Mathematical Logic

Guarantor

Šlapal Josef, prof. RNDr., CSc. (IM DAAG)

Language of instruction

Czech, English

Completion

Examination

Time span

Department

Dept. of Algebra and Discrete Mathematics (ÚM OAAG)

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