INF 227, Spring 2010

Literature

Lectures and group meetings

Exercises

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 | ||