Course details
Mathematical Logic
Guarantor
Šlapal Josef, prof. RNDr., CSc. (IM DAAG)
Language of instruction
Czech, English
Completion
Examination
Time span
- 26 hrs lectures
Department
Study literature
- E. Mendelson, Introduction to Mathematical Logic, Chapman&Hall, 2001
- A. Nerode, R.A. Shore, Logic for Applications, Springer-Verlag 1993
- D.M. Gabbay, C.J. Hogger, J.A. Robinson, Handbook of Logic for Artificial Intellogence and Logic Programming, Oxford Univ. Press 1993
- G. Metakides, A. Nerode, Principles of logic and logic programming, Elsevier, 1996
- Melvin Fitting, First order logic and automated theorem proving, Springer, 1996
- Sally Popkorn, First steps in modal logic, Cambridge Univ. Press, 1994
- A. Sochor, Klasická matematická logika, Karolinum, 2001
- V. Švejnar, Logika, neúplnost a složitost, Academia, 2002
Fundamental literature
- E. Mendelson, Introduction to Mathematical Logic, Chapman&Hall, 2001
- A. Nerode, R.A. Shore, Logic for Applications, Springer-Verlag 1993
- D.M. Gabbay, C.J. Hogger, J.A. Robinson, Handbook of Logic for Artificial Intelligence and Logic Programming, Oxford Univ. Press 1993
- G. Metakides, A. Nerode, Principles of logic and logic programming, Elsevier, 1996
- Melvin Fitting, First order logic and automated theorem proving, Springer, 1996
- Sally Popkorn, First steps in modal logic, Cambridge Univ. Press, 1994
Syllabus of lectures
- Basics of set theory and cardinal arithmetics
- Language, formulas and semantics of propositional calculus
- Formal theory of the propositional logic
- Provability in propositional logic, completeness theorem
- Language of the (first-order) predicate logic, terms and formulas
- Semantic of predicate logics
- Axiomatic theory of the first-order predicate logic
- Provability in predicate logic
- Theorems on compactness and completeness, prenex normal forms
- First-order theories and their models
- Undecidabilitry of first-order theories, Gödel's incompleteness theorems
- Second-order theories (monadic logic, SkS and WSkS)
- Some further logics (intuitionistic logic, modal and temporal logics, Presburger arithmetic)
Course inclusion in study plans