Logics for Computer Science

Course Texbook

AN INTRODUCTION TO CLASSICAL and NON-CLASSICAL LOGICS 
Anita Wasilewska 

Full Book Text and Lecture Slides are in Downloads 

Course Reading Book

Introduction to Mathematical Logic, Fourth Edition 
Elliot Mendelson 

General Course Description:

The goal of the course is to make student understand the need of logic as a field and to learn the its formality and basic techniques. I will progress relatively slowly, making sure that the pace is appropriate for all students in the class. The book is written with students on my mind so that they can read and learn by some parts by themselves. The book, and the course is developed to teach not only intuitive understanding of different logics, but (and mainly) to teach formal logic as scientific subject, with its languages, definitions, main theorems and problems

Course Content

The course will follow the book very closely and in particular we will cover some, or all of the following chapters and subjects. 
Chapter 1: Introduction: Mathematical Paradoxes and Computer Science Puzzles 
Chapter 2: Introduction to Classical Propositional Logic 
Chapter 3: Propositional Languages 
Chapter 4: Classical Propositional Semantics 
Chapter 5: Some Extentional Three and Many Valued Logics Semantics 
Chapter 6: Classical tautologies, Logical Equivalences and Equivalences of Languages
Chapter 7: General Proof Systems
Chapter 8: Hilbert Proof Systems; Deduction Theorem
Chapter 9: Two Proofs of Propositional Classical Logic Completeness Theorem
Chapter 10: Introduction to Intuitionistic Logic; Conections between Classical and Intuitionistic Logics.
Chapter 11: Classical Automated Proof systems: RS and original Gentzen
Chapter 12: Gentzen Proof System for Intuitionistic Logic.
Chapter 13: Classical Predicate Logic: Hilbert Formalization
Chapter 14: Classical Predicate Logic: Automated Proof System QRS
Chapter 15: Hilbert and Gentzen Proof Systems for Intuitionistic Predicate Logic
Chapter 16: Introduction to Modal Logics, Modal S4 and S5 and their connections with Intuitionistic logic.
Mendelson Book: Goedel Incompleteness Theorem

Book Slides

Chapter 1: Introduction: Mathematical Paradoxes and Computer Science Puzzles Slides 
Chapter 2: Introduction to Classical Propositional Logic Slides 
Chapter 3: Propositional Languages Slides 
Chapter 4: Classical Propositional Semantics Slides 
Chapter 5: Some Extentional Three and Many Valued Logics emantics Slides 
Chapter 6, part 1: Propositional Tautologies Examples Slides 
Chapter 6, part 2: Definability of Connectives, Languages Equivalence Slides 
Chapter 5, 6 Examples Slides 
Chapter 7: General Proof Systems Slides 
Chapter 8: Hilbert Proof Systems; Deduction Theorem Slides 
Chapter 8: Formal Proofs in H2 Examples Slides 
Chapter 8: Proof of Deduction Theorem Slides 
Chapter 9, System S and Completeness Theorem Slides 
Chapter 9, Proof 1 of Completeness Theorem and Examples Slides 
Chapter 9, Part 2: Proof 2 of Completeness Theorem Slides 
Chapter 10, Introduction to Intuitionistic Logic, Part 1 Slides 
Chapter 10, Introduction to Intuitionistic Logic, Part 2 Slides 
Chapter 11, Part 1: RS System Definition and Overview 
Chapter 11, Part 2: RS System: Decomposition Trees 
Chapter 11, Part 3: RS System: Proof of Completeness Theorem 
Chapter 11, Part 4: Gentzen Proof System for Classical Logic Slides 
Chapter 12, Gentzen Proof System for Intuitionistic Logic, Part 1 Slides 
Chapter 12, Gentzen Proof System for Intuitionistic Logic, Part 2 Slides 
Chapter 12, Gentzen Proof System for Intuitionistic Logic, Part 3 Slides 
GL, GI: FEW PROBLEMS 
Chapter 13, Predicate Languages, Slides 
Chapter 13, System QRS, Slides 

Book Chapters

Chapter 1: Introduction 
Chapter 2: Indroduction to Classical Propositional Logic 
Chapter 3: Propositional Languages 
Chapter 4: Classical Propositional Semantics 
Chapter 5 Some Extensional Multivalued Semantics 
Chapter 6 Classical Tautologies and Logical Equivalences 
Chapter 7 General Proof Systems 
Chapter 8 Hilbert Proof Systems, Deduction Theorem 
Chapter 9 Propositional Logic Completeness Theorem - NEW 
Chapter 10 Introduction to Intuitionistic Logic 
Chapter 11 Gentzen Style Proof Systems for Classical Logic 
Chapter 12 Gentzen Proof System for Intuitionistic Logic 
Chapter 13, Predicate languages 
Chapter 13, Part 1: System QRS Definition and Examples 
Chapter 13, Part 2: System QRS Completeness 
Chapter 14, Part 1: Hilbert System for Predicate Logic 
Chapter 14, Part 2: Hilbert System for Predicate Logic

More:-

TESTS

MIDTERM 1 as given in class to WORK ON AGAIN 
MIDTERM 1 SOLUTIONS 
PRACTICE MIDTERM 1 Solutions 
MAKE-UP MIDTERM 1 Solutions 

TAKE HOME MIDTERM 2 
TAKE HOME Extra Credit Short Test 
MIDTERM 2 SOLUTIONS

PRACTICE FINAL

NO Practice FINAL! 

SOME BASIC DEFINITIONS and FACTS

Operations on Sets, Functions, Relations, Equivalence Relations 
Order Relations, Lattices, Boolean Algebras 
Cardinalities of Sets 

Exercises - Homework Problems

Homework Exercise 0 - NEW 
Homework Exercise 01 - NEW 
Homework-Exercise 1 
Homework-Exercise 2 
Homework-Exercise 3 
Homework-Exercise 4 
Homework-Exercise 5 
Homework-Exercise 6 
Homework-Exercise 7 
Homework-Exercise 8 
Homework-Exercise 9 
Homework-Exercise 9(1)- NEW 
Extra Credit Exercise 9a 
Homework-Exercise 10 
Homework-Exercise 11 
Homework-Exercise 12 

Exercises - Homework SOLUTIONS

Homework-Exercise 0 Solutions - NEW 
Homework-Exercise 1 Solutions 
Homework-Exercise 2 Solutions 
Homework-Exercise 3 Solutions 
Homework-Exercise 4 Solutions 
Homework-Exercise 5 Solutions 
Homework-Exercise 6 Solutions 
Homework-Exercise 7 Solutions 
Homework-Exercise 8 Solutions 
Homework-Exercise 10 Solutions 
Homework-Exercise 11 Solutions 
Homework-Exercise 12 Solutions