Course details

# Mathematical Logic

MLD Acad. year 2015/2016 Summer semester

Guarantor

Language of instruction

Completion

Time span

Assessment points

Department

Lecturer

Subject specific learning outcomes and competences

Generic learning outcomes and competences

Learning objectives

Prerequisite kwnowledge and skills

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