PPT-Nested Quantifiers
Author : alexa-scheidler | Published Date : 2017-05-21
Goals Explain how to work with nested quantifiers S how that the order of quantification matters Work with logical expressions involving multiple quantifiers
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Nested Quantifiers: Transcript
Goals Explain how to work with nested quantifiers S how that the order of quantification matters Work with logical expressions involving multiple quantifiers Copyright . 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. ). . More examples: . ``student . is enrolled in class . ”. . . . 1. Someone in your class has an Internet connection but has not chatted with anyone else in the class.. 2. There are two students in the class who between them have chatted with everyone else in the class.. 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. . 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. A. n. v. e. s. h. . K. o. murave. l. l. i. work done at Carnegie Mellon University. Joint work with . Nikolaj. . Bjørner. , . Arie. . Gurfinkel. , and Kenneth McMillan. In essence…. 1. Efficiently under-approximating projections,. 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 . 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. 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 . Satisfiability. Modulo Theories . Frontiers . of . Computational Reasoning . 2009 . –. MSR Cambridge. Leonardo de Moura. Microsoft Research. Symbolic Reasoning. Quantifiers in . Satisfiability. One if statement inside another one. An if statement inside a loop. A loop inside an if statement. Control structures can be nested inside each other to any degree you need . Nested loops. The general principle of nesting loops is that the inner loop must completely finish its execution before the next iteration of the outer loop starts. 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. (First order Logic). Find the proposition whose Truth Table column is give.. Another form. Some slides have been taken from the sites. http://cse.unl.edu/~choueiry/S13-235/. and . http://. www.whitman.edu. 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)) .
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