Documents about Symbolic Logic
symbolic_logic_lesson
Southern Oregon, CS 1313
Excerpt: ... Symbolic Logic Outline 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. Symbolic Logic Outline What is Logic? How Do We Use Logic? Logical Inferences #1 Logical Inferences #2 Symbolic Logic #1 Symbolic Logic #2 What If a Premise is False? #1 What If a Premise is False? #2 What If a Premise is False? #3 What If Both Premises are False? Boolean Values #1 Boolean Values #2 Boolean Values #2 The AND Operation Truth Table for AND Operation 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. Another Boolean Operation Joining the Premises Together More on OR What If a Premise is False? #1 What If a Premise is False? #2 What If Both Premises are False? The OR Operation Truth Table for OR Operation Boolean OR is Inclusive What is Exclusive OR? The NOT Operation Truth Table for NOT Operation Symbolic Logic Lesson CS1313 Spring 2009 1 What is Logic? "Logic is the study of the methods and principles used to distinguish good (correct) from bad (incorrect) reasoning." Irving M. Copi, Introduction to Logic, 6th ed., Macmillan ...
|
|
symbolic_logic_lesson
Southern Oregon, CS 1313
Excerpt: ... Symbolic Logic Outline 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. Symbolic Logic Outline What is Logic? How Do We Use Logic? Logical Inferences #1 Logical Inferences #2 Symbolic Logic #1 Symbolic Logic #2 What If a Premise is False? #1 What If a Premise is False? #2 What If a Premise is False? #3 What If Both Premises are False? Boolean Values #1 Boolean Values #2 Boolean Values #2 The AND Operation Truth Table for AND Operation 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. Another Boolean Operation Joining the Premises Together More on OR What If a Premise is False? #1 What If a Premise is False? #2 What If Both Premises are False? The OR Operation Truth Table for OR Operation Boolean OR is Inclusive What is Exclusive OR? The NOT Operation Truth Table for NOT Operation Symbolic Logic Lesson CS1313 Spring 2009 1 What is Logic? Logic is the study of the methods and principles used to distinguish good (correct) from bad (incorrect) reasoning. Irving M. Copi, Introduction to Logic, 6th ed ...
|
|
symbolic_logic_lesson
Southern Oregon, CS 1313
Excerpt: ... Symbolic Logic Outline 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. Symbolic Logic Outline What is Logic? How Do We Use Logic? Logical Inferences #1 Logical Inferences #2 Symbolic Logic #1 Symbolic Logic #2 What If a Premise is False? #1 What If a Premise is False? #2 What If a Premise is False? #3 What If Both Premises are False? Boolean Values #1 Boolean Values #2 Boolean Values #2 The AND Operation Truth Table for AND Operation 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. Another Boolean Operation Joining the Premises Together More on OR What If a Premise is False? #1 What If a Premise is False? #2 What If Both Premises are False? The OR Operation Truth Table for OR Operation Boolean OR is Inclusive What is Exclusive OR? The NOT Operation Truth Table for NOT Operation Symbolic Logic Lesson CS1313 Spring 2007 1 What is Logic? "Logic is the study of the methods and principles used to distinguish good (correct) from bad (incorrect) reasoning." Irving M. Copi, Introduction to Logic, 6th ed., M ...
|
|
Lecture01
Columbia, PHIL V3411
Excerpt: ... PHIL V3411 / PHIL G4415 Introduction to Symbolic Logic Lecture 1 Introduction and Overview Introduction Logic is the study of arguments. An argument is a sequence of statements of which one is intended as a conclusion and the others, the premises, are intended to prove or at least provide good evidence for the conclusion. There are bad arguments as well as good ones. Examples: All humans are animals. All animals are mortal. Therefore, all humans are mortal. All humans are animals. Some animals are insects. Therefore, some humans are insects. } premises conclusion } premises conclusion Basic idea: an argument is good (or valid) if it is not possible for its conclusion to be false when the premises are all true. (Intuitively: whoever accepts the premises of a valid argument must also accept the conclusion.) The purpose of logic is precisely to develop methods and techniques to tell good (i.e., valid) arguments from bad ones. INTRODUCTION TO SYMBOLIC LOGIC , LECTU ...
|
|
Lecture03
Columbia, PHIL V3411
Excerpt: ... PHIL V3411 / PHIL G4415 Introduction to Symbolic Logic Lecture 3 Sentential Logic: The Conjunction Connective The Conjunction Connective (Section 2.1.2) For every pair of sentences A and B there is another sentence called the conjunction of A and B. English: A and B left conjunct right conjunct Symbolization: AB Semantics: A B is T if both A and B are T; otherwise A B is F Truth table: AB TT TF FT FF AB T F F F Note: the order of the conjuncts makes no difference to the truthvalue of the conjunction: Principle of Commutativity: A B has the same truth-value as B A (though they are different sentential expressions) INTRODUCTION TO SYMBOLIC LOGIC , LECTURE 3 P. 1 Repeated Applications and Grouping Since the conjunction of two sentences is itself a sentence, it can be conjoined with any other sentence. The conjunction of A B and C: The conjunction of A and B C: (A B) C A (B C) Parentheses are used to distinguis ...
|
|
Lecture05
Columbia, PHIL V3411
Excerpt: ... PHIL V3411 / PHIL G4415 Introduction to Symbolic Logic Lecture 5 Sentential Logic: The Disjunction Connective; Tautologies and Contradictions The Disjunction Connective (Section 2.2.2) For every pair of sentences A and B there is another sentence called the disjunction of A and B. English: Either A or B (or both) left disjunct right disjunct Symbolization: AB Semantics: A B is T if at least one of A and B is T; otherwise A B is F Truth table: AB TT TF FT FF AB T T T F Note: as with conjunction, the following general principles hold Principle of Commutativity: Principle of Associativity: AB BA (A B) C A (B C) INTRODUCTION TO SYMBOLIC LOGIC , LECTURE 5 P. 1 Disjunction in Natural Language (Section 3.1.3) Disjunction as a joiner of nouns Like conjunction, disjunction can be used as a joiner of nouns. But there is no room for a collective reading, so no problems here. Jack or Jill took driving lessons Jack took dri ...
|
|
Lecture02
Columbia, PHIL V3411
Excerpt: ... PHIL V3411 / PHIL G4415 Introduction to Symbolic Logic Lecture 2 Sentential Logic: Preliminaries; the Negation Connective Two more preliminary remarks Logic is useful for the purpose of assessing the goodness of certain arguments (put forward by us or by other people). It is also useful for the purpose of clarifying or formulating theories in a rigorous way (cp. Euclid and the axiomatic method). Arguments dont always come in a perspicuous format, as in: 1. All humans are animals. 2. All animals are mortal. 3. Therefore, all humans are mortal. Sometimes it takes a lot of work to identify the premises and conclusion of an argument and to reconstruct its form. Example If our children watch more than three hours of television per day, then either their power of imagination is improved or they become conditioned to expect constant excitement. But surely a childs power of imagination is not improved by watching television, unless he or she also spends some time reading. Thus, there is no do ...
|
|
Lecture04
Columbia, PHIL V3411
Excerpt: ... PHIL V3411 / PHIL G4415 Introduction to Symbolic Logic Lecture 4 Sentential Logic: Truth-tables, Logical equivalence A Puzzle You are on an island where there are two kinds of inhabitants: 1) Knights, who always tell the truth 2) Knaves, who always lie. You meet two of them, Alf and Beth. Alf says: At least one of us is a Knave. What are Alf and Beth? Solution Alf cannot be a Knave, since if he were, what he says would be true (which is impossible: Knaves always lie). So he must be a Knight. But if he is a Knight, then what he says is true. So the other person, Beth, must be a Knave. INTRODUCTION TO SYMBOLIC LOGIC , LECTURE 4 P. 1 Formal Explanation Alfs statement, At least one of us is a Knave, can be expressed as the negation of a conjunction: i.e. We are not both Knights It is not the case that (Alf is a Knight and Beth is a Knight) which has the logical form (A B) We can construct a truth-table for this expression: A T T F F Note: B T F T F AB T F F F (A B) F T T T T means ...
|
|
NatureofNegation
Delaware, MATH 210
Excerpt: ... Not (To be, or not to be) The nature of negating We now revisit something we touched on in the last lecture what happens when we negate and or or. Well also touch on double negation and what a tautology or contradiction is. To begin, let us turn our title into a statement written in symbolic logic . Well denote To be by p. So Not to be is p. In symbolic logic , we use for or and for and. So To be, or not to be would be p p. Finally, to negate Hamlet as we do in the title, we would write (p p). So now we have the title in symbolic logic . The thing is this is clearly not the simplest way to write this theres no way we would have spoken the title as it is written. So let us think a little more about this. Firstly, we all instinctively understand what the truth value of p or q (symbolically p q) is and we can easily write down the truth table for this: p T T F F q T F T F pq T T T F With this understanding now recorded, ...
|
|
wqo
Wisconsin, M 975
Excerpt: ... Some references on wqo, bqo, scattered types, Fraisse conjecture. A.Miller Fall 2006 October 3, 2006 Abraham, Uri; Bonnet, Robert Hausdorff's theorem for posets that satisfy the finite antichain property. Fund. Math. 159 (1999), no. 1, 5169. Generalizes Hausdorff's hierarchy of scattered linear order types. Argyros, Spiros A.; Todorcevic, Stevo Ramsey methods in analysis. Advanced Courses in Mathematics. CRM Barcelona. Birkhauser Verlag, Basel, 2005. viii+257 pp. ISBN: 978-3-7643-7264-4; 3-7643-7264-8 Todorcevic surveys bqo theory. Bonnet, Robert; Rubin, M. Elementary embedding between countable Boolean algebras. J. Symbolic Logic 56 (1991), no. 4, 12121229. Countable models of a complete theory of boolean algebras are wqo under elementary embeddability. Cholak, Peter; Marcone, Alberto; Solomon, Reed Reverse mathematics and the equivalence of definitions for well and better quasi-orders. J. Symbolic Logic 69 (2004), no. 3, 683712. Clote, P. The metamathematics of scattered linear orderings. Arch. Math. Lo ...
|
|
Conditional Study Guide
SEMO, PL 120
Excerpt: ... Symbolic Logic I Study Guide on Translating Conditionals Proper translation of conditionals from ordinary English into proper symbolic notation is both critical and difficult. Below are two lists, one of words and phrases that precede the antecedent of a conditional, the other of words and phrases that precede the consequent. Use these terms to help you identify the parts of a conditional. Terms that precede the antecedent: If Given that Insofar as Provided that So long as In case Follows from Is implied by Whenever Is a necessary condition for Terms that precede the Consequent: Then Only if It follows that Implies Leads to Means that Is a sufficient condition for NOTE: Sufficient conditions are antecedents of conditionals. Necessary conditions are consequents of conditionals. If one statement is both necessary and sufficient for another, then the relation between those statements is that of the biconditional. 1. Which of the following expressions should be translated as "P Q"? a. q, if p d. q, only if p g. ...
|
|
description
UGA, PHIL 2500
Excerpt: ... PHIL 2500 Spring 2009 PHIL 2500: Symbolic Logic Lecture: MW 12:20 1:10 p.m.; 115 Peabody Hall Discussion Sections: R or F, please check your schedule Instructor: Yuri Balashov Office: 124 Peabody Hall Tel: 706-583-0529; email: yuri@uga.edu Office hours: MW 1:152:15 pm and by appointment Teaching Assistant: Taylor Stone Office: 001 Peabody Hall Email: catguy50@gmail.com Office hours: T: 2:003:00 pm; R: 11:30 am 12:30 pm and by appointment COURSE OBJECTIVES: The goal of this course is to teach the basics of formal symbolic logic and its connection to argumentation and natural language. You will learn how to formalize arguments and evaluate them for validity. REQUIRED TEXT: Bergmann, Moor and Nelson, The Logic Book, 5th ed. We aim to cover chapters 1, 2, 3, 5, 7, and 10. Additional resources, including answers to selected exercises, are available at www.mhhe.com/bergmann5e WORK IN THE COURSE: In style, this course resembles a math course. And just like in a math class, learning logic is c ...
|
|
ch4
George Mason, FNAN 301
Excerpt: ... ent Assets: Inventory, A/R, Cash Fixed Assets: Plant and Equipment 10 1999 2002 Financial Forecasting and Planning Types of Assets & Liabilities 11 Spontaneous Those assets and liabilities that automatically change as sales change Examples Accounts Receivable Accounts Payable Inventories Retained Earnings Discretionary Those assets and liabilities that require a decision on the part of management before additional investments are made Examples Fixed Assets Long Term Debt Financial Forecasting and Planning Problem 12 Symbolic Logic Corp has recently patented an advanced version of its original path-breaking technology and expects sales to grow from its present level of $5 million to $8 by the end of the coming year. The firm is currently operating 24 hours per day-management realizes it must expand to increase production beyond current levels. The firm's net profit margin is 8 percent. Dividend payout is expected to be 62.5%. What amount of outside financing must be raised to enable SCL to ...
|
|
Examples 8.1
Arkansas, PHIL 2203
Excerpt: ... Notes 8.1 Symbols and Translation So, up to now, weve studied Categorical Logic and Symbolic Logic . But that leaves one more type of logic to go. Predicate Logic is just like the others, ultimately, in that it provides us with a method for analyzing the validity of arguments. Remember, this is really the point of the whole course: to understand why good arguments are good and why bad arguments are bad. Predicate Logic is important because its even more powerful than the Categorical and Symbolic Logic for analyzing arguments. Consider the following categorical syllogism (taken from the book, I swear!): All student hookups are quickie sexual encounters. No quickie sexual encounters are committed relationships. Therefore, no student hookups are committed relationships. Whats important here, of course, is the term (remember the major, minor, and middle terms?). The arrangement of the terms is what eventually becomes the important thing for categorical logic (remember the forms of categorical syllogisms-AAA-2, e ...
|
|
L16.17
University of Florida , CEN 6070
Excerpt: ... Lectures 16 and 17 Formal Program Specification and Intro to Axiomatic Verification Following a brief review of symbolic logic and recursive functions, we consider formal program specification via pre and postconditions and functions ("Formal Program Specification"). We then turn our attention to axiomatic verification and the weak correctness predicate. Our initial focus will be reasoning about the correctness of programs utilizing assignment statements, sequencing, and selection statements ("Axiomatic Verification I"). You will also read a paper by Steve King, et al., which addresses an interesting question: "Is proof more costeffective than testing? Formal Program Specification Context: We begin the second half of the course this week by shifting our focus from testing to formal program verification, which requires some familiarity with notations used to formally specify the functional behavior of programs. Purpose: The purpose of this week's first lecture is to review some basic ideas from sy ...
|
|
boolean_lesson_2up
Southern Oregon, CS 1313
Excerpt: ... Boolean Outline 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Boolean Outline Logic Symbolic Logic Symbolic Logic (continued) Boolean Logic The AND Operation Another Boolean Operation More on OR The OR Operation The NOT Operation Logic Logic is the study of the methods and principles used to distinguish good (correct) from bad (incorrect) reasoning. 1 Every day, we put logic to work in making decisions about our lives, such as: how to dress (e.g., Will it be hot or cold?); what to eat and drink (e.g., Will we need caffeine to stay up studying?) where to go (e.g., Is it a Monday, in which case I need to go to CS1313?) See Programming in Fortran 90/95, 1st or 2nd ed, Chapter 11, section 11.2. We make logical inferences to reason about the decisions we need to make: It's cold this morning, so I need to wear a sweatshirt and jeans, not just a t-shirt and shorts. I've got a big exam tomorrow that I haven't studied for, so I'd better drink a couple pots of coffee. It's Monday, so I'd better be on time for CS1313 or I'll ...
|
|
boolean_lesson
Southern Oregon, CS 1313
Excerpt: ... Boolean Outline 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Boolean Outline Logic Symbolic Logic Symbolic Logic (continued) Boolean Logic The AND Operation Another Boolean Operation More on OR The OR Operation The NOT Operation 1 Logic Logic is the study of the methods and principles used to distinguish good (correct) from bad (incorrect) reasoning.1 Every day, we put logic to work in making decisions about our lives, such as: how to dress (e.g., Will it be hot or cold?); what to eat and drink (e.g., Will we need caffeine to stay up studying?) where to go (e.g., Is it a Monday, in which case I need to go to CS1313?) We make logical inferences to reason about the decisions we need to make: It's cold this morning, so I need to wear a sweatshirt and jeans, not just a t-shirt and shorts. I've got a big exam tomorrow that I haven't studied for, so I'd better drink a couple pots of coffee. It's Monday, so I'd better be on time for CS1313 or I'll be late for the quiz. We can even construct more complicated chains ...
|
|
0802-008
UCLA, MATH 0802
Excerpt: ... The Bulletin of Symbolic Logic Volume 8, Number 2, June 2002 FOURTH INTERNATIONAL SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SOFTWARE (TACS2001) CO-SPONSORED BY THE ASSOCIATION FOR SYMBOLIC LOGIC Tohoku University, Sendai, Japan October 2931, 2001 TACS2001 is the Fourth International Symposium on Theoretical Aspects of Computer Software. It was held at Tohoku University, Sendai, Japan, on October 2931, 2001. The symposium focused on theoretical foundations of programming and their applications, including the following topics: logic, proof, specication and semantics of programs and languages; theories and models of concurrent, parallel and distributed computation; and, theory-based systems for specifying, synthesizing, transforming, and verifying computer software. The Symposium Chair was Takayasu Ito. The members of the Program Committee were: Zena Ariola, Cedric Fournet, Jacques Garrigue, Masami Hagiya, Robert Harper, Masahito Hasegawa, Nevin Heintze, Martin Hofmann, Zhenjiang Hu, Naoki Kobayash ...
|
|
lr-10-20
Georgia Tech, CS 3361
Excerpt: ... October 20, 1995 Lecture Record Nancy A. Babiarz Brief Outline: 0) Administrative 1) Semantic Networks 2) Midterm Information Administrative Info. - Lecture notes have been posted to the web site, as of yesterday. - Lecture notes will also be posted to the newsgroup - Prog1 will be handed back Wednesday. - Lucy will be "gone" for two weeks working on research, if questions re: grading of prog1 arise, she will be available on an appointment only schedule. - Word for the test may be available this weekend, pending approval from previous instructors. Watch the newsgroup/website. - UPDATE: NO WORD (previous instructor didn't grant permission) Semantic Networks Semantic Networks (SNs) were mentionned earlier in the class as being similar to frames, although the property of INHERITENCE was not. Note: relationship between frames/ SNs/ conceptual graphs/ Logic. Symbolic logic (includes first-order predicate logic) was originally the "queen" of logic repre ...
|
|
Lecture2
Toledo, PHL 245
Excerpt: ... Jabberwocky Modern Symbolic Logic 'Twas brillig and the slithy toves Did gyre and gimble in the wabe: All mimsy were the borogoves, And the mome raths outgrabe. . Lewis Carroll Alice Through the Looking Glass Lecture 2: Symbols and Translation Jabberwocky and Form Although we understand none of the significant words, we do understand the basic structure. For example, a "tove" is a thing, which has the property of being "slithy", and which performs actions such as "gyring" and "gimbling". Logical Form Logical form is similar to grammatical form. It gives us the basic logical structure of an argument. Logical form is usually identified through connecting words such as "and", "or", "if". This is because the grammatical form is clear. The key is to understand the connecting words "and", "in", "the" - which define the structure of the sentence. Symbolic Logic and Argument Form Validity of deductive arguments determined by form: If the toves are slithy, then the borogoves are mimsy. The t ...
|
|
4045
USF, LIT 4000
Excerpt: ... ave three singular nouns, in English, of plural form, series, species, and Sorites: in all three, the awkwardness, of using the same word for both singular and plural, must often have been felt: this has been remedied, in the case of series by coining the plural serieses, which has already found it way into the diction- aries: so I am no rash innovator, but am merely following suit, in using the new plural Soriteses. In conclusion, let me point out that even those, who are obliged to study Formal Logic, with a view to being able to answer Examination-Papers in that subject, will find the study of Symbolic Logic most helpful for this purpose, in throwing light upon many of the obscurities with which Formal Logic abounds, and in furnishing a delightfully easy method of testing the results arrived at by the cumbrous processes which Formal Logic enforces upon its votaries. This is, I believe, the very first attempt (with the excep- tion of my own little book, The Game of ...
|
|
0702-008
UCLA, MATH 0702
Excerpt: ... The Bulletin of Symbolic Logic Volume 7, Number 2, June 2001 INTERNATIONAL CONFERENCE ON THEORETICAL COMPUTER SCIENCE (IFIP TCS2000) CO-SPONSORED BY THE ASSOCIATION FOR SYMBOLIC LOGIC Tohoku University, Sendai, Japan August 1719, 2000 IFIP TCS2000 is the rst International Conference on Theoretical Computer Science, organized by the Technical Committee TC1 on Foundations of Computer Science, the International Federation of Information Processing (IFIP). It was held at Tohoku University, Sendai, Japan, on August 1719, 2000. The activities of TC1 cover the entire eld of theoretical computer science. Reecting the current activities in theoretical computer science, the major topics of the conference were chosen, forming two tracks: Track (1) on Algorithms, Complexity, and Models of Computation, Track (2) on Logic, Semantics, Specication, and Verication. The IFIP TCS2000 technical program consisted of three keynote plenary invited talks, three invited speakers for each track, and eighteen con ...
|
|
MAT290_Review1
William Jewell, MAT 290
Excerpt: ... f symbolic logic that we are studying and what do each primarily deal with? 2. Know the definitions of negation, conjunction, and disjunction. 3. Know how to construct truth tables for compound propositions. 4. What is a tautology? What is a contradiction? 5. How can we determine whether two propositional forms are equivalent? Section 1.2 1. Know the definitions of conditional and biconditional sentences. 2. Know what is meant by the antecedent and consequent of a conditional sentence, including the various ways that these sentences are written. 3. What is the converse and contrapositive of P Q ? Which of these is equivalent to P Q? Section 1.3 1. What is a open sentence or predicate? What is the truth set and the universe of discourse? 2. Know the definitions for a universally quantified sentence, (x )P( x ) , and an existentially quantified sentence, (x )P( x ) . 3. Be able to give symbolic translations of English sentences and vice versa, using the symbolic logic notation. 4. Know how to sym ...
|
|
4052
USF, LIT 4000
Excerpt: ... Symbollic Logic by Lewis Carroll Book 2: Chapter 1 Propositions Generally. Section 1. Introductory. Note that the word some is to be regarded, henceforward, as meaning one or more. The word Proposition, as used in ordinary conversation, may be applied to any word, or phrase, which conveys any information whatever. [Thus the words yes and no are Propositions in the ordinary sense of the word; and so are the phrases you owe me five farthings and I dont! Such words as oh! or never!, and such phrases as fetch me that book! which book do you mean? do not seem, at first sight, to convey any information; but they can easily be turned into equivalent forms which do so, viz. I am surprised, I will never consent to it, I order you to fetch me that book, I want to know which book you mean.] But a Proposition, as used in this First Part of Symbolic Logic , has a peculiar form, which may be called its Normal form ...
|
|
4069_mat
USF, LIT 2
Excerpt: ... Name _ Date _ Book Seven: Soriteses Chapter 2: Problems in Soriteses Symbolic Logic List the possible problems described. Created for Lit2Go on the web at fcit.usf.edu ...
|