PPT-Negations of Quantified Statements

All students in class passed this course There exists a student in class such that heshe did not pass this course Let D denote the set of students in class and let P x denote . 7. /21/15. Unit . 8.5 – Negations 1. Lesson Goal:. Students will know how to translate English sentences using appropriate negation signs.. Vocabularies. Negations. NOT (NOT+FINISH, NOT+MUST, SHOULD+NOT). Dr. Cynthia Bailey Lee. Dr. . Shachar. Lovett. .  .                          . Peer Instruction in Discrete Mathematics by . Cynthia . Lee. is. licensed under a . Creative Commons Attribution-. in. Constraint Programming. Shant Karakashian. , . Robert . J. Woodward. , Berthe . Y. Choueiry,. Steven D. Prestwich . and Eugene C. Freuder. 1. Outline. Interchangeability: Basics . P 3. Review. Ne…pas. Frame the verb. Makes the statement mean the opposite. “Ne” goes before pronouns. Irregular. Ne…jamais. Ne…personne. Ne…rien. Ne…plus. Ne…aucun(e). Ne…que. Ne…ni…ni. Why. are Quantified Statements Important?. The logical structure of quantified statements provides a basis for the construction and validation of . proofs.. Consider the quantified statements…. “For every positive number . 4th . year. PT student. Former. student . assistant. of QSI. The . Quantified. . Self. What. is . Quantified. . Self. ?. Over . to. . you. :. Whom. of . you. does . it. ?. Why. / . why. . not. 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. using. Model Checking and Abstract Interpretation. Anvesh Komuravelli, CMU. Joint work with Ken McMillan. The Problem. Array-Manipulating Program . P. + Assertions. Automatic analysis for. assertion failures. The Logic of Quantified Statements. Section 2.3. Multiple Quantifiers . Multiple Quantifiers. A statement may contain multiple quantifiers, ∀,∃ or ∃, ∀.. When multiple quantifiers are encountered treat them as they come, “in order”. . Siyao. . Guo. . . Ilan. . Komargodski. . New York University . . Weizman. . Institute of Science. Circuit. : directed acyclic graph. Gates labeled by . , . and . . operations. Fan-out 2.. (POPL’08). Presented by. M.Raveendra. Kumar. Some of the slides . adopted . from author’s . presentations. Motivating Example. 2. a[0] = 0;. for (. i. =1; . i. <n; . i. ++) a[. i. ] = 0;. Post condition. 22 – 26 August 2016. 3. The Logic of Quantified Statements. Summary. . 1. . 2. . 3. The Logic of Quantified Statements. Summary. 3. . . 3.1 Predicates and Quantified Statements I. Definition 3.1.1 (Predicate). In logic, predicates can be obtained by removing some or all of the nouns from a statement. For instance, . let . P. stand for “is a student at . UNC”. let . Q. stand for “is a student at”. The rule of . universal instantiation . says the following:. Universal instantiation is . the . fundamental tool of deductive reasoning. . Mathematical formulas, definitions, and theorems are like general templates that are used over and over in a wide variety of particular situations..