Subjects(version: 837)
Classical Logic Seminar - ALG110005
Title in English: Cvičení z logiky Department of Logic (21-KLOG) Faculty of Arts from 2017 winter 0 6 winter s.: summer s.: winter s.:0/2 C [hours/week] summer s.:0/2 C [hours/week] winter:unknown / unknown (unknown) summer:unknown / unknown (unknown) unlimited taught Czech full-time ALG110027 course can be enrolled in outside the study planenabled for web enrollment
Guarantor: Mgr. Marta Bílková, Ph.D.Mgr. Tomáš Lávička, Ph.D.
 Annotation - ---CzechEnglish
Last update: Mgr. Vít Bělič, CSc. (11.05.2009)
Introductory part of study of logic, essentially containing elements of mathematical logic (completeness, cardinality, compactness, categoricity etc.), but moreover paying special attention to philosophical, linguistic and methodological aspects of logic.
 Syllabus - ---CzechEnglish
Last update: LOGVACHK (01.09.2011)

1. Logical paradoxes, examples of mathematical theories, diferenece between language and metalanguage, Boolean algebra, types of proofs, Polish prefix notation

2. Propositional logic

Syntax - propositional variables, logical connectives, formuli and its properties

Semantics - tables of values, consequences, sets of assumptions, disjunction and conjunction normal form, tautologies and contradictions

Calculi - Hilbert calculi, Gentzen calculi, natural deduction calculi

Use of deduction theorem, sound theorem, completness and compactness theorem

Properties of inconsistent sets and maximal consistent sets

1. Predicate logic (winter semester)

Syntax - terms, formuli, free and bound variables, substitution

Semantics - normal forms, consequences, prenexace

Rules for quantifiers

Calculi - Hilbert calculi, Gentzen calculi, natural deduction calculi

Use of deduction theorem, sound theorem, completness and compactness theorem

Literature

Švejdar, Logika: neúplnost, složitost a nutnost, Academia, Praha, 2002.

van Dalen, Logic and Structure, Springer, 1994.

Expanding literature

Sochor, Klasická matematická logika, Karolinum, Praha 2001.

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