Course details

# Logic

LOG Acad. year 2019/2020 Summer semester 5 credits

Guarantor

Language of instruction

Completion

Time span

Assessment points

Department

Lecturer

Instructor

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)

Syllabus of numerical exercises

- Relational systems and universal algebras
- Sets, cardinal numbers and cardinal arithmetic
- Sentences, propositional connectives, truth tables,tautologies and contradictions
- Independence of propositional connectives, axioms of propositional logic
- Deduction theorem and proving formulas of propositional logic
- Terms and formulas of predicate logics
- Interpretation, satisfiability and truth
- Axioms and rules of inference of predicate logic
- Deduction theorem and proving formulas of predicate logic
- Transforming formulas into prenex normal forms
- First-order theories and some of their models
- Monadic logics SkS and WSkS
- Intuitionistic, modal and temporal logics, Presburger arithmetics

Progress assessment

Exam prerequisites

Course inclusion in study plans

- Programme IT-MSC-2, field MBI, MBS, MGM, MIN, MIS, MMI, MPV, any year of study, Elective
- Programme IT-MSC-2, field MMM, any year of study, Compulsory
- Programme IT-MSC-2, field MSK, 1st year of study, Compulsory-Elective group M
- Programme MITAI, specialisation NADE, NBIO, NCPS, NEMB, NGRI, NHPC, NIDE, NISD, NISY, NMAL, NMAT, NNET, NSEC, NSEN, NSPE, NVER, NVIZ, any year of study, Elective