460-4088/02 – Mathematical Logic (ML)

Gurantor departmentDepartment of Computer ScienceCredits4
Subject guarantorprof. RNDr. Marie Duží, CSc.Subject version guarantorprof. RNDr. Marie Duží, CSc.
Study levelundergraduate or graduateRequirementChoice-compulsory
Year1Semesterwinter
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 subject is to provide basic principles of logical proof calculi and axiomatic theories, and their application in the area of algebras and theory of lattices. A student should be able to exactly formulate and solve particular problems of computer science and applied mathematics.

Teaching methods

Lectures
Seminars
Individual consultations
Tutorials

Summary

The course deals with fundamentals of mathematical logic and formal proof calculi. The following main topics are covered: propositional logic, 1st-order predicate logic, 1st-order proof calculi of Gentzen and Hilbert style and general resolution method. These methods are used in many areas of informatics in order to achieve a rigorous formalisation of intuitive theories (automatic theorem proving and deduction, artificial intelligence, and many others).

Compulsory literature:

E. Mendelson. Introduction to Mathematical Logic, (4th edition). Chapman & Hall/CRC 1997.

Recommended literature:

Brown, J.R.: Philosophy of Mathematics. Routledge, 1999. Thayse, A.: From Standard Logic to Logic Programming, John Wiley & Sons, 1988 Nerode, Anil - Shore, Richard A. Logic for applications. New York : Springer-Verlag, 1993. Texts and Monographs in Computer Science. Richards, T.: Clausal Form Logic. An Introduction to the Logic of Computer Reasoning. Adison-Wesley, 1989.

Way of continuous check of knowledge in the course of semester

E-learning

Další požadavky na studenta

Additional requirements are placed on the student.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Lectures: 1. Introduction: deductively valid arguments 2. Propositional logic: language (syntax and semantics) 3. Fuzzy logic 4. Proof methods in the propositional logic, resolution method 5. Naive set-theory; relation, function, countable/uncountable sets 6. First-order predicate logic (FOL): language (syntax and semantics) 7. Semantics of FOL language (interpretation and models) 8. Semantic tableaus in FOL 9. Aristotle logic. Venn's diagrams 10. General resolution method in FOL 11. Foundations of logic programming 12. Proof calculi, Natural deduction and sequent calculus Seminars: Deductively valid arguments Propositional logic, language and semantics Resolution method in propositional logic Naive theory of sets First-order predicate logic, language and semantics Relation, function, countable and uncountable sets Semantic tableau Aristotelle logic Resolution method in FOL Logic programming Proof calculi: natural deduction Sequent calculus

Conditions for subject completion

Combined form (validity from: 2016/2017 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 40 (40) 15
                Credit test Written test 30  10
                Online tests Written test 10  0
        Examination Examination 60 (60) 21
                Test Written examination 40  21
                Oral exam Oral examination 20  0
Mandatory attendence parzicipation:

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 1 Choice-compulsory study plan
2019/2020 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K English Ostrava 1 Choice-compulsory study plan
2018/2019 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P English Ostrava 1 Choice-compulsory study plan
2018/2019 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K English Ostrava 1 Choice-compulsory study plan
2017/2018 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P English Ostrava 1 Choice-compulsory study plan
2017/2018 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K English Ostrava 1 Choice-compulsory study plan
2016/2017 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P English Ostrava 1 Choice-compulsory study plan
2016/2017 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K English Ostrava 1 Choice-compulsory study plan
2015/2016 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P English Ostrava 1 Choice-compulsory study plan
2015/2016 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K English Ostrava 1 Choice-compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner
V - ECTS - mgr. 2019/2020 Full-time English Optional 401 - Study Office stu. block
V - ECTS - mgr. 2018/2019 Full-time English Optional 401 - Study Office stu. block
V - ECTS - mgr. 2017/2018 Full-time English Optional 401 - Study Office stu. block
V - ECTS - mgr. 2016/2017 Full-time English Optional 401 - Study Office stu. block
V - ECTS - mgr. 2015/2016 Full-time English Optional 401 - Study Office stu. block