PPT-Predicates and Quantifiers

Dr Yasir Ali Predicates Quantifiers Universal Quantifiers Existential Quantifiers Negation of Quantifiers Universal Conditional Statement Negation of Universal Conditional Multiple Quantifiers. 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 © . Goal. : . Introduce predicate logic, . including existential . & universal quantification. Introduce translation between English sentences & logical expressions.. Copyright © Peter . Cappello. Propositional Logic Not Enough. Given the statements: . “All men are mortal.”. “Socrates is a man.”. It follows that “Socrates is mortal.”. This can’t be represented in propositional logic. . 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.. 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, . 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) . Goal. : . Introduce predicate logic, . including existential . & universal quantification. Introduce translation between English sentences & logical expressions.. Copyright © Peter . Cappello. Goals. : . Explain . how to work with nested . quantifiers. S. how that . the order . of quantification . matters. . Work . with . logical . expressions involving multiple . quantifiers.. Copyright © . Satisfiability. Modulo Theories . Frontiers . of . Computational Reasoning . 2009 . –. MSR Cambridge. Leonardo de Moura. Microsoft Research. Symbolic Reasoning. Quantifiers in . Satisfiability. Section 1.4. Section Summary. Predicates . Variables. Quantifiers. Universal Quantifier. Existential Quantifier. Negating Quantifiers. De Morgan’s Laws for Quantifiers. Translating English to Logic. Modulo Theories . Manchester 2009. Leonardo de Moura. Microsoft Research. Symbolic Reasoning. Quantifiers in . Satisfiability. Modulo Theories. PSpace. -complete. (QBF). Undecidable. (First-order logic). 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)) .