x !
Arkistoitu opetusohjelma 2016–2017
Selaat vanhentunutta opetusohjelmaa. Voimassa olevan opetusohjelman löydät täältä.
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
Matematiikan ja tilastotieteen tutkinto-ohjelma
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.