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