Reasoning for Humans: Clear Thinking in an Uncertain World PHIL 171 - PowerPoint PPT Presentation

Reasoning for Humans: Clear Thinking in an Uncertain World PHIL 171 Eric Pacuit Department of Philosophy University of Maryland pacuit.org

Recap: Truth Tables ( ϕ ∧ ψ ) ( ϕ ∨ ψ ) ϕ ψ ϕ ψ T T T T T T T F F T F T F T F F T T F F F F F F ϕ ψ ( ϕ → ψ ) ϕ ψ ( ϕ ↔ ψ ) T T T T T T T F F T F F F T T F T F F F T F F T ϕ ¬ ϕ T F F T 1

Valid Argument : 2

Valid Argument : An argument is valid provided that there is no truth value assignment that makes all the premises true and the conclusion false. 2

Valid Argument : An argument is valid provided that there is no truth value assignment that makes all the premises true and the conclusion false. (So, any truth-value assignment that makes all the premises true also makes the conclusion true). Invalid Argument : 2

Valid Argument : An argument is valid provided that there is no truth value assignment that makes all the premises true and the conclusion false. (So, any truth-value assignment that makes all the premises true also makes the conclusion true). Invalid Argument : An argument is invalid just in case it is not valid, i.e., if there is some truth-value assignment that makes the premises true and the conclusion false. Counterexample : A truth-value assignment that makes the premises of an argument true and its conclusion false is called a counterexample to the argument. 2

Valid Argument : An argument is valid provided that there is no truth value assignment that makes all the premises true and the conclusion false. (So, any truth-value assignment that makes all the premises true also makes the conclusion true). Invalid Argument : An argument is invalid just in case it is not valid, i.e., if there is some truth-value assignment that makes the premises true and the conclusion false. Counterexample : A truth-value assignment that makes the premises of an argument true and its conclusion false is called a counterexample to the argument. So, an argument if valid if there are no counterexamples. 2

Construct a truth table with columns for ϕ 1 , ϕ 2 , . . . , ϕ n , and ψ . Is there a row in which ϕ 1 , ϕ 2 , . . . , ϕ n are all true and ψ is false ? yes no The argument is invalid (there The argument is is a counterexample) valid 3

A → C B → C A ∨ B ∴ C A B C A → C B → C A ∨ B T T T T T T T T F F F T T F T T T T T F F F T T F T T T T T F T F T F T F F T T T F F F F T T F 4

A → C B → C A ∨ B ∴ C This argument is valid because there is no truth-value assignment that makes the premises true ( A → C , B → C and A ∨ B ) and the conclusion ( C ) false. 4

A → C B → C A ∨ B ∴ C A B C A → C B → C A ∨ B T T T T T T T T F F F T T F T T T T T F F F T T F T T T T T F T F T F T F F T T T F F F F T T F 4

A → C B → C A ∨ B ∴ C This argument is valid because in every row in which the conclusion ( C ) is false, at least one of the premises ( A → C , B → C or A ∨ B ) is false. 4

Is the following argument valid or invalid? You must show your answer. ( A ∨ B ) ( B → C ) ∴ ( B ∧ C ) 5

( A ∨ B ) ( B → C ) ∴ ( B ∧ C ) ( A ∨ B ) ( B → C ) ( B ∧ C ) A B C T T T T T T T T F T F F T F T T T F T F F T T F F T T T T T F T F T F F F F T F T F F F F F T F 6

( A ∨ B ) ( B → C ) ∴ ( B ∧ C ) ( A ∨ B ) ( B → C ) ( B ∧ C ) A B C T T T T T T T T F T F F T F T T T F T F F T T F F T T T T T F T F T F F F F T F T F F F F F T F The argument is invalid, because there is a counterexample. 6

Determine if the following arguments are valid or invalid. (You must explain your answers.) 1. ( A ∨ B ) , ( B → C ) ⇒ ( B ∧ C ) 2. ( A → ( B → C )) , ( B ∧ C ) ⇒ ¬¬ A 3. (( A ∧ B ) ∨ ( A → ¬ B )) , ( B → C ) ⇒ ( ¬ C → A ) 4. (( A ∧ B ) → ( B ∧ C )) , ( B ∧ D ) ⇒ ( A → ( C → ¬ D )) 7

Reasoning for Humans: Clear Thinking in an Uncertain World PHIL 171 - PowerPoint PPT Presentation

Reasoning for Humans: Clear Thinking in an Uncertain World PHIL 171 Eric Pacuit Department of Philosophy University of Maryland pacuit.org Recap: Truth Tables ( ) ( ) T T T T T T T F F T F T F

Reasoning for Humans: Clear Thinking in an Uncertain World PHIL 171 Eric Pacuit Department of

Reasoning for Humans: Clear Thinking in an Uncertain World PHIL 171 Eric Pacuit Department of

Reasoning for Humans: Clear Thinking in an Uncertain World PHIL 171 Eric Pacuit Department of

Reasoning for Humans: Clear Thinking in an Uncertain World PHIL 171 Eric Pacuit Department of

Reasoning for Humans: Clear Thinking in an Uncertain World PHIL 171 Eric Pacuit Department of

Reasoning for Humans: Clear Thinking in an Uncertain World PHIL 171 Eric Pacuit Department of

Reasoning for Humans: Clear Thinking in an Uncertain World PHIL 171 Eric Pacuit Department of

Reasoning for Humans: Clear Thinking in an Uncertain World PHIL 171 Eric Pacuit Department of

Reasoning for Humans: Clear Thinking in an Uncertain World PHIL 171 Eric Pacuit Department of

Reasoning for Humans: Clear Thinking in an Uncertain World PHIL 171 Eric Pacuit Department of

Reasoning for Humans: Clear Thinking in an Uncertain World PHIL 171 Eric Pacuit Department of

Uncertain Knowledge and Reasoning 9 AI Slides (6e) c Lin Zuoquan@PKU 1998-2020 9 1 9

Automated Reasoning (what this course is about) AUTOMATED REASONING machine does 'thinking'

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Be: Clear On What You Want & Get Clear On How Marketing REALLY Works What Do You ACTUALLY

Using Uncertain Knowledge Agents dont have complete knowledge about the world. Agents

Reasoning for Humans: Clear Thinking in an Uncertain World PHIL 171 - PowerPoint PPT Presentation

Reasoning for Humans: Clear Thinking in an Uncertain World PHIL 171 Eric Pacuit Department of Philosophy University of Maryland pacuit.org Recap: Truth Tables ( ) ( ) T T T T T T T F F T F T F

Reasoning for Humans: Clear Thinking in an Uncertain World PHIL 171 Eric Pacuit Department of

Reasoning for Humans: Clear Thinking in an Uncertain World PHIL 171 Eric Pacuit Department of

Reasoning for Humans: Clear Thinking in an Uncertain World PHIL 171 Eric Pacuit Department of

Reasoning for Humans: Clear Thinking in an Uncertain World PHIL 171 Eric Pacuit Department of

Reasoning for Humans: Clear Thinking in an Uncertain World PHIL 171 Eric Pacuit Department of

Reasoning for Humans: Clear Thinking in an Uncertain World PHIL 171 Eric Pacuit Department of

Reasoning for Humans: Clear Thinking in an Uncertain World PHIL 171 Eric Pacuit Department of

Reasoning for Humans: Clear Thinking in an Uncertain World PHIL 171 Eric Pacuit Department of

Reasoning for Humans: Clear Thinking in an Uncertain World PHIL 171 Eric Pacuit Department of

Reasoning for Humans: Clear Thinking in an Uncertain World PHIL 171 Eric Pacuit Department of

Reasoning for Humans: Clear Thinking in an Uncertain World PHIL 171 Eric Pacuit Department of

Uncertain Knowledge and Reasoning 9 AI Slides (6e) c Lin Zuoquan@PKU 1998-2020 9 1 9

Automated Reasoning (what this course is about) AUTOMATED REASONING machine does 'thinking'

Automated Reasoning (what this course is about) machine does 'thinking' user does 'thinking'

Assumption-based reasoning Assumption-based reasoning solving problems consisting of uncertain,

Stochastic Models of an Uncertain World x = F ( x , u ) x = F ( x , u , 1 ) Lecture

Reasoning with Uncertainty C h a p t e r 13 1 Outline Uncertainty Probability

Management of invasive species, pests and diseases: making decisions in an uncertain and complex

Course Overview Lecture 7 Introduction Uncertain knowledge and Logical Agents Reasoning

Visual Reasoning Peng Wang School of Computing and Information Technology University of

3. Reasoning in Agents Part 1: Introduction to Reasoning ems (SMA-UPC) Javier Vzquez-Salceda

2. Reasoning in Agents Part 1: D) ems Design (MASD Introduction to Reasoning Javier

Be: Clear On What You Want &amp; Get Clear On How Marketing REALLY Works What Do You ACTUALLY

Using Uncertain Knowledge Agents dont have complete knowledge about the world. Agents

Be: Clear On What You Want & Get Clear On How Marketing REALLY Works What Do You ACTUALLY