## 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 33-34 18.01.10 03 Group meeting 1: Weekly exercises Chapter 1 (Uwe) 3. 19.01.10 03 Chapter 1 - Sets, Functions, Relations Topics: - ordering relations - cardinality of sets, Theorem of Schroeder-Bernstein - infinite sets - Cantor's two diagonalizations 34-41 4. 20.01.10 03 Chapter 2 - Induction Topics: - motivating examples with complete induction - inductive definitions in general and structural induction - 1-1 definitions - inductive definitions and recursive programming 46-58 25.01.10 04 Group meeting 2: Weekly exercises Chapter 2 (Eva) 5. 26.01.10 04 Chapter 2 - Induction Topics: - induction vs. orderings - well-founded and well orderings 43-46 6. 27.01.10 04 Chapter 3 - Turing Machines Topics: - alphabets, strings, languages - Turing Machines - definition, composition - accepting vs. computing - Church's thesis 61-68 01.02.10 05 Group meeting 3: Weekly exercises Chapter 3 (Eva) 7. 02.02.10 05 Chapter 3 - Turing Machines Topics: - Universal Turing Machine - decidability and the halting problem 61-73 8. 03.02.10 05 Chapter 4 - SL: Syntax and Proof Systems Topics: - axiomatic systems - syntax of SL (statement logic) - Hilbert's system for SL - admissible rules 75-81 9. 08.02.10 06 Chapter 4 - Syntax and Proof Systems Topics: - natural deduction and deduction theorem - Hilbert vs. natural deduction - consistency 81-84 10. 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 - time for compulsory exercises 15.02.10 07 Group meeting 4: Questions Compulsory exercise set 1 (Eva) 16.02.10 07 no lecture - time for compulsory exercises 17.02.10 07 no lecture - time for compulsory exercises 22.02.10 08 Deadline Compulsory Exercise Set 1 at 16:00 23.02.10 08 no lecture - conference 24.02.10 08 no lecture - conference 01.03.10 09 no lecture - conference 11. 02.03.10 09 Chapter 5 - Semantics of SL Topics: - boolean interpretation of variables and connectives - structures and valuations - semantic properties of formulae - laws of semantics 91-97 03.03.10 09 Group meeting 5: Discussion solutions compulsory exercise set 1 (Eva) 08.03.10 10 Group meeting 6: Weekly exercise Chapter 5 (Eva) 12. 09.03.10 10 Chapter 5 - Semantics of SL Topics: - SL and set-valuations (Boolean Algebras) Chapter 6 - Soundness and Completeness Topics: - adequate sets of connectives - disjunctive and conjunctive normal form 92-106 13. 10.03.10 10 Chapter 6 - Soundness and Completeness Topics: - soundness - maximal consistent theories - completeness - applications 107-113 15.03.10 11 no lecture - time for compulsory exercises 107-113 16.03.10 11 no lecture - time for compulsory exercises 22.03.10 12 Group meeting 7: Questions Compulsory exercise set 2 (Eva) 23.03.10 12 no lecture - time for compulsory exercises 24.03.10 12 no lecture - time for compulsory exercises 30.03.10 13 no lecture - Easter holidays 31.03.10 13 no lecture - Easter holidays 06.04.10 14 no lecture - time for compulsory exercises 07.04.10 14 Deadline Compulsory Exercise Set 2 at 16:00 12.04.10 15 Group meeting 8: Discussion solutions compulsory exercise set 2 (Eva) 14. 13.04.10 15 Chapter 7 - Syntax and Proof System of FOL Topics: - constants, variables, terms, formulae - scope of quantifiers and free variables 116-122 15. 14.04.10 15 Chapter 7 - Syntax and Proof System of FOL Topics: - natural deduction proof system - substitution - deduction theorem - Gentzen's system for FOL 122-127 19.04.10 16 Group meeting 9: Weekly exercise Chapter 7 (Uwe) 16. 20.04.10 16 Chapter 8 - Semantics of FOL Topics: - FOL structures - interpretation of terms and formulae 130-134 17. 21.04.10 16 Chapter 8 - Semantics of FOL Topics: - Semantic properties of formulae - open vs. closed formulae - Prenex Normal Form - Skolemization 134-142 26.04.10 17 Group meeting 10: Questions Compulsory exercise set 3 (Uwe) 27.04.10 17 no lecture - time for compulsory exercises 28.04.10 17 no lecture - time for compulsory exercises 18. 04.05.10 18 Chapter 10 - Soundness, Completeness Topics: - soundness - maximal consistent, Henkin-, and complete Henkin-theories 19. 05.05.10 18 Deadline Compulsory Exercise Set 3 at 14:00 Chapter 10 - Soundness, Completeness Topics: - proof of completeness - 10.05.10 19 Group meeting 11: Discussion solutions compulsory exercise set 3 and Chapter 10 (Uwe) 11.05.10 19 no lecture - preparation exam 20 no lecture - preparation exam 25.05.10 21 Exam