Teaching Schedule
2016–2017

Archived teaching schedules 2016–2017

You are browsing archived teaching schedule. Current teaching schedules can be found here.

MTTS1
IF-Logic
5
ECTS

Periods

Language of instruction

English

Type or level of studies

Advanced studies

Course unit descriptions in the curriculum

- MTTS1 Other course (advanced)

Degree Programme in Mathematics and Statistics

School of Information Sciences

School of Information Sciences

After the course the student is familiar with the basic semantical and proof-theoretical aspects of IF logic; the student knows how to interpret and manipulate IF formulas, and is able to follow metamathematical arguments about IF logic.

**Prerequisities**

Familiarity with first-order logic.

**Topics for lectures**

1st LESSON

Henkin quantifiers:

-informal presentation of Skolem semantics -a sentence expressing infinity Syntax of IF logic, free and bound variables. Game-theoretical semantics.

2nd LESSON

Hodges' signalling sentence. The correct notion of Skolemization.

Expressive power of sentences:

-the Walkoe-Ehrenfeucht theorem. Panoramic of model-theoretic properties.

3rd LESSON

The debate on compositionality. Team semantics. 1-coherence of first-order logic. The Cameron-Hodges theorem.

Expressive power of open formulas (Kontinen-Vaananen).

4th LESSON

Downward monotonicity, non-contradiction. Substitution Truth equivalence:

-dummy variables in teams (cartesian extension) and in slash sets -locality of sentences

5th LESSON Equivalence in context (1):

-substitution of equivalents

-propositional laws

-shrinking of slash sets

-distribution of quantifiers

6th LESSON

Equivalence in context (2):

-vacuous quantifiers and requantification -quantifier swapping -quantifier extraction -renaming

7th LESSON Equivalence in context (3):

-prenex normal form

-strong regularization

An application: the perfect recall fragment

Enrolment time has expired

Fausto Barbero, Teacher responsible

Lauri Hella, Teacher responsible

Lauri.Hella[ät]uta.fi

5-Sep-2016
–
20-Oct-2016

Lectures

Mon 5-Sep-2016 - 17-Oct-2016 weekly at 14-16, Pinni A3107

Exercises

Independent work

Thu 15-Sep-2016 - 27-Oct-2016 weekly at 12-14, Pinni B1083

Exceptions:

Exceptions:

27-Oct-2016
, Pinni B0016

Pass/fail.

Active participation in classroom work and written exercises.

Lectures

Mann, Sandu, Sevenster "Independence-Friendly logic: a game-theoretical approach"

Kontinen-Väänänen paper "On definability in Dependence logic"

Course can be a part of advanced studies in mathematics.