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.DateWeekTopicsPages
1.12.01.10 02Short 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 02Chapter 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 03Chapter 2 - Induction
Topics: - motivating examples
- well-founded and well orderings
- inductive definitions in general		 43-50
4.20.01.10 03Chapter 2 - Induction
Topics: - 1-1 definitions
- inductive definitions and recursive programming
- structural induction		 51-59
5.26.01.10 04Chapter 3 - Turing Machines
Topics: - alphabets, strings, languages
- Turing Machines - definition, composition
- accepting vs. computing 		61-68
6.27.01.10 04Chapter 3 - Turing Machines
Topics: - Universal Turing Machine
- decidability and the halting problem
- Church's thesis		61-73
7.02.02.10 05Chapter 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 05Chapter 4 - Syntax and Proof Systems
Topics: - natural deduction and deduction theorem
- Hilbert vs. natural deduction
- consistency		 81-84
9.09.02.10 06Chapter 4 - Syntax and Proof Systems
Topics: - compactness theorem
- equivalence of formulae
- Gentzen's system 		84-89
10.02.10 06no lecture - Compulsory Exercises I
16.02.10 07no lecture - Compulsory Exercises I 84-89
17.02.10 07no lecture - Compulsory Exercises I
10.23.02.10 08Chapter 5 - Semantics of SL
Topics: - structures and valuations
- semantic properties of formulae		91-96
11.24.02.10 08Chapter 5 - Semantics of SL
Topics: - laws of semantics
- SL and set-valuations 		96-102
12.02.03.10 09Chapter 6 - Soundness and Completeness
Topics: - adequate sets of connectives
- disjunctive and conjunctive normal form 		104-106
13.03.03.10 09Chapter 6 - Soundness and Completeness
Topics: - soundness
- maximal consistent theories
- completeness
- applications		 107-113
15.09.03.10 10Chapter 6 - Soundness and Completeness
Topics: -
-
10.03.10 10no lecture - Compulsory Exercises II
16.03.10 11no lecture - Compulsory Exercises II
17.03.10 11no lecture - Compulsory Exercises II
23.03.10 12no lecture - Compulsory Exercises II
24.03.10 12no lecture - Compulsory Exercises II
30.03.10 13no lecture - Easter holidays
31.03.10 13no lecture - Easter holidays
16.06.04.10 14Chapter 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 14Chapter 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 15Chapter 8 - Semantics of FOL
Topics: - FOL structures
- interpretation of terms and formulae
19.14.04.10 15Chapter 8 - Semantics of FOL
Topics: -
-
20.04.10 16no lecture - Compulsory Exercises III
21.04.10 16no lecture - Compulsory Exercises III
20.27.04.10 17Chapter 9 - More Semantics
Topics: - Prenex Normal Form
- classifications
21.28.04.10 17Chapter 9 - More Semantics
Topics: - "syntactic" semantics
22.04.05.10 18Chapter 10 - Soundness, Completeness
Topics: - soundness
- maximal consistent, Henkin-, and complete Henkin-theories
23.05.05.10 18Chapter 10 - Soundness, Completeness
Topics: - proof of completeness
-
19no lecture - preparation exam
20no lecture - preparation exam
25.05.10 21 Exam