Course detail
Mathematical Logic
FIT-MLDAcad. year: 2010/2011
Not applicable.
Language of instruction
Czech, English
Mode of study
Not applicable.
Guarantor
Learning outcomes of the course unit
Not applicable.
Prerequisites
Not applicable.
Co-requisites
Not applicable.
Planned learning activities and teaching methods
Not applicable.
Assesment methods and criteria linked to learning outcomes
Not applicable.
Course curriculum
Not applicable.
Work placements
Not applicable.
Aims
Not applicable.
Specification of controlled education, way of implementation and compensation for absences
Not applicable.
Recommended optional programme components
Not applicable.
Prerequisites and corequisites
Not applicable.
Basic 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
Recommended reading
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
Classification of course in study plans
Type of course unit
Lecture
26 hod., optionally
Teacher / Lecturer
Syllabus
- 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)