UIINFNP015 Vybrané partie z logiky

Faculty of Philosophy and Science in Opava
Summer 2025
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Radka Poláková, Ph.D. (lecturer)
RNDr. Radka Poláková, Ph.D. (seminar tutor)
Guaranteed by
RNDr. Radka Poláková, Ph.D.
Institute of Computer Science – Faculty of Philosophy and Science in Opava
Prerequisites
The course assumes basic knowledge of mathematical logic.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
In this course, students will be acquainted in detail with the classical first-order logics with regard to other scientific disciplines. Students will be acquainted with axiomatic theories (relational, algebraic) and further with models of theories of formal languages and automata. At the end of the course, students will get acquainted with higher-order logics, namely Transparent Intentional Logic, which will point out the fact of high expressive power and advantages of use as a specification language in information systems as opposed to systems based on first-order logics.
Syllabus
  • 1. Natural deduction system PL1.
  • 2. Formal Hilbert-type system.
  • 3. Certainty, correctness, completeness, partial decidability of calculus PL1.
  • 4. Formalized theories - Introduction, Hilbert's program.
  • 5. Relation theory.
  • 6. Algebraic theories.
  • 7. Gödel's theorems on the completeness of the calculus PL1.
  • 8. Robinson and Pean formal arithmetic, Gödel's theorems on incompleteness of formal arithmetic.
  • 9. Transparent intensional logic - Introduction 10. TIL formalism and its advantages.
  • 11. Comparison of the particular formal systems.
Teaching methods
Lecture, seminars
Assessment methods
Lecture, seminars
Language of instruction
Czech
The course is also listed under the following terms Summer 2022, Summer 2023, Summer 2024.
  • Enrolment Statistics (Summer 2025, recent)
  • Permalink: https://is.slu.cz/course/fpf/summer2025/UIINFNP015