PPT-Predicates and Quantified Statements I

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. Dr. Cynthia Bailey Lee. Dr. . Shachar. Lovett. .  .                          . Peer Instruction in Discrete Mathematics by . Cynthia . Lee. is. licensed under a . Creative Commons Attribution-. Senior Comp. practice. Identify Subject. Grammar. Subjects/Predicates. SIMPLE Subjects. Our solar system has nine planets.. The Earth rotates around the sun in twelve months.. The most distant planet from the sun is Pluto.. in. Constraint Programming. Shant Karakashian. , . Robert . J. Woodward. , Berthe . Y. Choueiry,. Steven D. Prestwich . and Eugene C. Freuder. 1. Outline. Interchangeability: Basics . 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. Practices 8-15. Degree of Predicate. The . DEGREE of a predicate is a . number. indicating the number of . arguments. . it is normally understood to have in simple sentences. . A sleep . is a predicate of degree one (often called a one-place predicate) . 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”. Lecture . 13: Symbolic model checking without BDDs. Alex Aiken. David Dill. 1. Bounded model checking. Simple idea: “Unroll” description, use SAT to find a property violation.. State description:. (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). “All students in class passed this course”. “There exists a student in class such that he/she did not pass this course.”. Let . D. denote the set of students in class, and let . P. (. x. ) denote “. 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..