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Archived teaching schedules 2016–2017
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MTTS1 IF-Logic 5 ECTS
Periods
Period I Period II Period III Period IV
Language of instruction
English
Type or level of studies
Advanced studies
Course unit descriptions in the curriculum
Degree Programme in Mathematics and Statistics
School of Information Sciences

Learning outcomes

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.

General description

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 for University Studies

Enrolment time has expired

Teachers

Fausto Barbero, Teacher responsible
Lauri Hella, Teacher responsible
Lauri.Hella[ät]uta.fi

Teaching

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:
27-Oct-2016 , Pinni B0016

Evaluation

Pass/fail.

Evaluation criteria

Active participation in classroom work and written exercises.

Study materials

Lectures

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

Kontinen-Väänänen paper "On definability in Dependence logic"

Further information

Course can be a part of advanced studies in mathematics.