic Quantifiers Translations in Monadic Predicate Logic Translations in Polyadic Predicate Logic Restrictive Clauses Review Monadic and Polyadic Predicates Polyadic or relational predicates are those that are applied to more than one thing....
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ln3 - Unit 3 Notes Predicate Logic Quantifiers Translations...

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