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Terminated in academic year 2022/2023

Advanced Logic

Type of study Follow-up Master
Language of instruction Czech
Code 460-4034/02
Abbreviation VPL
Course title Advanced Logic
Credits 4
Coordinating department Department of Computer Science
Course coordinator prof. RNDr. Marie Duží, CSc.

Subject syllabus

Lectures:
1) Proof calculi, consistence and completeness.
2) Hilbert-style proof calculus.
3) Logical theories; completeness and incompleteness of a theory, decidability.
4) Theory of relations; equivalence and orderings.
5) Algebraic theories; groups, rings and fields.
6) Lattice theory, conceptual lattices.
7) Theories of arithmetic, Gödel results; incompleteness theorems.
8) Theory of recursive functions and algorithms.
9) Sequent calculi
10) Intensional logics and Kripke semantics.

Seminars:
1) Proof calculi, consistence and completeness.
2) Hilbert-style proof calculus.
3) Logical theories; completeness and incompleteness of a theory, decidability.
4) Theory of relations; equivalence and orderings.
5) Algebraic theories; groups, rings and fields.
6) Lattice theory, conceptual lattices.
7) Theories of arithmetic, Gödel results; incompleteness theorems.
8) Theory of recursive functions and algorithms.
9) Sequent calculi
10) Intensional logics and Kripke semantics.

Literature

E. Mendelson. Introduction to Mathematical Logic. Chapman & Hall/CRC, 2001.
P. Hájek: Metamathematics of Fuzzy Logic. Kluwer, 1998.

Advised literature

P. Hájek: Metamathematics of Fuzzy Logic. Kluwer, 1998.