CS 730/730W/830: Intro AI What is KR? Prop. Logic Reasoning 2 - PowerPoint PPT Presentation

CS 730/730W/830: Intro AI What is KR? Prop. Logic Reasoning 2 handouts: slides, assignment 2 730W entries were due Wheeler Ruml (UNH) Lecture 7, CS 730 – 1 / 15

What is KR? ■ What is KR? ■ History of Logic ■ Advice Taker ■ The PSSH Prop. Logic Reasoning Introduction to Knowledge Representation and Reasoning Wheeler Ruml (UNH) Lecture 7, CS 730 – 2 / 15

What is Knowledge Representation? Representing facts ■ What is KR? Reasoning with facts ■ What is KR? ■ ■ History of Logic ■ Advice Taker Can computers be meaningful? ■ The PSSH Prop. Logic Reasoning Wheeler Ruml (UNH) Lecture 7, CS 730 – 3 / 15

History of Logic Philo of Megara (5C BC): truth tables What is KR? ■ What is KR? Aristotle (322BC): tautologies of proper arguments ■ History of Logic Leibniz (1646-1716): inference as math-like logic (but bogus ■ Advice Taker ■ The PSSH system) Prop. Logic George Boole (1854): The Laws of Thought (almost Reasoning propositional logic) Gottlob Frege (1879): Conceptual Notation (propositional and first-order logic) Dartmouth Conference (1956): modern AI movement CYCorp (1984- , www.cyc.com): slightly more complicated than first-order logic Wheeler Ruml (UNH) Lecture 7, CS 730 – 4 / 15

The Advice Taker (1958) What is KR? ■ What is KR? ■ History of Logic ■ Advice Taker ■ The PSSH Prop. Logic Reasoning John McCarthy: “AI”, Lisp, time-sharing Wheeler Ruml (UNH) Lecture 7, CS 730 – 5 / 15

Empirical Philosophy = Science The Physical Symbol System Hypothesis: A physical What is KR? symbol system has the necessary and sufficient means for ■ What is KR? ■ History of Logic general intelligent action. (Newell and Simon) ■ Advice Taker ■ The PSSH where a Prop. Logic Reasoning Symbol is a designating pattern that can be combined with others to form another designating pattern and Designation means standing in for something in the world Wheeler Ruml (UNH) Lecture 7, CS 730 – 6 / 15

What is KR? Prop. Logic ■ Prop. Logic ■ Logic ■ An Example ■ Break Reasoning Propositional Logic Wheeler Ruml (UNH) Lecture 7, CS 730 – 7 / 15

Propositional Logic it − is − raining What is KR? i − am − wet Prop. Logic ■ Prop. Logic it − is − raining → i − am − wet ■ Logic ■ An Example ■ Break x ∧ y x → y x y x y modus x → y x Reasoning T T T T T T ponens y T F F T F F F T F F T T ∧ , ∨ , ¬ , → ( ⊃ , ⇒ ) , ↔ F F F F F T Wheeler Ruml (UNH) Lecture 7, CS 730 – 8 / 15

Logic A logic is a formal system: What is KR? Prop. Logic syntax: defines sentences ■ ■ Prop. Logic semantics: relation to world ■ ■ Logic ■ An Example inference rules: reaching new conclusions ■ ■ Break three layers: proof, models, reality Reasoning flexible, general, principled Wheeler Ruml (UNH) Lecture 7, CS 730 – 9 / 15

Encode in Propositional Logic If the unicorn is mythical, then it is immortal, but if it is not What is KR? mythical, then it is a mortal mammal. If the unicorn is either Prop. Logic ■ Prop. Logic immortal or a mammal, then it is horned. The unicorn is magical ■ Logic if it is horned. ■ An Example ■ Break Reasoning Wheeler Ruml (UNH) Lecture 7, CS 730 – 10 / 15

Break asst 1: ■ What is KR? asst 2: first-order logic ■ Prop. Logic ■ Prop. Logic office hours ■ ■ Logic third exam: 10:30-11:50 May 11, N133 ■ ■ An Example ■ Break Reasoning Wheeler Ruml (UNH) Lecture 7, CS 730 – 11 / 15

What is KR? Prop. Logic Reasoning ■ CNF ■ Reasoning ■ EOLQs Reasoning Wheeler Ruml (UNH) Lecture 7, CS 730 – 12 / 15

Conversion to Conjunctive Normal Form Syntax: ∧ , ∨ , ¬ , → ( ⊃ , ⇒ ) , ↔ What is KR? Prop. Logic 1. eliminate ↔ Reasoning 2. eliminate → ■ CNF ■ Reasoning 3. move ¬ inward: ¬¬ x , ¬ ( x ∧ y ) , , ¬ ( x ∨ y ) ■ EOLQs 4. distribute ∨ : x ∨ ( y ∧ z ) Wheeler Ruml (UNH) Lecture 7, CS 730 – 13 / 15

Propositional Reasoning modes ponens What is KR? resolution (do unicorn proof) Prop. Logic Reasoning ■ CNF ■ Reasoning ■ EOLQs Wheeler Ruml (UNH) Lecture 7, CS 730 – 14 / 15

EOLQs Please write down the most pressing question you have about What is KR? the course material covered so far and put it in the box on your Prop. Logic way out. Reasoning ■ CNF Thanks! ■ Reasoning ■ EOLQs Wheeler Ruml (UNH) Lecture 7, CS 730 – 15 / 15