Title:  Logic 

Code:  QM4 

Ac.Year:  ukončen 2003/2004 

Term:  Summer 

Language of Instruction:  Czech 

Completion:  examination (verbal) 

Type of instruction:  Hour/sem  Lectures  Seminar Exercises  Laboratory Exercises  Computer Exercises  Other 

Hours:  39  0  0  0  0 

 Exams  Tests  Exercises  Laboratories  Other 

Points:  0  0  0  0  0 



Guarantor:  Havel Václav, prof. RNDr., DrSc. (DMAT) 

Lecturer:  Havel Václav, prof. RNDr., DrSc. (DMAT) 
Faculty:  Faculty of Electrical Engineering and Communication BUT 

Department:  Department of Mathematics FEEC BUT 

 Learning objectives: 

  The aim of the object is above all a methodological one: to make deeper the undergradual knowledges of the predicate logic by detailed analysis of specific reasonings in separate chapters of the subject.  Description: 

  Finiteness,countability,cardinalities,continuum hypothesis and axiom of choice.Semantics and syntax of proposition logic. Theorems:on compactness,on finiteness,on completeness.Semantics and syntax of the predicate logic of first order. Prenex formulas.Theorems on correctness and oncompleteness.Theorems:of Herbrand,of Hilbert and Ackermann,of Skolem.Interpretation of one langage in another one. Comments to temporal logic,to combinatorial logic and to logical programming.  Learning outcomes and competences: 

  Deeper understanding of specific reasonings in mathematical logic. Active dominating of its ideas and procedures for purposes of applications in informatics.  Syllabus of lectures: 

  Finite and countable sets, a mild axiomatic approach (FraenkelZermelo).
 Comparing of cardinalities. Continuum hypothesis, axiom of choice.
 Semantics and syntax of proposition logic.
 Compactness theorem (with a turning into general topology), finiteness theorem, completeness theorem.
 Semantics and syntax of first order predicate logic.
 Classic questions on prenex formulas.
 Correctness theorem and completeness theorem. Several words about Kurt Gödel and Alfred Tarski.
 Theorem of Henkin, theorem of Lindenbaum, theorem on compactness.
 Theorem of Herbrand, theorem of Hilbert and Ackermann, theorem of Skolem.
 Interpretation of one language in another one.
 Comments to temporal and modal logic.
 Comments to combinatorial logic.
 Comments to logical programming.
 Syllabus  others, projects and individual work of students: 

  One prescribed seminar work.
 Fundamental literature: 

  Stepanek,Mathematical logic (in Czech),Prague 1982
 Brabec,Mathematical logic (in Czech),Prague 1975
 Delahay,Outils logiques pour l'Intelligence artificielle,Paris 1988
 SalatSmital,Set theory (in Slovak),Bratislava 1985
 Bukovsky,Sets and various things about them (in Slovak),Bratislava 1986
 van Leeuwen,Handbook of theoretical computer science,Amsterdam 1990
 Engeler,Metamathematik der Elementatmathematik,Berlin 1983
 Study literature: 

  An original introduction to predicate logic by Peter Vopenka,appearing in 1977 under title "Sets and natural numbers" (in Czech) in State pedagogic publishing house,Prague,with purposeful omitting of the name of the author.
 ErshovPaljutin,Mathematical logic,Nauka,Moscow (in Russian)
 LavrowMaksimova,Problems in set theory,mathematical logic and algorithm theory,Nauka,Moscow (in Russian)
 PottmannWallner,Computational Line Geometry,Berlin
 HeidelbergNew York 2001Leitsch,The Resolution Calculus,BerlinHeidelbergNew York 1997,inv.č.5330
 
