Course details

# Logic

LOG Acad. year 2010/2011 Summer semester 5 credits

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Lecturer

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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

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