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 | 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 | ||