Course details

Logic

QM4 Acad. year 2007/2008 Summer semester

Current academic year

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.

Guarantor

Havel Václav, prof. RNDr., DrSc.

Language of instruction

Czech

Completion

Examination

Time span

  • 39 hrs lectures

Department

Department of Mathematics (UMAT)

Subject specific 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.

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.

Prerequisite knowledge and skills

There are no prerequisites

Study literature

  • Originální úvod do predikátové logiky od Petra Vopěnky, vydaný v r. 1977 ve Státním nakladatelství pedagogické literatury pod názvem "Množiny a přirozená čísla" s úmyslným vynecháním autora.
  • Jeršov-Paljutin, Matěmatičeskaja logika, Nauka, Moskva, 1987.
  • Lavrov/Maksimova, Zadači po těoriji množestv v matěmatičeskoj logike i těorii algoritmov, Nauka, Moskva, 1984.
  • Pottmann-Wallner, Computational Line Geometry, Berlin-Heidelberg-New York, 2001.
  • Leitsch, The Resolution Calculus, Berlin-Heidelberg-New York 1997, inv.č. 5330.

Fundamental literature

  • Petr Štěpánek, Matematická logika, SPN, Praha, 1982.
  • Jiří Brabec, Matematická logika, ČVUT, Praha, 1975.
  • Delahaye, Outils logiques pour l'Intelligence artificielle, Eyrolles, Paris, 1988.
  • Šalát-Smítal, Teória množin, Alfa, Bratislava, 1986.
  • Bukovský, Množiny a všeličo kolem nich, Alfa, Bratislava, 1985.
  • J.van Leeuwen, Handbook of theoretical computer science, Elsevier, Amsterdam, 1990.
  • Engeler, Metamathematik der Elementarmathematik, Springer, Berlin, 1983.
  • A.Sochor:Klasická matematické logika,Karolinum, Praha, 2001
  • R.M.Smullyan:Gödel´s Incompleteness Theorems,Oxford University Press,New York-Oxford,1992
  • J.L.Bell: Notes on Formal Logic; viz  http://publish.uwo.ca/~jbell/LNOTES.pdf
  • S. Biliniuk,A Problem Course in Mathematical Logic,Trent University Ontario, 2006;viz http://euclid.trentu.ca/math/sb/pcml/
  • Greg Restall:Relevant and Substructural Logics, pp.289-398 in Handbook of the History of Logic,vol.7 (ed. D.Gabbay and J.Woods).Elsevier, 2006
  • J.Peregrin:Logika a logiky,Academia, Praha, 2004
    R.Bělohlávek,Matematická logika-poznámky k přednáškám,Universita Palackého Olomouc, 2004
  • P.Jirků-J.Vejnarová:Logika,VŠE+FF UK Praha,2004

Syllabus of lectures

  • Finite and countable sets, a mild axiomatic approach (Fraenkel-Zermelo).
  • 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.

Progress assessment

Study evaluation is based on marks obtained for specified items. Minimimum number of marks to pass is 50.

Controlled instruction

There are no checked study.

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