https://www.cs.vsb.cz/duzi/MatLog-English.html
https://www.cs.vsb.cz/duzi/TIL_English.html
Mathematical logic
| Type of study | Follow-up Master |
|---|---|
| Language of instruction | English |
| Code | 460-4171/01 |
| Abbreviation | MLO |
| Course title | Mathematical logic |
| Credits | 4 |
| Coordinating department | Department of Computer Science |
| Course coordinator | prof. RNDr. Marie Duží, CSc. |
Subject syllabus
Lectures.
Theory of sets, relations and functions, countable vs uncountable sets.
First-order predicate logic (FOL); syntax and semantics
Semantics of the FOL language; interpretation and models
General resolution method in FOL..
Foundations of logic programming.
Proof calculi: natural deduction and sequent calculus.
Semantic schema of TIL; procedures as meanings
Definitions: ramified theory of types, constructions, procedures, quantifiers.
Method of analysis; Parmenides principle
Empirical vs analytical expressions; partiality, compositionality, requisites and pre-requisites
Inference rules for syntactic computing; alpha-, beta- and gamma-reduction
Three kinds of context, the substitution method, and TIL applications
Natural deduction in TIL
Seminars.
Deductively valid arguments.
Theory of sets, relations and functions.
First-order predicate logic; language, semantics and models
General resolution method in FOL.
Logic programming
Proof calculi: natural deduction and sequent calculus.
Semantic schema of TIL; procedures as meanings
Ramified theory of types, constructions, procedures, quantifiers.
Method of analysis; Parmenides principle
Empirical vs analytical expressions; partiality, compositionality, requisites and pre-requisites
Inference rules for syntactic computing; alpha-, beta- and gamma-reduction
Three kinds of contexts, substitution method, TIL applications
Theory of sets, relations and functions, countable vs uncountable sets.
First-order predicate logic (FOL); syntax and semantics
Semantics of the FOL language; interpretation and models
General resolution method in FOL..
Foundations of logic programming.
Proof calculi: natural deduction and sequent calculus.
Semantic schema of TIL; procedures as meanings
Definitions: ramified theory of types, constructions, procedures, quantifiers.
Method of analysis; Parmenides principle
Empirical vs analytical expressions; partiality, compositionality, requisites and pre-requisites
Inference rules for syntactic computing; alpha-, beta- and gamma-reduction
Three kinds of context, the substitution method, and TIL applications
Natural deduction in TIL
Seminars.
Deductively valid arguments.
Theory of sets, relations and functions.
First-order predicate logic; language, semantics and models
General resolution method in FOL.
Logic programming
Proof calculi: natural deduction and sequent calculus.
Semantic schema of TIL; procedures as meanings
Ramified theory of types, constructions, procedures, quantifiers.
Method of analysis; Parmenides principle
Empirical vs analytical expressions; partiality, compositionality, requisites and pre-requisites
Inference rules for syntactic computing; alpha-, beta- and gamma-reduction
Three kinds of contexts, substitution method, TIL applications
E-learning
Literature
Duží M., Jespersen B. and Materna P. (2010): Procedural Semantics for Hyperintensional Logic. Foundations and Applications of Transparent Intensional Logic. First edition. Berlin: Springer, series Logic, Epistemology, and the Unity of Science, vol. 17, ISBN 978-90-481-8811-6.
Gensler, H. J. (2010): Introduction to Logic (2nd ed.). Londýn, New York: Routlege
Manna, Z.: Mathematical Theory of Computation. McGraw-Hill, 1974.
Gensler, H. J. (2010): Introduction to Logic (2nd ed.). Londýn, New York: Routlege
Manna, Z.: Mathematical Theory of Computation. McGraw-Hill, 1974.
Advised literature
Manna, Z.: Mathematical Theory of Computation. (Reprint), Dover, 2003
Fitting, M.: First-order logic and automated theorem proving [1996]. 2nd ed. New York: Springer, 1996. Graduate texts in computer science.
Fitting, M.: First-order logic and automated theorem proving [1996]. 2nd ed. New York: Springer, 1996. Graduate texts in computer science.