CT214 – Logical Foundations of Computing Darren Doherty Rm. 311 Dept. of Information Technology NUI Galway

Slides:

Advertisements

Similar presentations

Artificial Intelligence

Advertisements

Rules of Inference Rosen 1.5.

Rules of Inferences Section 1.5. Definitions Argument: is a sequence of propositions (premises) that end with a proposition called conclusion. Valid Argument:

The Foundations: Logic and Proofs

1 Logic Logic in general is a subfield of philosophy and its development is credited to ancient Greeks. Symbolic or mathematical logic is used in AI. In.

Deduction In addition to being able to represent facts, or real- world statements, as formulas, we want to be able to manipulate facts, e.g., derive new.

CLASSICAL LOGIC and FUZZY LOGIC. CLASSICAL LOGIC In classical logic, a simple proposition P is a linguistic, or declarative, statement contained within.

CSE115/ENGR160 Discrete Mathematics 01/26/12 Ming-Hsuan Yang UC Merced 1.

Chapter 1 The Logic of Compound Statements. Section 1.3 Valid & Invalid Arguments.

CS128 – Discrete Mathematics for Computer Science

This is Introductory Logic PHI 120 Get a syllabus online, if you don't already have one Presentation: "Good Arguments"

Uses for Truth Tables Determine the truth conditions for any compound statementDetermine the truth conditions for any compound statement Determine whether.

Logic 3 Tautological Implications and Tautological Equivalences

Syllabus Every Week: 2 Hourly Exams +Final - as noted on Syllabus

TR1413: Discrete Mathematics For Computer Science Lecture 3: Formal approach to propositional logic.

Essential Deduction Techniques of Constructing Formal Expressions and Evaluating Attempts to Create Valid Arguments.

1 Chapter 7 Propositional and Predicate Logic. 2 Chapter 7 Contents (1) l What is Logic? l Logical Operators l Translating between English and Logic l.

Essential Deduction Techniques of Constructing Formal Expressions Evaluating Attempts to Create Valid Arguments.

Proof by Deduction. Deductions and Formal Proofs A deduction is a sequence of logic statements, each of which is known or assumed to be true A formal.

Discussion #9 1/9 Discussion #9 Tautologies and Contradictions.

Discrete Mathematics and its Applications

Adapted from Discrete Math

Chapter 3 Section 4 – Slide 1 Copyright © 2009 Pearson Education, Inc. AND.

CSCI 115 Chapter 2 Logic. CSCI 115 §2.1 Propositions and Logical Operations.

1 Logic Logic is a discipline that studies the principles and methods used in correct reasoning It includes: A formal language for expressing statements.

1 Chapter 7 Propositional and Predicate Logic. 2 Chapter 7 Contents (1) l What is Logic? l Logical Operators l Translating between English and Logic l.

Discrete Mathematics CS 2610 August 24, Agenda Last class Introduction to predicates and quantifiers This class Nested quantifiers Proofs.

COS 150 Discrete Structures Assoc. Prof. Svetla Boytcheva Fall semester 2014.

INTRODUCTION TO LOGIC Jennifer Wang Fall 2009 Midterm Review Quiz Game.

1 CMSC 250 Discrete Structures CMSC 250 Lecture 1.

Fundamentals of Logic 1. What is a valid argument or proof? 2. Study system of logic 3. In proving theorems or solving problems, creativity and insight.

Hazırlayan DISCRETE COMPUTATIONAL STRUCTURES Propositional Logic PROF. DR. YUSUF OYSAL.

Philosophical Method  Logic: A Calculus For Good Reason  Clarification, Not Obfuscation  Distinctions and Disambiguation  Examples and Counterexamples.

1 Introduction to Abstract Mathematics Expressions (Propositional formulas or forms) Instructor: Hayk Melikya

CS6133 Software Specification and Verification

Chapter 1: The Foundations: Logic and Proofs

Propositional Logic Predicate Logic

Rules of Inference Section 1.6. Arguments in Propositional Logic A argument in propositional logic is a sequence of propositions. All but the final proposition.

What is Reasoning  Logical reasoning is the process of drawing conclusions from premises using rules of inference.  These inference rules are results.

Chapter 2 Fundamentals of Logic 1. What is a valid argument or proof?

Chapter 7. Propositional and Predicate Logic Fall 2013 Comp3710 Artificial Intelligence Computing Science Thompson Rivers University.

ARTIFICIAL INTELLIGENCE Lecture 2 Propositional Calculus.

Outline Logic Propositional Logic Well formed formula Truth table

Foundations of Discrete Mathematics Chapter 1 By Dr. Dalia M. Gil, Ph.D.

1 Propositional Proofs 1. Problem 2 Deduction In deduction, the conclusion is true whenever the premises are true.  Premise: p Conclusion: (p ∨ q) 

Symbolic Logic and Rules of Inference. whatislogic.php If Tom is a philosopher, then Tom is poor. Tom is a philosopher.

Discrete Mathematical Structures: Theory and Applications 1 Logic: Learning Objectives  Learn about statements (propositions)  Learn how to use logical.

Discrete Math by R.S. Chang, Dept. CSIE, NDHU1 Fundamentals of Logic 1. What is a valid argument or proof? 2. Study system of logic 3. In proving theorems.

March 3, 2016Introduction to Artificial Intelligence Lecture 12: Knowledge Representation & Reasoning I 1 Back to “Serious” Topics… Knowledge Representation.

Sound Arguments and Derivations. Topics Sound Arguments Derivations Proofs –Inference rules –Deduction.

Deductive Reasoning. Inductive: premise offers support and evidenceInductive: premise offers support and evidence Deductive: premises offers proof that.

Chapter 1 Logic and proofs

 Conjunctive Normal Form: A logic form must satisfy one of the following conditions 1) It must be a single variable (A) 2) It must be the negation of.

Chapter 7. Propositional and Predicate Logic

2. The Logic of Compound Statements Summary

Lecture Notes 8 CS1502.

Discrete Mathematics Logic.

Formal Logic CSC 333.

Rules of Inference Section 1.6.

CS201: Data Structures and Discrete Mathematics I

3.5 Symbolic Arguments.

CS 270 Math Foundations of CS

CS 220: Discrete Structures and their Applications

Back to “Serious” Topics…

Computer Security: Art and Science, 2nd Edition

Discrete Mathematics Logic.

Chapter 7. Propositional and Predicate Logic

CS201: Data Structures and Discrete Mathematics I

The Foundations: Logic and Proofs

3.5 Symbolic Arguments.

Presentation transcript:

CT214 – Logical Foundations of Computing Darren Doherty Rm. 311 Dept. of Information Technology NUI Galway

 Course 12 weeks  1 Lecture per week -10am Thurs in IT125G  Section B of Exam paper – Answer 2 out of 3 questions  

1. Propositional calculus (using properties of connectives to manipulate logical expressions without using truth tables) (3 weeks) 2. Writing proofs in propositional calculus using the rules of inference (modus ponens, modus tollens, disjunctive syllogism, etc.) (3 weeks) 3. Introduction to predicate calculus (if get time, discuss how it can map to a programming language ) (4 weeks) 4. Revision lecture (1 week)

Contradiction – a logical incompatibility between two or more propositions e.g. paul plays tennis AND paul does not play tennis (P ^ ¬P) Tautology – a propositional formula that is true under any possible valuation of its propositional variables e.g. paul plays tennis OR paul does not play tennis (P v ¬P) Contingency – a propositional formula that is not logically necessarily true or false

Argument – a sequence of one or more declarative sentences (premises) followed by a conclusion Inductive argument – truth of conclusion is supported by the premises Deductive argument – truth of conclusion is a logical consequence of the premises P 1 ^ P 2 ^ P 3 ^ … ^ P N -> C