Discrete Mathematic教学课件（华南理工大学）Ch01-3 1-4 PredicatesAndQuantifiers2.pdfVIP

Discrete Mathematic Chapter 1: Logic and Proof 1.3 Predicates and Quantifiers 1.4 Nested Quantifiers Dr Patrick Chan School of Computer Science and Engineering South China University of Technology Cha pter 1.3 1.4 2 Agenda Ch1.3 Predicates and Quantifiers Predicates Quantifiers Quantifiers with Restricted Domains Precedence of Quantifiers Logical Equivalences Involving Quantifiers Translation Ch1.4 Nested Quantifiers Nested Quantifiers Cha pter 1.3 1.4 3 Limitation of Propositional Logic Limitation 1: p : John is a SCUT studentis a SCUT student q : Peter is a SCUT studentis a SCUT student r : Mary is a SCUT student is a SCUT student Try to represent them using propositional variable However, these propositions are very similar A more powerful type of logic named Predicate Logic will be introduced Cha pter 1.3 1.4 4 Predicates Predicate logic is an extension of propositional logic that permits concisely reasoning about whole classes of entities John Peter Mary ???? Propositional Logic Predicate Logic treats simple distinguishes the subject propositions as atomic of a sentence from its entities predicate Cha pter 1.3 1.4 5 Predicates Predicate is a function of proposition Example: Convention: • lowercase variables de