Course detail

Mathematical Logic

FIT-MLDAcad. year: 2010/2011

Not applicable.

Language of instruction

Czech

Number of ECTS credits

0

Mode of study

Not applicable.

Guarantor

prof. RNDr. Josef Šlapal, CSc.

Department

Dept. of Algebra and Discrete Mathematics (ÚM OAAG)

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

  • Programme VTI-DR-4 Doctoral

    branch DVI4 , any year of study, summer semester, elective

  • Programme VTI-DR-4 Doctoral

    branch DVI4 , any year of study, summer semester, elective

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

prof. RNDr. Josef Šlapal, CSc.

Syllabus

  1. Basics of set theory and cardinal arithmetics
  2. Language, formulas and semantics of propositional calculus
  3. Formal theory of the propositional logic
  4. Provability in propositional logic, completeness theorem
  5. Language of the (first-order) predicate logic, terms and formulas
  6. Semantic of predicate logics
  7. Axiomatic theory of the first-order predicate logic
  8. Provability in predicate logic
  9. Theorems on compactness and completeness, prenex normal forms
  10. First-order theories and their models
  11. Undecidabilitry of first-order theories, Gödel's incompleteness theorems
  12. Second-order theories (monadic logic, SkS and WSkS)
  13. Some further logics (intuitionistic logic, modal and temporal logics, Presburger arithmetic)