460-4034/03 – Advanced Logic (VPL)

Gurantor departmentDepartment of Computer ScienceCredits4
Subject guarantorprof. RNDr. Marie Duží, CSc.Subject version guarantorprof. RNDr. Marie Duží, CSc.
Study levelundergraduate or graduateRequirementOptional
Year2Semestersummer
Study languageEnglish
Year of introduction2015/2016Year of cancellation
Intended for the facultiesFEIIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
DUZ48 prof. RNDr. Marie Duží, CSc.
MEN059 Mgr. Marek Menšík, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Combined Credit and Examination 10+0

Subject aims expressed by acquired skills and competences

The goal of the course is providing knowledge on particular methods of reasoning and automatic theorem proving. We focus on the development of these methods in the area of relational and algebraic theories and philosophy of mathematics. The course also aims at using the proof methods in theoretical computer science.

Teaching methods

Lectures
Seminars
Individual consultations
Tutorials

Summary

The goal of the course is providing knowledge on particular methods of reasoning and automatic theorem proving. We focus on the development of these methods in the area of relational and algebraic theories and philosophy of mathematics. The course also aims at using the proof methods in theoretical computer science.

Compulsory literature:

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

Recommended literature:

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

Way of continuous check of knowledge in the course of semester

E-learning

Další požadavky na studenta

There are not defined other requirements for student.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

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.

Conditions for subject completion

Combined form (validity from: 2015/2016 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit  
        Examination Examination 100  51
Mandatory attendence parzicipation: obligatory participation at all exercises, 3 absences with excused leave are acceptable

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2019/2020 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P English Ostrava 2 Optional study plan
2019/2020 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K English Ostrava 2 Optional study plan
2018/2019 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P English Ostrava 2 Optional study plan
2018/2019 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K English Ostrava 2 Optional study plan
2017/2018 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P English Ostrava 2 Optional study plan
2017/2018 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K English Ostrava 2 Optional study plan
2016/2017 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P English Ostrava 2 Optional study plan
2016/2017 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K English Ostrava 2 Optional study plan
2015/2016 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P English Ostrava 2 Optional study plan
2015/2016 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K English Ostrava 2 Optional study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner