PPT-Quantifiers and logical inference

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 . . A School Leader’s Guide for Improvement. 1. Georgia Department of Education . Dr. John D. Barge, State School Superintendent . All Rights Reserved. The Purpose of this Module is to…. p. rovide school leaders an opportunity to strengthen their understanding of low inference feedback.. 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. ). . 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. . Chapter 2. Predicates and quantifiers. Can be used to express the meaning of a. . wide range of statements. Allow us to reason and explore relationship between objects. 2. Predicates. statements involving variables, . 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,. Warm up. Share your picture with the people at your table group.. Make sure you have your Science notebook, agenda and a sharpened pencil. use tape to put it in front of your table of contents. Describe the difference between observations and inferences. 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 . Satisfiability. Modulo Theories . Frontiers . of . Computational Reasoning . 2009 . –. MSR Cambridge. Leonardo de Moura. Microsoft Research. Symbolic Reasoning. Quantifiers in . Satisfiability. 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.. 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. ). . P(4) . is true, but . 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)) .