DERIVATIONS IN SYMBOLIC LOGIC I

13. APPENDIX 1: THE SYNTAX OF PREDICATE LOGIC

394 Hardegree, Symbolic Logic 13. APPENDIX 1: THE SYNTAX OF PREDICATE LOGIC In this appendix, we review the syntactic features of predicate logic that are crucial to understanding derivations in predicate

SYMBOLIC LOGIC UNIT 10: SINGULAR SENTENCES

SYMBOLIC LOGIC UNIT 10: SINGULAR SENTENCES Singular Sentences name Paris is beautiful (monadic) predicate (monadic) predicate letter Bp individual constant Singular Sentences Bp These are our new simple

Announcements & Overview

Branden Fitelson Philosophy 4515 (Advanced Logic) Notes 1 Announcements & Overview Administrative Stuff HW #3 grades and solutions have been posted HW #4 s due date extended to next Friday (LMPL/L2PL proofs)

DERIVATIONS AND TRUTH TABLES

DERIVATIONS AND TRUTH TABLES Tomoya Sato Department of Philosophy University of California, San Diego Phil120: Symbolic Logic Summer 2014 TOMOYA SATO LECTURE 3: DERIVATIONS AND TRUTH TABLES 1 / 65 WHAT

Answers to the Exercises -- Chapter 3

Answers to the Exercises -- Chapter 3 SECTION 1 1. a. Fred is an orangutan. Of b. Gertrude is an orangutan but Fred isn't. Gertrude is an orangutan [and] Fred is not [an orangutan]. Og ~Of c. Tony Blair

All psychiatrists are doctors All doctors are college graduates All psychiatrists are college graduates

Predicate Logic In what we ve discussed thus far, we haven t addressed other kinds of valid inferences: those involving quantification and predication. For example: All philosophers are wise Socrates is

Predicate Logic. 1 Predicate Logic Symbolization

1 Predicate Logic Symbolization innovation of predicate logic: analysis of simple statements into two parts: the subject and the predicate. E.g. 1: John is a giant. subject = John predicate =... is a giant

INTRODUCTION. Tomoya Sato. Department of Philosophy University of California, San Diego. Phil120: Symbolic Logic Summer 2014

INTRODUCTION Tomoya Sato Department of Philosophy University of California, San Diego Phil120: Symbolic Logic Summer 2014 TOMOYA SATO LECTURE 1: INTRODUCTION 1 / 51 WHAT IS LOGIC? LOGIC Logic is the study

1 Introduction to Predicate Resolution

1 Introduction to Predicate Resolution The resolution proof system for Predicate Logic operates, as in propositional case on sets of clauses and uses a resolution rule as the only rule of inference. The

Topic DPL: Answers. Exercise 1.1a Explain why the rule &E for MPL is a sound rule.

Topic DPL: Answers Exercise 1.1a Explain why the rule &E for MPL is a sound rule. In MPL, if (φ&ψ) is true under some interpretation then φ and ψ are true under that interpretation too. Thus, if (φ&ψ)

Formal Logic: Quantifiers, Predicates, and Validity. CS 130 Discrete Structures

Formal Logic: Quantifiers, Predicates, and Validity CS 130 Discrete Structures Variables and Statements Variables: A variable is a symbol that stands for an individual in a collection or set. For example,

If you can figure out this derivation, better yet if you can reproduce it yourself, then you have truly mastered the universal-out rule!

Chapter 8: Derivations in Predicate Logic 357 Example 5 (1) x(fx yrxy) Pr (2) x y(rxy zgz) Pr (3) ~Gb Pr (4) : ~Fa ID (5) Fa As (6) : DD (7) Fa yray 1, O (8) yray 5,7, O (9) Rab 8, O (10) y(ray zgz) 2,

Denote John by j and Smith by s, is a bachelor by predicate letter B. The statements (1) and (2) may be written as B(j) and B(s).

PREDICATE CALCULUS Predicates Statement function Variables Free and bound variables Quantifiers Universe of discourse Logical equivalences and implications for quantified statements Theory of inference

First-Order Natural Deduction. Part 1: Universal Introduction and Elimination

First-Order Natural Deduction Part 1: Universal Introduction and Elimination Happy Birthday to Talan Two years old! Business Homework #7 will be posted later today. It is due on Monday, October 21. The

2. Use quantifiers to express the associative law for multiplication of real numbers.

1. Define statement function of one variable. When it will become a statement? Statement function is an expression containing symbols and an individual variable. It becomes a statement when the variable

Inverse Functions. One-to-one. Horizontal line test. Onto

Inverse Functions One-to-one Suppose f : A B is a function. We call f one-to-one if every distinct pair of objects in A is assigned to a distinct pair of objects in B. In other words, each object of the

Predicate Logic Quantifier Rules

Predicate Logic Quantifier Rules CS251 at CCUT, Spring 2017 David Lu May 8 th, 2017 Contents 1. Universal Instantiation (UI) 2. Existential Generalization (EG) 3. Universal Generalization (UG) 4. Existential

Formal (Natural) Deduction for Predicate Calculus

Formal (Natural) Deduction for Predicate Calculus Lila Kari University of Waterloo Formal (Natural) Deduction for Predicate Calculus CS245, Logic and Computation 1 / 42 Formal deducibility for predicate

Lecture 10: Predicate Logic and Its Language

Discrete Mathematics (II) Spring 2017 Lecture 10: Predicate Logic and Its Language Lecturer: Yi Li 1 Predicates and Quantifiers In this action, we show you why a richer language should be introduced than

Phil 2B03 (McMaster University Final Examination) Page 1 of 4

Phil 2B03 (McMaster University Final Examination) Page 1 of 4 1. [SL proof] (a) Prove the formal validity of the following sequent: (F & G), F H, H G H (1) (F & G) Prem (2) F H Prem (3) H G Prem (4) H

Predicate Logic combines the distinctive features of syllogistic and propositional logic.

Predicate Logic combines the distinctive features of syllogistic and propositional logic. The fundamental component in predicate logic is the predicate, which is always symbolized with upper case letters.

Philosophy 240 Symbolic Logic Russell Marcus Hamilton College Fall 2014

Philosophy 240 Symbolic Logic Russell Marcus Hamilton College Fall 2014 Class #23 - Translation into Predicate Logic II ( 3.2) Only as a Quantifier P Only Ps are Qs is logically equivalent to all Qs are

Section 1.1 Propositions

Set Theory & Logic Section 1.1 Propositions Fall, 2009 Section 1.1 Propositions In Chapter 1, our main goals are to prove sentences about numbers, equations or functions and to write the proofs. Definition.

Lecture 10 CS 1813 Discrete Mathematics. Quantify What? Reasoning with Predicates

Lecture 10 CS 1813 Discrete Mathematics Quantify What? Reasoning with Predicates 1 More Examples with Forall the Universal Quantifier L predicate about qsort L(n) length(qsort[a 1, a 2,, a n ] ) = n Universe

Introduction to Predicate Logic Part 1. Professor Anita Wasilewska Lecture Notes (1)

Introduction to Predicate Logic Part 1 Professor Anita Wasilewska Lecture Notes (1) Introduction Lecture Notes (1) and (2) provide an OVERVIEW of a standard intuitive formalization and introduction to

Technische Universität München Summer term 2011 Theoretische Informatik Prof. Dr. Dr. h.c J. Esparza / M. Luttenberger / R.

Technische Universität München Summer term 2011 Theoretische Informatik Prof. Dr. Dr. h.c J. Esparza / M. Luttenberger / R. Neumann SOLUTION Logic Endterm 2 Please note : If not stated otherwise, all answers

DO NOT FORGET!!! WRITE YOUR NAME HERE. Philosophy 109 Final Exam, Spring 2007 (80 points total) ~ ( x)

Page 1 of 13 DO NOT FORGET!!! WRITE YOUR NAME HERE Philosophy 109 Final Exam, Spring 2007 (80 points total) ~ ( x) Part I: Symbolization into RL: Provide symbolizations of the following sentences, using

CogSysI Lecture 8: Automated Theorem Proving

CogSysI Lecture 8: Automated Theorem Proving Intelligent Agents WS 2004/2005 Part II: Inference and Learning Automated Theorem Proving CogSysI Lecture 8: Automated Theorem Proving p. 200 Remember......

G52DOA - Derivation of Algorithms Predicate Logic

G52DOA - Derivation of Algorithms Predicate Logic Venanzio Capretta Predicate Logic So far, we studied propositional logic, in which we started with unspecified propositional variables A, B, C, and combined

2-4: The Use of Quantifiers

2-4: The Use of Quantifiers The number x + 2 is an even integer is not a statement. When x is replaced by 1, 3 or 5 the resulting statement is false. However, when x is replaced by 2, 4 or 6 the resulting

The predicate calculus is complete

The predicate calculus is complete Hans Halvorson The first thing we need to do is to precisify the inference rules UI and EE. To this end, we will use A(c) to denote a sentence containing the name c,

Interpretations of PL (Model Theory)

Interpretations of PL (Model Theory) 1. Once again, observe that I ve presented topics in a slightly different order from how I presented them in sentential logic. With sentential logic I discussed syntax

MATH 1090 Problem Set #3 Solutions March York University

York University Faculties of Science and Engineering, Arts, Atkinson MATH 1090. Problem Set #3 Solutions Section M 1. Use Resolution (possibly in combination with the Deduction Theorem, Implication as

Logic: First Order Logic

Logic: First Order Logic Raffaella Bernardi bernardi@inf.unibz.it P.zza Domenicani 3, Room 2.28 Faculty of Computer Science, Free University of Bolzano-Bozen http://www.inf.unibz.it/~bernardi/courses/logic06

Intermediate Logic. First-Order Logic

Intermediate Logic Lecture Four First-Order Logic Rob Trueman rob.trueman@york.ac.uk University of York Introducing First-Order Logic First-Order Logic Introducing First-Order Logic Names Predicates Quantifiers

LOWELL WEEKLY JOURNAL

Y G q G Y Y 29 8 $ 29 G 6 q )

Chapter 3. The Logic of Quantified Statements

Chapter 3. The Logic of Quantified Statements 3.1. Predicates and Quantified Statements I Predicate in grammar Predicate refers to the part of a sentence that gives information about the subject. Example:

First-order logic Syntax and semantics

1 / 43 First-order logic Syntax and semantics Mario Alviano University of Calabria, Italy A.Y. 2017/2018 Outline 2 / 43 1 Motivation Why more than propositional logic? Intuition 2 Syntax Terms Formulas

Predicate Logic. Example. Statements in Predicate Logic. Some statements cannot be expressed in propositional logic, such as: Predicate Logic

Predicate Logic Predicate Logic (Rosen, Chapter 1.4-1.6) TOPICS Predicate Logic Quantifiers Logical Equivalence Predicate Proofs Some statements cannot be expressed in propositional logic, such as: All

Notes on Propositional and First-Order Logic (CPSC 229 Class Notes, January )

Notes on Propositional and First-Order Logic (CPSC 229 Class Notes, January 23 30 2017) John Lasseter Revised February 14, 2017 The following notes are a record of the class sessions we ve devoted to the

6. COMPLEX PREDICATES

318 Hardegree, Symbolic Logic (1) x... y...rxy (1a) x(sx & y(py Rxy)) (1b) x(px & y(sy Rxy)) (2) x... y...ryx (2a) x(sx & y(py Ryx)) (2b) x(px & y(sy Ryx)) (3) x... y...rxy (3a) x(sx y(py & Rxy)) (3b)

Functional Equations Problems. Amir Hossein Parvardi June 13, Dedicated to pco.

Functional Equations Problems Amir Hossein Parvardi June 13, 2011 Dedicated to pco. email: ahpwsog@gmail.com, blog: http://math-olympiad.blogsky.com. 1 1 Definitions N is the set of positive integers.

INTRODUCTION TO LOGIC

Introduction INTRODUCTION TO LOGIC 6 Natural Deduction Volker Halbach Definition Let Γ be a set of sentences of L 2 and ϕ a sentence of L 2. Then Γ ϕ if and only if there is no L 2 -structure in which

Normal Forms for First-Order Logic

Logic and Proof Hilary 2016 James Worrell Normal Forms for First-Order Logic In this lecture we show how to transform an arbitrary formula of first-order logic to an equisatisfiable formula in Skolem form.

PHIL 50 INTRODUCTION TO LOGIC 1 FREE AND BOUND VARIABLES MARCELLO DI BELLO STANFORD UNIVERSITY DERIVATIONS IN PREDICATE LOGIC WEEK #8

PHIL 50 INTRODUCTION TO LOGIC MARCELLO DI BELLO STANFORD UNIVERSITY DERIVATIONS IN PREDICATE LOGIC WEEK #8 1 FREE AND BOUND VARIABLES Before discussing the derivation rules for predicate logic, we should

Predicate Calculus. Lila Kari. University of Waterloo. Predicate Calculus CS245, Logic and Computation 1 / 59

Predicate Calculus Lila Kari University of Waterloo Predicate Calculus CS245, Logic and Computation 1 / 59 Predicate Calculus Alternative names: predicate logic, first order logic, elementary logic, restricted

8 General first order representation

Intro. to Artificial Intelligence: Dale Schuurmans, Relu Patrascu 1 8 General first order representation 8.1 First order language Propositional core constants A, B, C, D predicates on(, ) associated arity,

CHAPTER 2. FIRST ORDER LOGIC

CHAPTER 2. FIRST ORDER LOGIC 1. Introduction First order logic is a much richer system than sentential logic. Its interpretations include the usual structures of mathematics, and its sentences enable us

Propositional Logic Not Enough

Section 1.4 Propositional Logic Not Enough If we have: All men are mortal. Socrates is a man. Does it follow that Socrates is mortal? Can t be represented in propositional logic. Need a language that talks

Logical Structures in Natural Language: First order Logic (FoL)

Logical Structures in Natural Language: First order Logic (FoL) Raffaella Bernardi Università degli Studi di Trento e-mail: bernardi@disi.unitn.it Contents 1 How far can we go with PL?................................

MAT 243 Test 1 SOLUTIONS, FORM A

t MAT 243 Test 1 SOLUTIONS, FORM A 1. [10 points] Rewrite the statement below in positive form (i.e., so that all negation symbols immediately precede a predicate). ( x IR)( y IR)((T (x, y) Q(x, y)) R(x,

First-Order Logic (FOL)

First-Order Logic (FOL) Also called Predicate Logic or Predicate Calculus 2. First-Order Logic (FOL) FOL Syntax variables x, y, z, constants a, b, c, functions f, g, h, terms variables, constants or n-ary

06 From Propositional to Predicate Logic

Martin Henz February 19, 2014 Generated on Wednesday 19 th February, 2014, 09:48 1 Syntax of Predicate Logic 2 3 4 5 6 Need for Richer Language Predicates Variables Functions 1 Syntax of Predicate Logic

Automated Reasoning Lecture 5: First-Order Logic

Automated Reasoning Lecture 5: First-Order Logic Jacques Fleuriot jdf@inf.ac.uk Recap Over the last three lectures, we have looked at: Propositional logic, semantics and proof systems Doing propositional

Stat 5101 Notes: Algorithms (thru 2nd midterm)

Stat 5101 Notes: Algorithms (thru 2nd midterm) Charles J. Geyer October 18, 2012 Contents 1 Calculating an Expectation or a Probability 2 1.1 From a PMF........................... 2 1.2 From a PDF...........................

INTRODUCTION TO LOGIC

INTRODUCTION TO LOGIC 6 Natural Deduction Volker Halbach There s nothing you can t prove if your outlook is only sufficiently limited. Dorothy L. Sayers http://www.philosophy.ox.ac.uk/lectures/ undergraduate_questionnaire

Foundations of Mathematics MATH 220 FALL 2017 Lecture Notes

Foundations of Mathematics MATH 220 FALL 2017 Lecture Notes These notes form a brief summary of what has been covered during the lectures. All the definitions must be memorized and understood. Statements

INSTITIÚID TEICNEOLAÍOCHTA CHEATHARLACH INSTITUTE OF TECHNOLOGY CARLOW PREDICATE LOGIC

1 CHAPTER 7. PREDICATE LOGIC 1 INSTITIÚID TEICNEOLAÍOCHTA CHEATHARLACH INSTITUTE OF TECHNOLOGY CARLOW PREDICATE LOGIC 1 Predicate Logic 1.1 Introduction There are various arguments which cannot be dealt

AAA615: Formal Methods. Lecture 2 First-Order Logic

AAA615: Formal Methods Lecture 2 First-Order Logic Hakjoo Oh 2017 Fall Hakjoo Oh AAA615 2017 Fall, Lecture 2 September 24, 2017 1 / 29 First-Order Logic An extension of propositional logic with predicates,

This is logically equivalent to the conjunction of the positive assertion Minimal Arithmetic and Representability

16.2. MINIMAL ARITHMETIC AND REPRESENTABILITY 207 If T is a consistent theory in the language of arithmetic, we say a set S is defined in T by D(x) if for all n, if n is in S, then D(n) is a theorem of

Identity. "At least one dog has fleas" is translated by an existential quantifier"

Identity Quantifiers are so-called because they say how many. So far, we've only used the quantifiers to give the crudest possible answers to the question "How many dogs have fleas?": "All," "None," "Some,"

7 Classical Quantified Logic

7 Classical Quantified Logic efore examining quantified modal logic, we review a bare-bones system for first-order predicate or quantificational logic, i.e., that involving the quantifiers x... and x...,

First-Order Logic. 1 Syntax. Domain of Discourse. FO Vocabulary. Terms

First-Order Logic 1 Syntax Domain of Discourse The domain of discourse for first order logic is FO structures or models. A FO structure contains Relations Functions Constants (functions of arity 0) FO

Knowledge representation in AI Symbolic Logic

Lecture No. 2 Knowledge representation in AI Symbolic Logic Simbolic logic representation Formal system Propositional logic Predicate logic Theorem proving 1. Knowledge representation Why Symbolic logic

Computational Logic. Davide Martinenghi. Spring Free University of Bozen-Bolzano. Computational Logic Davide Martinenghi (1/26)

Computational Logic Davide Martinenghi Free University of Bozen-Bolzano Spring 2010 Computational Logic Davide Martinenghi (1/26) Propositional Logic - algorithms Complete calculi for deciding logical

3. The Logic of Quantified Statements Summary. Aaron Tan August 2017

3. The Logic of Quantified Statements Summary Aaron Tan 28 31 August 2017 1 3. The Logic of Quantified Statements 3.1 Predicates and Quantified Statements I Predicate; domain; truth set Universal quantifier,

Logic. Lesson 3: Tables and Models. Flavio Zelazek. October 22, 2014

Logic Lesson 3: Tables and Models Flavio Zelazek flavio.zelazek@gmail.com October 22, 2014 Flavio Zelazek (flavio.zelazek@gmail.com) Logic (Lesson 3: Tables and Models) October 22, 2014 1 / 29 Previous

RULES OF UNIVERSAL INSTANTIATION AND GENERALIZATION, EXISTENTIAL INSTANTIATION AND GENERALIZATION, AND RULES OF QUANTIFIER EQUIVALENCE

1 UNIT 2 RULES OF UNIVERSAL INSTANTIATION AND GENERALIZATION, EXISTENTIAL INSTANTIATION AND GENERALIZATION, AND RULES OF QUANTIFIER EQUIVALENCE Contents 2.0 Objectives 2.1 Introduction 2.2 Rules of Quantification

CS2742 midterm test 2 study sheet. Boolean circuits: Predicate logic:

x NOT ~x x y AND x /\ y x y OR x \/ y Figure 1: Types of gates in a digital circuit. CS2742 midterm test 2 study sheet Boolean circuits: Boolean circuits is a generalization of Boolean formulas in which

Predicate Logic: Syntax

Predicate Logic: Syntax Alice Gao Lecture 12 Based on work by J. Buss, L. Kari, A. Lubiw, B. Bonakdarpour, D. Maftuleac, C. Roberts, R. Trefler, and P. Van Beek 1/31 Outline Syntax of Predicate Logic Learning

LING 501, Fall 2004: Quantification

LING 501, Fall 2004: Quantification The universal quantifier Ax is conjunctive and the existential quantifier Ex is disjunctive Suppose the domain of quantification (DQ) is {a, b}. Then: (1) Ax Px Pa &

Intermediate Logic Spring. Second-Order Logic

Intermediate Logic Spring Lecture Five Second-Order Logic Rob Trueman rob.trueman@york.ac.uk University of York 1 / 47 Introduction Second-Order Logic Introduction The Language of SOL Introduction and

3/29/2017. Logic. Propositions and logical operations. Main concepts: propositions truth values propositional variables logical operations

Logic Propositions and logical operations Main concepts: propositions truth values propositional variables logical operations 1 Propositions and logical operations A proposition is the most basic element

Stat 5101 Notes: Algorithms

Stat 5101 Notes: Algorithms Charles J. Geyer January 22, 2016 Contents 1 Calculating an Expectation or a Probability 3 1.1 From a PMF........................... 3 1.2 From a PDF...........................

SOLUTIONS TO ADDITIONAL EXERCISES FOR II.1 AND II.2

SOLUTIONS TO ADDITIONAL EXERCISES FOR II.1 AND II.2 Here are the solutions to the additional exercises in betsepexercises.pdf. B1. Let y and z be distinct points of L; we claim that x, y and z are not

First Order Differential Equations

Chapter 2 First Order Differential Equations 2.1 9 10 CHAPTER 2. FIRST ORDER DIFFERENTIAL EQUATIONS 2.2 Separable Equations A first order differential equation = f(x, y) is called separable if f(x, y)

Second-Order Modal Logic

Hardegree, Modal Logic, 11: Second-Order Modal Logic 16 XI-1 11 Second-Order Modal Logic 1. Introduction...2 2. Second-Order Considerations...2 3. Monadic Plurals...4 4. Syntax for Modal Logic with Plurals

4 Quantifiers and Quantified Arguments 4.1 Quantifiers

4 Quantifiers and Quantified Arguments 4.1 Quantifiers Recall from Chapter 3 the definition of a predicate as an assertion containing one or more variables such that, if the variables are replaced by objects

A Gentle Introduction to Stein s Method for Normal Approximation I

A Gentle Introduction to Stein s Method for Normal Approximation I Larry Goldstein University of Southern California Introduction to Stein s Method for Normal Approximation 1. Much activity since Stein

Section Summary. Section 1.5 9/9/2014

Section 1.5 Section Summary Nested Quantifiers Order of Quantifiers Translating from Nested Quantifiers into English Translating Mathematical Statements into Statements involving Nested Quantifiers Translated

h(x) lim H(x) = lim Since h is nondecreasing then h(x) 0 for all x, and if h is discontinuous at a point x then H(x) > 0. Denote

Real Variables, Fall 4 Problem set 4 Solution suggestions Exercise. Let f be of bounded variation on [a, b]. Show that for each c (a, b), lim x c f(x) and lim x c f(x) exist. Prove that a monotone function

About This Document. MTH299 - Examples Weeks 1-6; updated on January 5, 2018

About This Document This is the examples document for MTH 299. Basically it is a loosely organized universe of questions (examples) that we think are interesting, helpful, useful for practice, and serve

Lecture 11: Continuous-valued signals and differential entropy

Lecture 11: Continuous-valued signals and differential entropy Biology 429 Carl Bergstrom September 20, 2008 Sources: Parts of today s lecture follow Chapter 8 from Cover and Thomas (2007). Some components

Meta-logic derivation rules

Meta-logic derivation rules Hans Halvorson February 19, 2013 Recall that the goal of this course is to learn how to prove things about (as opposed to by means of ) classical first-order logic. So, we will

2.2 Separable Equations

2.2 Separable Equations Definition A first-order differential equation that can be written in the form Is said to be separable. Note: the variables of a separable equation can be written as Examples Solve

COMP4418: Knowledge Representation and Reasoning First-Order Logic

COMP4418: Knowledge Representation and Reasoning First-Order Logic Maurice Pagnucco School of Computer Science and Engineering University of New South Wales NSW 2052, AUSTRALIA morri@cse.unsw.edu.au COMP4418

HOMEWORK ASSIGNMENT 5

HOMEWORK ASSIGNMENT 5 DUE 1 MARCH, 2016 1) Let f(x) = 1 if x is rational and f(x) = 0 if x is irrational. Show that f is not continuous at any real number. Solution Fix any x R. We will show that f is

Announcements. Today s Menu

Announcements Reading Assignment: > Nilsson chapters 13-14 Announcements: > LISP and Extra Credit Project Assigned Today s Handouts in WWW: > Homework 10-13 > Outline for Class 26 > www.mil.ufl.edu/eel5840

Discrete Mathematics Basic Proof Methods

Discrete Mathematics 1-2. Basic Proof Methods Nature & Importance of Proofs In mathematics, a proof is: a correct(well-reasoned, logically valid) and complete (clear, detailed) argument that rigorously

1 Predicates and Quantifiers

1 Predicates and Quantifiers We have seen how to represent properties of objects. For example, B(x) may represent that x is a student at Bryn Mawr College. Here B stands for is a student at Bryn Mawr College

Recall that the expression x > 3 is not a proposition. Why?

Predicates and Quantifiers Predicates and Quantifiers 1 Recall that the expression x > 3 is not a proposition. Why? Notation: We will use the propositional function notation to denote the expression "

DRAFT - Math 101 Lecture Note - Dr. Said Algarni

2 Limits 2.1 The Tangent Problems The word tangent is derived from the Latin word tangens, which means touching. A tangent line to a curve is a line that touches the curve and a secant line is a line that

Semantics I, Rutgers University Week 3-1 Yimei Xiang September 17, Predicate logic

Semantics I, Rutgers University Week 3-1 Yimei Xiang September 17, 2018 Predicate logic 1. Why propositional logic is not enough? Discussion: (i) Does (1a) contradict (1b)? [Two sentences are contradictory

Logic and Modelling. Introduction to Predicate Logic. Jörg Endrullis. VU University Amsterdam

Logic and Modelling Introduction to Predicate Logic Jörg Endrullis VU University Amsterdam Predicate Logic In propositional logic there are: propositional variables p, q, r,... that can be T or F In predicate

MATH 104: INTRODUCTORY ANALYSIS SPRING 2008/09 PROBLEM SET 8 SOLUTIONS

MATH 04: INTRODUCTORY ANALYSIS SPRING 008/09 PROBLEM SET 8 SOLUTIONS. Let f : R R be continuous periodic with period, i.e. f(x + ) = f(x) for all x R. Prove the following: (a) f is bounded above below

1 FUNDAMENTALS OF LOGIC NO.10 HERBRAND THEOREM Tatsuya Hagino hagino@sfc.keio.ac.jp lecture URL https://vu5.sfc.keio.ac.jp/slide/ 2 So Far Propositional Logic Logical connectives (,,, ) Truth table Tautology

Predicate Calculus lecture 1

Predicate Calculus lecture 1 Section 1.3 Limitation of Propositional Logic Consider the following reasoning All cats have tails Gouchi is a cat Therefore, Gouchi has tail. MSU/CSE 260 Fall 2009 1 MSU/CSE

CSE Discrete Structures

CSE 2315 - Discrete Structures Homework 2- Fall 2010 Due Date: Oct. 7 2010, 3:30 pm Proofs using Predicate Logic For all your predicate logic proofs you can use only the rules given in the following tables.

2/2/2018. CS 103 Discrete Structures. Chapter 1. Propositional Logic. Chapter 1.1. Propositional Logic

CS 103 Discrete Structures Chapter 1 Propositional Logic Chapter 1.1 Propositional Logic 1 1.1 Propositional Logic Definition: A proposition :is a declarative sentence (that is, a sentence that declares

Ling 130 Notes: Predicate Logic and Natural Deduction

Ling 130 Notes: Predicate Logic and Natural Deduction Sophia A. Malamud March 7, 2014 1 The syntax of Predicate (First-Order) Logic Besides keeping the connectives from Propositional Logic (PL), Predicate