SubjectsSubjects(version: 825)
Course, academic year 2017/2018
   Login via CAS
Classical Logic Seminar - ALG110005
Czech title: Cvičení z logiky
Guaranteed by: Department of Logic (21-KLOG)
Faculty: Faculty of Arts
Actual: from 2017
Semester: winter
Points: 0
E-Credits: 6
Examination process: winter s.:
summer s.:
Hours per week, examination: winter s.:0/2 C [hours/week]
summer s.:0/2 C [hours/week]
Capacity: winter:unknown / unknown (unknown)
summer:unknown / unknown (unknown)
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Level:  
Is provided by: ALG110027
Note: it is possible to enroll in the course outside of study plan
enabled for web enrollment
Guarantor: Mgr. Marta Bílková, Ph.D.
Mgr. Tomáš Lávička
Annotation -
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 -
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.

 
Charles University | Information system of Charles University | http://www.cuni.cz/UKEN-329.html