PPT-Arguments with Quantified Statements

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. Reference. :. Humphrey, S., Love, K., & . Droga. , L. (2011). . Working Grammar: An introduction for secondary English teachers. . Victoria: Pearson.. Contrast. Contrast. is an important tool in persuasive writing. . 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 . Symbolic Logic I. H. . Hamner. Hill. CSTL-CLA.SEMO.EDU/HHILL/PL120. Logic is the science of . arguments. Separate good arguments from bad ones. Identify the characteristics of good arguments (validity and soundness). 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. 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”. (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). Falsifiability. Understanding facts and arguments. Which arguments require which evidence. Logic of argumentation. Falsifiability – arguments must be able to be wrong. Logic of argumentation. Kinds of statements that are not falsifiable are:. 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”. “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 “. Thinking . clearly and following rules of logic and . rationality. It’s not being argumentative just for the sake of arguing. Academics disagree about which departments do critical thinking in their courses. Philosophers like to think that they are the main ones doing it!.