460-4088/02 – Mathematical Logic (ML)
Gurantor department | Department of Computer Science | Credits | 4 |
Subject guarantor | prof. RNDr. Marie Duží, CSc. | Subject version guarantor | prof. RNDr. Marie Duží, CSc. |
Study level | undergraduate or graduate | | |
| | Study language | English |
Year of introduction | 2015/2016 | Year of cancellation | |
Intended for the faculties | FEI | Intended for study types | Follow-up Master |
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:
[1] E. Mendelson. Introduction to Mathematical Logic, (4th edition). Chapman & Hall/CRC 1997.
Recommended literature:
[1] Brown, J.R.: Philosophy of Mathematics. Routledge, 1999.
[2] Thayse, A.: From Standard Logic to Logic Programming, John Wiley & Sons, 1988
[3] Nerode, Anil - Shore, Richard A. Logic for applications. New York : Springer-Verlag, 1993. Texts and Monographs in Computer Science.
[4] Richards, T.: Clausal Form Logic. An Introduction to the Logic of Computer Reasoning. Adison-Wesley, 1989.
Additional study materials
Way of continuous check of knowledge in the course of semester
During the semester, the students must pass the credit test, and at the end of the semester, the exam. The exam consists of a written test and an oral exam.
E-learning
Other requirements
There are no additional requirements imposed on the students.
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
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.