PPT-QUANTIFIERS

MUCH We use it with UNCOUNTABLE nouns I dont have much money It is more usual in negative and interrogative sentences We didnt spend. Special thanks are due to Kai von Fintel and Irene Heim. We would also like to thank Judy Baek, Elizabeth Lauren 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 . Goals. : . Explain . how to work with nested . quantifiers. S. how that . the order . of quantification . matters. . Work . with . logical . expressions involving multiple . quantifiers.. Copyright © . 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. ). . 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 . Andrew Reynolds. Cesare. . Tinelli. Leonardo De . Moura. July 18, 2014. Outline of Talk. SMT solvers:. . Efficient. methods for . ground. constraints. . Heuristic. methods for . quantified. formulas. 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. What . is your quantifier quotient (QQ)?. Barbara . Zurer. . Pearson. bpearson@research.umass.edu. University of Massachusetts . Amherst. Language Acquisition . Colloquium. Background. This work is part of the preliminary studies for an . Goals. : . Explain . how to work with nested . quantifiers. S. how that . the order . of quantification . matters. . Work . with . logical . expressions involving multiple . quantifiers.. Copyright © . Satisfiability. Modulo Theories . Frontiers . of . Computational Reasoning . 2009 . –. MSR Cambridge. Leonardo de Moura. Microsoft Research. Symbolic Reasoning. Quantifiers in . Satisfiability. 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. .