Knowledge Representation a) There are no crazy UMB students. x (UMBStudent(x)  Crazy(x)) b) All computer scientists are either rich or crazy, but not both. x (CS(x)  [Rich(x)  Crazy(x)]  [Rich(x)  Crazy(x)] ) c) All UMB students except one are intelligent. x (UMBStudent(x)  Intelligent(x))  x,y (UMBStudent(x)  UMBStudent(y)  Identical(x, y)  Intelligent(x)  Intelligent(y)) d) Jerry and Betty have the same friends. x ([Friends(Betty, x)  Friends(Jerry, x)]  [Friends(Jerry, x)  Friends(Betty, x)]) e) No mouse is bigger than an elephant. x,y (Mouse(x)  Elephant(y)  BiggerThan(x, y)) October 18, 2018 Introduction to Artificial Intelligence Lecture 14: Knowledge Representation & Reasoning III

Rules of Inference x P(x) Universal instantiation __________  P(c) if cU Universal instantiation P(c) for an arbitrary cU ___________________  x P(x) Universal generalization x P(x) ______________________  P(c) for some element cU Existential instantiation P(c) for some element cU ____________________  x P(x) Existential generalization October 18, 2018 Introduction to Artificial Intelligence Lecture 14: Knowledge Representation & Reasoning III

Rules of Inference Example: Every UMB student is a genius. George is a UMB student. Therefore, George is a genius. U(x): “x is a UMB student.” G(x): “x is a genius.” October 18, 2018 Introduction to Artificial Intelligence Lecture 14: Knowledge Representation & Reasoning III

Rules of Inference The following steps are used in the argument: Step 1: x (U(x)  G(x)) Hypothesis Step 2: U(George)  G(George) Univ. instantiation using Step 1 Step 3: U(George) Hypothesis Step 4: G(George) Modus ponens using Steps 2 & 3 x P(x) __________  P(c) if cU Universal instantiation October 18, 2018 Introduction to Artificial Intelligence Lecture 14: Knowledge Representation & Reasoning III