PPT-Quantifiers in

Satisfiability Modulo Theories Frontiers of Computational Reasoning 2009 MSR Cambridge Leonardo de Moura Microsoft Research Symbolic Reasoning Quantifiers in Satisfiability. Special thanks are due to Kai von Fintel and Irene Heim. We would also like to thank Judy Baek, Elizabeth Lauren Goals. : . Explain . how to work with nested . quantifiers. S. how that . the order . of quantification . matters. . Work . with . logical . expressions involving multiple . quantifiers.. Copyright © . Goal. : . Introduce predicate logic, . including existential . & universal quantification. Introduce translation between English sentences & logical expressions.. Copyright © Peter . Cappello. 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 . 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, . 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 . Dr. . Yasir Ali. Predicates. Quantifiers. . Universal Quantifiers . Existential Quantifiers. Negation of Quantifiers. Universal Conditional Statement. Negation of Universal Conditional. Multiple Quantifiers. Section 1.4. Section Summary. Predicates . Variables. Quantifiers. Universal Quantifier. Existential Quantifier. Negating Quantifiers. De Morgan’s Laws for Quantifiers. Translating English to Logic. 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.. (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. 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. .