PPT-Predicates and Quantifiers

Dr Yasir Ali Predicates Quantifiers Universal Quantifiers Existential Quantifiers Negation of Quantifiers Universal Conditional Statement Negation of Universal Conditional Multiple Quantifiers. Nested Quantifiers. Needed to express statements with multiple variables . Example 1. : “. x+y. = . y+x. for all real numbers” . . xy. (. x+y. = . y+x. ) . where the domains of . x. and . Logic and Proof. Fall . 2011. Sukumar Ghosh. Predicate Logic. Propositional logic has limitations. Consider this:. Is . x. . > 3. a proposition? No, it is a . predicate. . Call it . P(x. ). . Goal. : . Introduce predicate logic, . including existential . & universal quantification. Introduce translation between English sentences & logical expressions.. Copyright © Peter . Cappello. Propositional Logic Not Enough. Given the statements: . “All men are mortal.”. “Socrates is a man.”. It follows that “Socrates is mortal.”. This can’t be represented in propositional logic. . There are different types of determiners. . The . type of determiner depends on the type of noun. Singular nouns always need a determiner. Plural nouns the determiner is optional. Uncountable nouns the determiner is also optional. . Predicate Logic. 1 Aug 2013. Predicate Logic (§1.3). Predicate logic. is an extension of propositional logic that permits concisely reasoning about whole . classes. of entities.. Propositional logic (recall) treats simple . Day 3, 1.4 Quantifiers. 1. 3. Predicates. A lot like functions that return . booleans. Let P(x) denote x<12. P(2) = . P(50) = . Let P(x, y, z) denote x-y<z. P(5, 4, 2) = . P(10, 5, 1) = . 4. Quantifiers. Not all noun phrases (NPs) are (by nature) directly referential like names. Quantifiers. : . “. something to do with indicating the quantity of something. ”. Examples. :. every. child. nobody. two. Goals. : . Explain . how to work with nested . quantifiers. S. how that . the order . of quantification . matters. . Work . with . logical . expressions involving multiple . quantifiers.. Copyright © . Structures. Logic and Proof. Spring 2014. Sukumar Ghosh. Predicate Logic. Propositional logic has limitations. Consider this:. Is . x. . > 3. a proposition? No, it is a . predicate. . Call it . Lecture 5. Predicate Logic. Spring 2013. 1. Announcements. Reading assignments. Predicates and Quantifiers. 1.4, 1.5 7. th. Edition. 1.3, 1.4 6. th. . Edition. Hand in Homework 1 now. Homework 2 is available on the website. Objectives. Identify English sentences that are statements.. Express statements using symbols.. Form the negation of a statement.. Express negations using symbols.. Translate a negation represented by symbols into English.. Exercise 4. Exercise . Translate . these statements into English, where C(x) is “. x. . is a comedian” and F(x) is “x is funny” and the domain . consists . of all people. . . a)∀. x(C(x)→F(x)) . Adapted from Patrick J. Hurley, . A Concise Introduction to Logic. (Belmont: Thomson Wadsworth, 2008).. Predicate Logic. Before I go on to explain quantifiers, first let me address different ways of symbolizing statements. Previously, we used one letter to symbolize one statement. But there is another way to symbolize certain kinds of statements that are relevant to quantifiers. We can also symbolize statements by symbolizing the predicate and subject separately. .