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 LanguagesChapter 7: General Proof SystemsChapter 8: Hilbert Proof Systems; Deduction TheoremChapter 9: Two Proofs of Propositional Classical Logic Completeness TheoremChapter 10: Introduction to Intuitionistic Logic; Conections between Classical and Intuitionistic Logics.Chapter 11: Classical Automated Proof systems: RS and original GentzenChapter 12: Gentzen Proof System for Intuitionistic Logic.Chapter 13: Classical Predicate Logic: Hilbert FormalizationChapter 14: Classical Predicate Logic: Automated Proof System QRSChapter 15: Hilbert and Gentzen Proof Systems for Intuitionistic Predicate LogicChapter 16: Introduction to Modal Logics, Modal S4 and S5 and their connections with Intuitionistic logic.Mendelson Book: Goedel Incompleteness TheoremBook 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
More:-
TESTS
PRACTICE FINAL
SOME BASIC DEFINITIONS and FACTS
Exercises - Homework Problems
Exercises - Homework SOLUTIONS
