## INF 227, Spring 2010

### Literature

Michal Walicki "Introduction to Logic", Manuscript, 2006. The first part, History of Logic, is not part of the syllabus, and neither is chapter 11 nor the parts marked in thext as 'optional' .

### Lectures and group meetings

The idea is to spend one week, i.e., two double-hour lectures, for each chapter. In practice, however, it may take more then two lectures for some chapters. There will be weekly group meetings where the exercises will be discussed.

### Exercises

Exercises follow after each chapter. The exercises after chapter 4, 6, and 8, respectively, are compulsory exercises. Each compulsory exercise must be passed (at least E) and each counts 10% to the final exam. You will have, at least, a week to solve each compulsory exercise. In this week I drop the lectures, but there will be always one group meeting for asking questions.
You can discuss the solutions in groups, but each student has to deliver its own answers - without using the notes from the group meeting. Solutions which are too similar are failures.
It's planned that the group meeting after the deadline for a compulsory is for going through the solutions.

## Plan of Lectures

 Nr. Date Week Topics Pages 1. 12.01.10 02 Short introduction and overview Chapter 1 - Sets, Functions, Relations Topics: - set and set building operations - functions and basic properties - set-isomorphisms 29-33 2. 13.01.10 02 Chapter 1 - Sets, Functions, Relations Topics: - relations with composition and properties - equivalence relations and equivalence classes - ordering relations - cardinality of sets - infinite sets - Cantor's two diagonalizations, Russels Paradox 34-41 3. 19.01.10 03 Chapter 2 - Induction Topics: - motivating examples - well-founded and well orderings - inductive definitions in general 43-50 4. 20.01.10 03 Chapter 2 - Induction Topics: - 1-1 definitions - inductive definitions and recursive programming - structural induction 51-59 5. 26.01.10 04 Chapter 3 - Turing Machines Topics: - alphabets, strings, languages - Turing Machines - definition, composition - accepting vs. computing 61-68 6. 27.01.10 04 Chapter 3 - Turing Machines Topics: - Universal Turing Machine - decidability and the halting problem - Church's thesis 61-73 7. 02.02.10 05 Chapter 4 - Syntax and Proof Systems Topics: - axiomatic systems - syntax of SL (statement logic) - Hilbert's system for SL - admissible rules 75-81 8. 03.02.10 05 Chapter 4 - Syntax and Proof Systems Topics: - natural deduction and deduction theorem - Hilbert vs. natural deduction - consistency 81-84 9. 09.02.10 06 Chapter 4 - Syntax and Proof Systems Topics: - compactness theorem - equivalence of formulae - Gentzen's system 84-89 10.02.10 06 no lecture - Compulsory Exercises I 16.02.10 07 no lecture - Compulsory Exercises I 84-89 17.02.10 07 no lecture - Compulsory Exercises I 10. 23.02.10 08 Chapter 5 - Semantics of SL Topics: - structures and valuations - semantic properties of formulae 91-96 11. 24.02.10 08 Chapter 5 - Semantics of SL Topics: - laws of semantics - SL and set-valuations 96-102 12. 02.03.10 09 Chapter 6 - Soundness and Completeness Topics: - adequate sets of connectives - disjunctive and conjunctive normal form 104-106 13. 03.03.10 09 Chapter 6 - Soundness and Completeness Topics: - soundness - maximal consistent theories - completeness - applications 107-113 15. 09.03.10 10 Chapter 6 - Soundness and Completeness Topics: - - 10.03.10 10 no lecture - Compulsory Exercises II 16.03.10 11 no lecture - Compulsory Exercises II 17.03.10 11 no lecture - Compulsory Exercises II 23.03.10 12 no lecture - Compulsory Exercises II 24.03.10 12 no lecture - Compulsory Exercises II 30.03.10 13 no lecture - Easter holidays 31.03.10 13 no lecture - Easter holidays 16. 06.04.10 14 Chapter 7 - Syntax and Proof System of FOL Topics: - constants, variables, terms, formulae - scope of quantifiers and free variables - substitution 116-123 17. 07.04.10 14 Chapter 7 - Syntax and Proof System of FOL Topics: - natural deduction proof system - deduction theorem - Gentzen's system for FOL 123-127 18. 13.04.10 15 Chapter 8 - Semantics of FOL Topics: - FOL structures - interpretation of terms and formulae 19. 14.04.10 15 Chapter 8 - Semantics of FOL Topics: - - 20.04.10 16 no lecture - Compulsory Exercises III 21.04.10 16 no lecture - Compulsory Exercises III 20. 27.04.10 17 Chapter 9 - More Semantics Topics: - Prenex Normal Form - classifications 21. 28.04.10 17 Chapter 9 - More Semantics Topics: - "syntactic" semantics 22. 04.05.10 18 Chapter 10 - Soundness, Completeness Topics: - soundness - maximal consistent, Henkin-, and complete Henkin-theories 23. 05.05.10 18 Chapter 10 - Soundness, Completeness Topics: - proof of completeness - 19 no lecture - preparation exam 20 no lecture - preparation exam 25.05.10 21 Exam