# Name: Course: CAP 4601 Semester: Summer 2013 Assignment: Assignment 06 Date: 08 JUL Complete the following written problems:

Size: px
Start display at page:

Download "Name: Course: CAP 4601 Semester: Summer 2013 Assignment: Assignment 06 Date: 08 JUL Complete the following written problems:"

Transcription

1 Name: Course: CAP 4601 Semester: Summer 2013 Assignment: Assignment 06 Date: 08 JUL 2013 Complete the following written problems: 1. Alpha-Beta Pruning (40 Points). Consider the following min-max tree. max min

2 a. Given that we search depth first from left to right, list all leaf nodes above that we need to search/expand. (35 Points) max 25 min or less 20 or less 15<25 20< Therefore, the leaf nodes that are search/expanded are 50, 25, 75, 15, 30, and 20. b. What is the final value at the top of the tree? (5 Points) The final value at the top of the tree is 25.

3 2. The Wumpus World (70 Points). Suppose that an agent in the Wumpus World has perceived nothing in (1,1), a breeze in (2,1), and a stench in (1,2): 1,4 2,4 3,4 4,4 A = Agent B = Breeze G = Glitter, Gold OK = Safe Square P = Pit S = Stench 1,3 2,3 3,3 4,3 V = Visited W = Wumpus 1,2 2,2 3,2 4,2 1,1 S V OK 2,1 3,1 4,1 V OK B V OK Given this Knowledge Base, the agent now concerns itself with the contents of (1,3), (2,2), and (3,1). Each of these locations can contain a pit (P). At most, one location can contain a Wumpus (W). A location can contain nothing (N). Construct the set of all possible worlds. Each possible world should be represented by a list representing the contents of each location in the following order: (1,3), (2,2), and (3,1). Example: N,P,W means that there is nothing in (1,3), a pit in (2,2), and a Wumpus in (3,1). Hint: There are 32 possible worlds. Mark the worlds in which the Knowledge Base (KB) is true and those in which each of the following sentences is true: A2 "There is not pit in 2,2." Hence, show that KB A2 and KB A3. A3 "There is a Wumpus in 1,3."

4 If the world is not supported by the KB, then mark the world False for "KB?". If the world does not support A2, then mark the world False for "A2?". If the world does not support A3, then mark the world False for "A3?". Number World KB? A2? A3? 1. N,N,N In (1,2), stench and no breeze: False and, in (2,1), no stench and breeze: False;, False True False 2. N,N,P In (1,2), stench and no breeze: False and, in (2,1), no stench and breeze: True;, False True False 3. N,P,N In (1,2), stench and no breeze: False and, in (2,1), no stench and breeze: True;, False False False 4. N,P,P In (1,2), stench and no breeze: False and, in (2,1), no stench and breeze: True;, False False False 5. P,N,N In (1,2), stench and no breeze: False and, in (2,1), no stench and breeze: False;, False True False 6. P,N,P In (1,2), stench and no breeze: False and, in (2,1), no stench and breeze: True;, False True False 7. P,P,N In (1,2), stench and no breeze: False and, in (2,1), no stench and breeze: True;, False False False 8. P,P,P In (1,2), stench and no breeze: False and, in (2,1), no stench and breeze: True;, False False False 9. N,N,W In (1,2), stench and no breeze: False and, in (2,1), no stench and breeze: False;, False True False 10. N,N,P&W In (1,2), stench and no breeze: False and, in (2,1), no stench and breeze: False;, False True False 11. N,P,W In (1,2), stench and no breeze: False and, in (2,1), no stench and breeze: False;, False False False 12. N,P,P&W In (1,2), stench and no breeze: False and, in (2,1), no stench and breeze: False;, False False False 13. P,N,W In (1,2), stench and no breeze: False and, in (2,1), no stench and breeze: False;, False True False 14. P,N,P&W In (1,2), stench and no breeze: False and, in (2,1), no stench and breeze: False;, False True False 15. P,P,W In (1,2), stench and no breeze: False and, in (2,1), no stench and breeze: False;, False False False 16. P,P,P&W In (1,2), stench and no breeze: False and, in (2,1), no stench and breeze: False;, False False False 17. N,W,N In (1,2), stench and no breeze: True and, in (2,1), no stench and breeze: False;, False True False 18. N,W,P In (1,2), stench and no breeze: True and, in (2,1), no stench and breeze: False;, False True False 19. N,P&W,N In (1,2), stench and no breeze: False and, in (2,1), no stench and breeze: False;, False False False 20. N,P&W,P In (1,2), stench and no breeze: False and, in (2,1), no stench and breeze: False;, False False False 21. P,W,N In (1,2), stench and no breeze: False and, in (2,1), no stench and breeze: False;, False True False 22. P,W,P In (1,2), stench and no breeze: False and, in (2,1), no stench and breeze: False;, False True False 23. P,P&W,N In (1,2), stench and no breeze: False and, in (2,1), no stench and breeze: False;, False False False 24. P,P&W,P In (1,2), stench and no breeze: False and, in (2,1), no stench and breeze: False;, False False False 25. W,N,N In (1,2), stench and no breeze: True and, in (2,1), no stench and breeze: False;, False True True 26. W,N,P In (1,2), stench and no breeze: True and, in (2,1), no stench and breeze: True;, True True True 27. W,P,N In (1,2), stench and no breeze: False and, in (2,1), no stench and breeze: True;, False False True 28. W,P,P In (1,2), stench and no breeze: False and, in (2,1), no stench and breeze: True;, False False True 29. P&W,N,N In (1,2), stench and no breeze: False and, in (2,1), no stench and breeze: False;, False True True 30. P&W,N,P In (1,2), stench and no breeze: False and, in (2,1), no stench and breeze: True;, False True True 31. P&W,P,N In (1,2), stench and no breeze: False and, in (2,1), no stench and breeze: True;, False False True 32. P&W,P,P In (1,2), stench and no breeze: False and, in (2,1), no stench and breeze: True;, False False True Note: From Page 237, the agent will perceive a Stench in the square containing the wumpus and in directly (not diagonally) adjacent squares. Additionally, the agent will perceive a Breeze in the squares directly adjacent to a pit. If there were a pit in either (1,3) or (2,2), then we would perceive a Breeze in (1,2); however, we do not. If there were a wumpus in either (2,2) or (3,1), the we would perceive a Stench in (2,1); however, we do not. Therefore, we must have a wumpus only in (1,3), nothing in (2,2), and a pit only in (3,1).

5 3. Propositional Logic (60 Points). Given the following paragraph: If the unicorn is mythical, then it is immortal, but if it is not mythical, then it is a mortal mammal. If the unicorn is either immortal or a mammal, then it is horned. The unicorn is magical if it is horned. And the following propositions: UnicornIsMythical: The unicorn is mythical. UnicornIsMortal: The unicorn is mortal. UnicornIsMammal: The unicorn is a mammal. UnicornIsHorned: The unicorn is horned. UnicornIsMagical: The unicorn is magical. Note: The names for the following rules are based on Figure 7.11 on Page 249 and Section 7.5 (Propositional Theorem Proving; Pages ). Below are two of the many ways these can be proved. a. Use propositional logic to prove that the unicorn is magical. List each premise and indicate each inference rule used in your proof. You may use more or less lines than in the table below. (30 Points) Line Sentence Rule 1. UnicornIsMythical UnicornIsMortal Premise 2. UnicornIsMythical UnicornIsMortal UnicornIsMammal Premise 3. UnicornIsMortal UnicornIsMammal UnicornIsHorned Premise 4. UnicornIsHorned UnicornIsMagical Premise 5. UnicornIsMythical UnicornIsMortal From 1 by 6. UnicornIsMythical UnicornIsMortal UnicornIsMammal From 2 by 7. UnicornIsMythical UnicornIsMortal UnicornIsMammal From 6 by Double Negation 8. UnicornIsMortal UnicornIsMortal UnicornIsMammal From 5 and 7 by Resolution 9. UnicornIsMortal UnicornIsMortal UnicornIsMortal UnicornIsMammal From 8 by Distributivity of over 10. UnicornIsMortal UnicornIsMammal From 9 by Tautology

6 11. UnicornIsMortal From 10 by And 13. UnicornIsMortal UnicornIsMammal UnicornIsHorned From 3 by 14. UnicornIsMortal UnicornIsMammal UnicornIsHorned From 13 by De 15. UnicornIsMortal UnicornIsMammal UnicornIsHorned Morgan From 14 by Double Negation 16. UnicornIsMortal UnicornIsHorned UnicornIsMammal UnicornIsHorned From 15 by Distributivity of over 17. UnicornIsMortal UnicornIsHorned From 16 by And 18. UnicornIsMortal UnicornIsHorned From 17 by Double Negation 19. UnicornIsMortal UnicornIsHorned From 18 by 20. UnicornIsHorned From 11 and 19 by Modus Ponens 21. UnicornIsMagical From 4 and 20 by Modus Ponens b. Use propositional logic to prove that the unicorn is horned. List each premise and indicate each inference rule used in your proof. You may use more or less lines than in the table below. (30 Points) Line Sentence 1. UnicornIsMythical UnicornIsMortal 2. UnicornIsMythical UnicornIsMortal UnicornIsMammal 3. UnicornIsMortal UnicornIsMammal UnicornIsHorned 4. UnicornIsHorned UnicornIsMagical 5. UnicornIsMythical UnicornIsMortal Rule Premise Premise Premise Premise From 1 by

7 6. UnicornIsMythical UnicornIsMortal UnicornIsMammal From 2 by 7. UnicornIsMythical UnicornIsMortal UnicornIsMammal From 6 by Double Negation 8. UnicornIsMortal UnicornIsMortal UnicornIsMammal From 5 and 7 by Resolution 9. UnicornIsMortal UnicornIsMortal UnicornIsMortal UnicornIsMammal From 8 by Distributivity of over 10. UnicornIsMortal UnicornIsMammal From 9 by Tautology 11. UnicornIsMortal From 10 by And 13. UnicornIsMortal UnicornIsMammal UnicornIsHorned From 3 by 14. UnicornIsMortal UnicornIsMammal UnicornIsHorned From 13 by De Morgan 15. UnicornIsMortal UnicornIsMammal UnicornIsHorned From 14 by Double Negation 16. UnicornIsMortal UnicornIsHorned UnicornIsMammal UnicornIsHorned From 15 by Distributivity of over 17. UnicornIsMortal UnicornIsHorned From 16 by And 18. UnicornIsMortal UnicornIsHorned From 17 by Double Negation 19. UnicornIsMortal UnicornIsHorned From 18 by 20. UnicornIsHorned From 11 and 19 by Modus Ponens

8 4. Conjunctive Normal Form (50 Points). Consider the following sentence: Food Party Drinks Party Food Drinks Party a. Using the procedure starting on page 253, convert this sentence into Conjunctive Normal Form showing each step. (Points 40) (1) Eliminate, replacing with with : Food Party Drinks Party Food Drinks Party (2) Eliminate, replacing with : Food Party Drinks Party Food Drinks Party Food Party Drinks Party Food Drinks Party Food Party Drinks Party Food Drinks Party Food Party Drinks Party Food Drinks Party Food Party Drinks Party Food Drinks Party (3) CNF requires to appear only in literals, so we "move inwards" by repeated application. of the following equivalences:,, and Food Party Drinks Party Food Drinks Party Food Party Drinks Party Food Drinks Party Food Party Drinks Party Food Drinks Party Food Party Drinks Party Food Dr inks Party Food Party Drinks Party Food Drinks Party Food Party Drinks Party Food Drinks Party Food Party Drinks Party Food Drinks Party

9 (4) Now we have a sentence containing nested and operators applied to literals. We apply the distributivity law (distributing over wherever possible): Food Party Drinks Party Food Drinks Party Food Party Drinks Party Food Drinks Party Food Food Drinks Party Party Food Drinks Party Drinks Food Drinks Party Party Food Drinks Party Food Food Drinks Party Party Food Drinks Party Drinks Food Drinks Party Party Food Drinks Party Food Food Drinks Party Party Party Food Drinks Drinks Drinks Food Party Party Party Food Drinks

10 b. Using resolution, determine if this sentence is valid, satisfiable (but not valid), or unsatisfiable. (Points 10) Therefore, this sentence is valid. Food Food Drinks Party Party Party Food Drinks Drinks Drinks Food Party Party Party Food Drinks Food Food Drinks Party Party Party Food Drinks Drinks Drinks Food Party Party Party Food Drinks True Drinks Party True Food Drinks True Food Party True Food Drinks True True True True True

11 5. Resolution (40 Points). A propositional 2-CNF expression is a conjunction of clauses, each containing exactly 2 literals, e.g., A B A C B D C G D G Prove using resolution that the above sentence entails G. Line Sentence 1. A B A C B D C G D G Rule 2. A B From 1 by And 3. A C From 1 by And 4. B C From 2 and 3 by Resolution 5. B D From 1 by And 6. C D From 4 and 5 by Resolution 7. C G From 1 by And 8. D G From 6 and 7 by Resolution 9. D G From 1 by And 10. G G From 8 and 9 by Resolution 11. G From 10 by Logical Equivalence

12 6. First Order Logic (100 Points). Given the following vocabulary with the following symbols: Student x : Predicate. Person x is a student., Course x : Predicate. Subject x is a course., Knows x y : Predicate. Student x knows concept y. Takes x y : Predicate. Student x takes course y. Covers x, y : Predicate. Course x covers concept y. Amy, Brian : Constants denoting people. MAC 1140 : Constants denoting the course College Algebra. MatrixMethods : Constant denoting the concept of matrix methods. Convert the following sentences to first-order logic: a. Amy is a student and knows matrix methods. (5 Points) Student Amy Knows Amy, MatrixMethods b. Some student knows matrix methods. (10 Points) Knows x MatrixMethods x, Student x, c. Every student takes MAC (10 Points) Takes x MAC x, Student x, 1140 d. MAC 1140 is a course that the student, Brian, has not taken. (10 Points) Student Brian Taken Brian, MAC1140 e. There is some course that every student has not taken. (20 Points) x, Course x y, Student y Taken y, x f. If Brian is a student, takes the course MAC 1140, and MAC 1140 covers matrix methods, then Brian knows matrix methods. (15 Points), ,, Student Brian Takes Brian MAC Covers MAC MatrixMethods Knows Brian MatrixMethods

13 g. If a student takes a course and the course covers some concept, then the student knows that concept. (30 Points) x, y, z, Student x Coursey Takes x, y Covers y, z Knows x, z 7. First Order Logic (90 Points). This exercise uses the function MapColor and predicates In x, y, Borders x, y, and Country x, whose arguments are geographical regions, along with constant symbols for various regions. In each of the following, we give an English sentence and a number of candidate logical expressions. For each of the logical expressions, state whether it (1) correctly expresses the English sentence, (2) is syntactically invalid and therefore meaningless, or (3) is syntactically valid but does not express the meaning of the English sentence. a. Paris and Marseilles are both in France. In Paris Marseilles, France (10 Points) (i) (2) syntactically invalid and therefore meaningless (ii) InParis, France InMarseilles, France (10 Points) (1) correctly expresses the English sentence (iii) InParis, France InMarseilles, France (10 Points) (3) is syntactically valid but does not express the meaning of the English sentence NOTE: This incorrectly reads: Either Paris is in France, Marseilles is in France, or both are in France. b. There is a country that borders both Iraq and Pakistan. c Country c Border c, Iraq Border c, Pakistan (10 Points) (i) (1) correctly expresses the English sentence (ii) c Country c Border c, Iraq Border c, Pakistan (10 Points) (3) is syntactically valid but does not express the meaning of the English sentence NOTE: This incorrectly reads: If there is a country, then that country borders Iraq and Pakistan.

15 This assignment has no programming problems. After completing Assignment 06, create an assignment_06_lastname.pdf file for your written assignment. Upload your assignment_06_lastname.pdf file for your written assignment to the Assignment 06 location on the BlackBoard site:

### Module 5. Knowledge Representation and Logic (Propositional Logic) Version 2 CSE IIT, Kharagpur

Module 5 Knowledge Representation and Logic (Propositional Logic) Lesson 12 Propositional Logic inference rules 5.5 Rules of Inference Here are some examples of sound rules of inference. Each can be shown

### Artificial Intelligence: Valid Arguments and Proof Systems. Prof. Deepak Khemani. Department of Computer Science and Engineering

Artificial Intelligence: Valid Arguments and Proof Systems Prof. Deepak Khemani Department of Computer Science and Engineering Indian Institute of Technology, Madras Module 02 Lecture - 03 So in the last

### Semantic Entailment and Natural Deduction

Semantic Entailment and Natural Deduction Alice Gao Lecture 6, September 26, 2017 Entailment 1/55 Learning goals Semantic entailment Define semantic entailment. Explain subtleties of semantic entailment.

### (Refer Slide Time 03:00)

Artificial Intelligence Prof. Anupam Basu Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur Lecture - 15 Resolution in FOPL In the last lecture we had discussed about

### Revisiting the Socrates Example

Section 1.6 Section Summary Valid Arguments Inference Rules for Propositional Logic Using Rules of Inference to Build Arguments Rules of Inference for Quantified Statements Building Arguments for Quantified

### Artificial Intelligence. Clause Form and The Resolution Rule. Prof. Deepak Khemani. Department of Computer Science and Engineering

Artificial Intelligence Clause Form and The Resolution Rule Prof. Deepak Khemani Department of Computer Science and Engineering Indian Institute of Technology, Madras Module 07 Lecture 03 Okay so we are

### Artificial Intelligence Prof. P. Dasgupta Department of Computer Science & Engineering Indian Institute of Technology, Kharagpur

Artificial Intelligence Prof. P. Dasgupta Department of Computer Science & Engineering Indian Institute of Technology, Kharagpur Lecture- 10 Inference in First Order Logic I had introduced first order

### INTERMEDIATE LOGIC Glossary of key terms

1 GLOSSARY INTERMEDIATE LOGIC BY JAMES B. NANCE INTERMEDIATE LOGIC Glossary of key terms This glossary includes terms that are defined in the text in the lesson and on the page noted. It does not include

### MATH1061/MATH7861 Discrete Mathematics Semester 2, Lecture 5 Valid and Invalid Arguments. Learning Goals

MAH1061/MAH7861 Discrete Mathematics Semester 2, 2016 Learning Goals 1. Understand the meaning of necessary and sufficient conditions (carried over from Wednesday). 2. Understand the difference between

### An Introduction to. Formal Logic. Second edition. Peter Smith, February 27, 2019

An Introduction to Formal Logic Second edition Peter Smith February 27, 2019 Peter Smith 2018. Not for re-posting or re-circulation. Comments and corrections please to ps218 at cam dot ac dot uk 1 What

### Chapter 8 - Sentential Truth Tables and Argument Forms

Logic: A Brief Introduction Ronald L. Hall Stetson University Chapter 8 - Sentential ruth ables and Argument orms 8.1 Introduction he truth-value of a given truth-functional compound proposition depends

### A. Problem set #3 it has been posted and is due Tuesday, 15 November

Lecture 9: Propositional Logic I Philosophy 130 1 & 3 November 2016 O Rourke & Gibson I. Administrative A. Problem set #3 it has been posted and is due Tuesday, 15 November B. I am working on the group

### 16. Universal derivation

16. Universal derivation 16.1 An example: the Meno In one of Plato s dialogues, the Meno, Socrates uses questions and prompts to direct a young slave boy to see that if we want to make a square that has

### A Judgmental Formulation of Modal Logic

A Judgmental Formulation of Modal Logic Sungwoo Park Pohang University of Science and Technology South Korea Estonian Theory Days Jan 30, 2009 Outline Study of logic Model theory vs Proof theory Classical

### 1 Clarion Logic Notes Chapter 4

1 Clarion Logic Notes Chapter 4 Summary Notes These are summary notes so that you can really listen in class and not spend the entire time copying notes. These notes will not substitute for reading the

### Pastor-teacher Don Hargrove Faith Bible Church September 8, 2011

Pastor-teacher Don Hargrove Faith Bible Church http://www.fbcweb.org/doctrines.html September 8, 2011 Building Mental Muscle & Growing the Mind through Logic Exercises: Lesson 4a The Three Acts of the

### What would count as Ibn Sīnā (11th century Persia) having first order logic?

1 2 What would count as Ibn Sīnā (11th century Persia) having first order logic? Wilfrid Hodges Herons Brook, Sticklepath, Okehampton March 2012 http://wilfridhodges.co.uk Ibn Sina, 980 1037 3 4 Ibn Sīnā

### Logic I or Moving in on the Monkey & Bananas Problem

Logic I or Moving in on the Monkey & Bananas Problem We said that an agent receives percepts from its environment, and performs actions on that environment; and that the action sequence can be based on

### What are Truth-Tables and What Are They For?

PY114: Work Obscenely Hard Week 9 (Meeting 7) 30 November, 2010 What are Truth-Tables and What Are They For? 0. Business Matters: The last marked homework of term will be due on Monday, 6 December, at

### Logic Appendix: More detailed instruction in deductive logic

Logic Appendix: More detailed instruction in deductive logic Standardizing and Diagramming In Reason and the Balance we have taken the approach of using a simple outline to standardize short arguments,

### Selections from Aristotle s Prior Analytics 41a21 41b5

Lesson Seventeen The Conditional Syllogism Selections from Aristotle s Prior Analytics 41a21 41b5 It is clear then that the ostensive syllogisms are effected by means of the aforesaid figures; these considerations

### The way we convince people is generally to refer to sufficiently many things that they already know are correct.

Theorem A Theorem is a valid deduction. One of the key activities in higher mathematics is identifying whether or not a deduction is actually a theorem and then trying to convince other people that you

### 4.1 A problem with semantic demonstrations of validity

4. Proofs 4.1 A problem with semantic demonstrations of validity Given that we can test an argument for validity, it might seem that we have a fully developed system to study arguments. However, there

### What is the Nature of Logic? Judy Pelham Philosophy, York University, Canada July 16, 2013 Pan-Hellenic Logic Symposium Athens, Greece

What is the Nature of Logic? Judy Pelham Philosophy, York University, Canada July 16, 2013 Pan-Hellenic Logic Symposium Athens, Greece Outline of this Talk 1. What is the nature of logic? Some history

### Is the law of excluded middle a law of logic?

Is the law of excluded middle a law of logic? Introduction I will conclude that the intuitionist s attempt to rule out the law of excluded middle as a law of logic fails. They do so by appealing to harmony

### UC Berkeley, Philosophy 142, Spring 2016

Logical Consequence UC Berkeley, Philosophy 142, Spring 2016 John MacFarlane 1 Intuitive characterizations of consequence Modal: It is necessary (or apriori) that, if the premises are true, the conclusion

### HANDBOOK (New or substantially modified material appears in boxes.)

1 HANDBOOK (New or substantially modified material appears in boxes.) I. ARGUMENT RECOGNITION Important Concepts An argument is a unit of reasoning that attempts to prove that a certain idea is true by

### Announcements. CS311H: Discrete Mathematics. First Order Logic, Rules of Inference. Satisfiability, Validity in FOL. Example.

Announcements CS311H: Discrete Mathematics First Order Logic, Rules of Inference Instructor: Işıl Dillig Homework 1 is due now! Homework 2 is handed out today Homework 2 is due next Wednesday Instructor:

### Russell: On Denoting

Russell: On Denoting DENOTING PHRASES Russell includes all kinds of quantified subject phrases ( a man, every man, some man etc.) but his main interest is in definite descriptions: the present King of

### Prompt: Explain van Inwagen s consequence argument. Describe what you think is the best response

Prompt: Explain van Inwagen s consequence argument. Describe what you think is the best response to this argument. Does this response succeed in saving compatibilism from the consequence argument? Why

### Philosophy 1100: Ethics

Philosophy 1100: Ethics Topic 1 - Course Introduction: 1. What is Philosophy? 2. What is Ethics? 3. Logic a. Truth b. Arguments c. Validity d. Soundness What is Philosophy? The Three Fundamental Questions

### Constructive Logic, Truth and Warranted Assertibility

Constructive Logic, Truth and Warranted Assertibility Greg Restall Department of Philosophy Macquarie University Version of May 20, 2000....................................................................

### Logic: A Brief Introduction. Ronald L. Hall, Stetson University

Logic: A Brief Introduction Ronald L. Hall, Stetson University 2012 CONTENTS Part I Critical Thinking Chapter 1 Basic Training 1.1 Introduction 1.2 Logic, Propositions and Arguments 1.3 Deduction and Induction

### Logic & Proofs. Chapter 3 Content. Sentential Logic Semantics. Contents: Studying this chapter will enable you to:

Sentential Logic Semantics Contents: Truth-Value Assignments and Truth-Functions Truth-Value Assignments Truth-Functions Introduction to the TruthLab Truth-Definition Logical Notions Truth-Trees Studying

### Announcements. CS243: Discrete Structures. First Order Logic, Rules of Inference. Review of Last Lecture. Translating English into First-Order Logic

Announcements CS243: Discrete Structures First Order Logic, Rules of Inference Işıl Dillig Homework 1 is due now Homework 2 is handed out today Homework 2 is due next Tuesday Işıl Dillig, CS243: Discrete

### Informalizing Formal Logic

Informalizing Formal Logic Antonis Kakas Department of Computer Science, University of Cyprus, Cyprus antonis@ucy.ac.cy Abstract. This paper discusses how the basic notions of formal logic can be expressed

### Lecture 3 Arguments Jim Pryor What is an Argument? Jim Pryor Vocabulary Describing Arguments

Lecture 3 Arguments Jim Pryor What is an Argument? Jim Pryor Vocabulary Describing Arguments 1 Agenda 1. What is an Argument? 2. Evaluating Arguments 3. Validity 4. Soundness 5. Persuasive Arguments 6.

### Does Deduction really rest on a more secure epistemological footing than Induction?

Does Deduction really rest on a more secure epistemological footing than Induction? We argue that, if deduction is taken to at least include classical logic (CL, henceforth), justifying CL - and thus deduction

### Courses providing assessment data PHL 202. Semester/Year

1 Department/Program 2012-2016 Assessment Plan Department: Philosophy Directions: For each department/program student learning outcome, the department will provide an assessment plan, giving detailed information

### Can Gödel s Incompleteness Theorem be a Ground for Dialetheism? *

논리연구 20-2(2017) pp. 241-271 Can Gödel s Incompleteness Theorem be a Ground for Dialetheism? * 1) Seungrak Choi Abstract Dialetheism is the view that there exists a true contradiction. This paper ventures

### PHI 1500: Major Issues in Philosophy

PHI 1500: Major Issues in Philosophy Session 3 September 9 th, 2015 All About Arguments (Part II) 1 A common theme linking many fallacies is that they make unwarranted assumptions. An assumption is a claim

### Study Guides. Chapter 1 - Basic Training

Study Guides Chapter 1 - Basic Training Argument: A group of propositions is an argument when one or more of the propositions in the group is/are used to give evidence (or if you like, reasons, or grounds)

### Logical Omniscience in the Many Agent Case

Logical Omniscience in the Many Agent Case Rohit Parikh City University of New York July 25, 2007 Abstract: The problem of logical omniscience arises at two levels. One is the individual level, where an

### TDT4136 Logic and Reasoning Systems

TDT4136 Logic and Reasoning Systems Chapter 8 - First-Order Logic Lester Solbakken solbakke@idi.ntnu.no Norwegian University of Science and Technology 13.09.2011 1 Lester Solbakken TDT4136 Logic and Reasoning

### Exercise Sets. KS Philosophical Logic: Modality, Conditionals Vagueness. Dirk Kindermann University of Graz July 2014

Exercise Sets KS Philosophical Logic: Modality, Conditionals Vagueness Dirk Kindermann University of Graz July 2014 1 Exercise Set 1 Propositional and Predicate Logic 1. Use Definition 1.1 (Handout I Propositional

### PHILOSOPHY 102 INTRODUCTION TO LOGIC PRACTICE EXAM 1. W# Section (10 or 11) 4. T F The statements that compose a disjunction are called conjuncts.

PHILOSOPHY 102 INTRODUCTION TO LOGIC PRACTICE EXAM 1 W# Section (10 or 11) 1. True or False (5 points) Directions: Circle the letter next to the best answer. 1. T F All true statements are valid. 2. T

### Complications for Categorical Syllogisms. PHIL 121: Methods of Reasoning February 27, 2013 Instructor:Karin Howe Binghamton University

Complications for Categorical Syllogisms PHIL 121: Methods of Reasoning February 27, 2013 Instructor:Karin Howe Binghamton University Overall Plan First, I will present some problematic propositions and

### What Is On The Final. Review. What Is Not On The Final. What Might Be On The Final

What Is On he inal Review Everything that has important! written next to it on the slides Everything that I said was important ECE457 Applied Artificial Intelligence all 27 ecture #14 ECE457 Applied Artificial

### An alternative understanding of interpretations: Incompatibility Semantics

An alternative understanding of interpretations: Incompatibility Semantics 1. In traditional (truth-theoretic) semantics, interpretations serve to specify when statements are true and when they are false.

### Comments on Truth at A World for Modal Propositions

Comments on Truth at A World for Modal Propositions Christopher Menzel Texas A&M University March 16, 2008 Since Arthur Prior first made us aware of the issue, a lot of philosophical thought has gone into

### SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Exam Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Draw a Venn diagram for the given sets. In words, explain why you drew one set as a subset of

### Philosophy 220. Truth Functional Properties Expressed in terms of Consistency

Philosophy 220 Truth Functional Properties Expressed in terms of Consistency The concepts of truth-functional logic: Truth-functional: Truth Falsity Indeterminacy Entailment Validity Equivalence Consistency

### MCQ IN TRADITIONAL LOGIC. 1. Logic is the science of A) Thought. B) Beauty. C) Mind. D) Goodness

MCQ IN TRADITIONAL LOGIC FOR PRIVATE REGISTRATION TO BA PHILOSOPHY PROGRAMME 1. Logic is the science of-----------. A) Thought B) Beauty C) Mind D) Goodness 2. Aesthetics is the science of ------------.

### A Primer on Logic Part 1: Preliminaries and Vocabulary. Jason Zarri. 1. An Easy \$10.00? a 3 c 2. (i) (ii) (iii) (iv)

A Primer on Logic Part 1: Preliminaries and Vocabulary Jason Zarri 1. An Easy \$10.00? Suppose someone were to bet you \$10.00 that you would fail a seemingly simple test of your reasoning skills. Feeling

### Chapter 9- Sentential Proofs

Logic: A Brief Introduction Ronald L. Hall, Stetson University Chapter 9- Sentential roofs 9.1 Introduction So far we have introduced three ways of assessing the validity of truth-functional arguments.

### HANDBOOK. IV. Argument Construction Determine the Ultimate Conclusion Construct the Chain of Reasoning Communicate the Argument 13

1 HANDBOOK TABLE OF CONTENTS I. Argument Recognition 2 II. Argument Analysis 3 1. Identify Important Ideas 3 2. Identify Argumentative Role of These Ideas 4 3. Identify Inferences 5 4. Reconstruct the

### Ling 98a: The Meaning of Negation (Week 1)

Yimei Xiang yxiang@fas.harvard.edu 17 September 2013 1 What is negation? Negation in two-valued propositional logic Based on your understanding, select out the metaphors that best describe the meaning

### Chapter 3: Basic Propositional Logic. Based on Harry Gensler s book For CS2209A/B By Dr. Charles Ling;

Chapter 3: Basic Propositional Logic Based on Harry Gensler s book For CS2209A/B By Dr. Charles Ling; cling@csd.uwo.ca The Ultimate Goals Accepting premises (as true), is the conclusion (always) true?

### Conditionals II: no truth conditions?

Conditionals II: no truth conditions? UC Berkeley, Philosophy 142, Spring 2016 John MacFarlane 1 Arguments for the material conditional analysis As Edgington [1] notes, there are some powerful reasons

### Lecture 17:Inference Michael Fourman

Lecture 17:Inference Michael Fourman 2 Is this a valid argument? Assumptions: If the races are fixed or the gambling houses are crooked, then the tourist trade will decline. If the tourist trade declines

### 9 Methods of Deduction

M09_COPI1396_13_SE_C09.QXD 10/19/07 3:46 AM Page 372 9 Methods of Deduction 9.1 Formal Proof of Validity 9.2 The Elementary Valid Argument Forms 9.3 Formal Proofs of Validity Exhibited 9.4 Constructing

### HOW TO ANALYZE AN ARGUMENT

What does it mean to provide an argument for a statement? To provide an argument for a statement is an activity we carry out both in our everyday lives and within the sciences. We provide arguments for

### PROPOSITIONAL LOGIC OF SUPPOSITION AND ASSERTION 1

PROPOSITIONAL LOGIC OF SUPPOSITION AND ASSERTION 1 1. LANGUAGE AND SPEECH ACTS In this paper I develop a system of what I understand to be illocutionary logic. In order to motivate this system and make

### Noncognitivism in Ethics, by Mark Schroeder. London: Routledge, 251 pp.

Noncognitivism in Ethics, by Mark Schroeder. London: Routledge, 251 pp. Noncognitivism in Ethics is Mark Schroeder s third book in four years. That is very impressive. What is even more impressive is that

### Criticizing Arguments

Kareem Khalifa Criticizing Arguments 1 Criticizing Arguments Kareem Khalifa Department of Philosophy Middlebury College Written August, 2012 Table of Contents Introduction... 1 Step 1: Initial Evaluation

### 2.3. Failed proofs and counterexamples

2.3. Failed proofs and counterexamples 2.3.0. Overview Derivations can also be used to tell when a claim of entailment does not follow from the principles for conjunction. 2.3.1. When enough is enough

### What is an argument? PHIL 110. Is this an argument? Is this an argument? What about this? And what about this?

What is an argument? PHIL 110 Lecture on Chapter 3 of How to think about weird things An argument is a collection of two or more claims, one of which is the conclusion and the rest of which are the premises.

### Philosophy 57 Day 10. Chapter 4: Categorical Statements Conversion, Obversion & Contraposition II

Branden Fitelson Philosophy 57 Lecture 1 Branden Fitelson Philosophy 57 Lecture 2 Chapter 4: Categorical tatements Conversion, Obversion & Contraposition I Philosophy 57 Day 10 Quiz #2 Curve (approximate)

### Broad on Theological Arguments. I. The Ontological Argument

Broad on God Broad on Theological Arguments I. The Ontological Argument Sample Ontological Argument: Suppose that God is the most perfect or most excellent being. Consider two things: (1)An entity that

### ILLOCUTIONARY ORIGINS OF FAMILIAR LOGICAL OPERATORS

ILLOCUTIONARY ORIGINS OF FAMILIAR LOGICAL OPERATORS 1. ACTS OF USING LANGUAGE Illocutionary logic is the logic of speech acts, or language acts. Systems of illocutionary logic have both an ontological,

### God of the gaps: a neglected reply to God s stone problem

God of the gaps: a neglected reply to God s stone problem Jc Beall & A. J. Cotnoir January 1, 2017 Traditional monotheism has long faced logical puzzles (omniscience, omnipotence, and more) [10, 11, 13,

### SMITH ON TRUTHMAKERS 1. Dominic Gregory. I. Introduction

Australasian Journal of Philosophy Vol. 79, No. 3, pp. 422 427; September 2001 SMITH ON TRUTHMAKERS 1 Dominic Gregory I. Introduction In [2], Smith seeks to show that some of the problems faced by existing

### Philosophy 57 Day 10

Branden Fitelson Philosophy 57 Lecture 1 Philosophy 57 Day 10 Quiz #2 Curve (approximate) 100 (A); 70 80 (B); 50 60 (C); 40 (D); < 40 (F) Quiz #3 is next Tuesday 03/04/03 (on chapter 4 not tnanslation)

### Transition to Quantified Predicate Logic

Transition to Quantified Predicate Logic Predicates You may remember (but of course you do!) during the first class period, I introduced the notion of validity with an argument much like (with the same

### Artificial Intelligence Prof. P. Dasgupta Department of Computer Science & Engineering Indian Institute of Technology, Kharagpur

Artificial Intelligence Prof. P. Dasgupta Department of Computer Science & Engineering Indian Institute of Technology, Kharagpur Lecture- 9 First Order Logic In the last class, we had seen we have studied

### The Problem of the External World

The Problem of the External World External World Skepticism Consider this painting by Rene Magritte: Is there a tree outside? External World Skepticism Many people have thought that humans are like this

### b) The meaning of "child" would need to be taken in the sense of age, as most people would find the idea of a young child going to jail as wrong.

Explanation for Question 1 in Quiz 8 by Norva Lo - Tuesday, 18 September 2012, 9:39 AM The following is the solution for Question 1 in Quiz 8: (a) Which term in the argument is being equivocated. (b) What

### Unit. Categorical Syllogism. What is a syllogism? Types of Syllogism

Unit 8 Categorical yllogism What is a syllogism? Inference or reasoning is the process of passing from one or more propositions to another with some justification. This inference when expressed in language

### TWO VERSIONS OF HUME S LAW

DISCUSSION NOTE BY CAMPBELL BROWN JOURNAL OF ETHICS & SOCIAL PHILOSOPHY DISCUSSION NOTE MAY 2015 URL: WWW.JESP.ORG COPYRIGHT CAMPBELL BROWN 2015 Two Versions of Hume s Law MORAL CONCLUSIONS CANNOT VALIDLY

### Knowledge, Time, and the Problem of Logical Omniscience

Fundamenta Informaticae XX (2010) 1 18 1 IOS Press Knowledge, Time, and the Problem of Logical Omniscience Ren-June Wang Computer Science CUNY Graduate Center 365 Fifth Avenue, New York, NY 10016 rwang@gc.cuny.edu

### Rosen, Discrete Mathematics and Its Applications, 6th edition Extra Examples

Rosen, Discrete Mathematics and Its Applications, 6th edition Extra Examples Section 1.1 Propositional Logic Page references correspond to locations of Extra Examples icons in the textbook. p.2, icon at

### HANDBOOK (New or substantially modified material appears in boxes.)

1 HANDBOOK (New or substantially modified material appears in boxes.) I. ARGUMENT RECOGNITION Important Concepts An argument is a unit of reasoning that attempts to prove that a certain idea is true by

### A Model of Decidable Introspective Reasoning with Quantifying-In

A Model of Decidable Introspective Reasoning with Quantifying-In Gerhard Lakemeyer* Institut fur Informatik III Universitat Bonn Romerstr. 164 W-5300 Bonn 1, Germany e-mail: gerhard@uran.informatik.uni-bonn,de

### In Defense of The Wide-Scope Instrumental Principle. Simon Rippon

In Defense of The Wide-Scope Instrumental Principle Simon Rippon Suppose that people always have reason to take the means to the ends that they intend. 1 Then it would appear that people s intentions to

### SUPPOSITIONAL REASONING AND PERCEPTUAL JUSTIFICATION

SUPPOSITIONAL REASONING AND PERCEPTUAL JUSTIFICATION Stewart COHEN ABSTRACT: James Van Cleve raises some objections to my attempt to solve the bootstrapping problem for what I call basic justification

### SAVING RELATIVISM FROM ITS SAVIOUR

CRÍTICA, Revista Hispanoamericana de Filosofía Vol. XXXI, No. 91 (abril 1999): 91 103 SAVING RELATIVISM FROM ITS SAVIOUR MAX KÖLBEL Doctoral Programme in Cognitive Science Universität Hamburg In his paper

### Paradox of Deniability

1 Paradox of Deniability Massimiliano Carrara FISPPA Department, University of Padua, Italy Peking University, Beijing - 6 November 2018 Introduction. The starting elements Suppose two speakers disagree

### What is a logical argument? What is deductive reasoning? Fundamentals of Academic Writing

What is a logical argument? What is deductive reasoning? Fundamentals of Academic Writing Logical relations Deductive logic Claims to provide conclusive support for the truth of a conclusion Inductive

### In this section you will learn three basic aspects of logic. When you are done, you will understand the following:

Basic Principles of Deductive Logic Part One: In this section you will learn three basic aspects of logic. When you are done, you will understand the following: Mental Act Simple Apprehension Judgment

### 9.1 Intro to Predicate Logic Practice with symbolizations. Today s Lecture 3/30/10

9.1 Intro to Predicate Logic Practice with symbolizations Today s Lecture 3/30/10 Announcements Tests back today Homework: --Ex 9.1 pgs. 431-432 Part C (1-25) Predicate Logic Consider the argument: All

### A Liar Paradox. Richard G. Heck, Jr. Brown University

A Liar Paradox Richard G. Heck, Jr. Brown University It is widely supposed nowadays that, whatever the right theory of truth may be, it needs to satisfy a principle sometimes known as transparency : Any

### Aquinas' Third Way Modalized

Philosophy of Religion Aquinas' Third Way Modalized Robert E. Maydole Davidson College bomaydole@davidson.edu ABSTRACT: The Third Way is the most interesting and insightful of Aquinas' five arguments for

### 1/5. The Critique of Theology

1/5 The Critique of Theology The argument of the Transcendental Dialectic has demonstrated that there is no science of rational psychology and that the province of any rational cosmology is strictly limited.

### Ayer on the criterion of verifiability

Ayer on the criterion of verifiability November 19, 2004 1 The critique of metaphysics............................. 1 2 Observation statements............................... 2 3 In principle verifiability...............................

### Introduction to Logic

University of Notre Dame Fall, 2015 Arguments Philosophy is difficult. If questions are easy to decide, they usually don t end up in philosophy The easiest way to proceed on difficult questions is to formulate

### LGCS 199DR: Independent Study in Pragmatics

LGCS 99DR: Independent Study in Pragmatics Jesse Harris & Meredith Landman September 0, 203 Last class, we discussed the difference between semantics and pragmatics: Semantics The study of the literal

### Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world

Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world Visit us on the World Wide Web at: www.pearsoned.co.uk Pearson Education Limited 2014

### Logic -type questions

Logic -type questions [For use in the Philosophy Test and the Philosophy section of the MLAT] One of the questions on a test may take the form of a logic exercise, starting with the definition of a key