Skip to main content

Part of the book series: Synthese Library ((SYLI,volume 122))

Abstract

There are two types of systems of natural deduction: the first is based on an indirect rule for the elimination of the existential quantifier; and the second is based on a direct rule for the elimination of the existential quantifier.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  • L. Borkowski and J. Slupecki, ‘A logical system based on rules’, Studia Logica 7 (1958).

    Google Scholar 

  • A. Γ. Дparaлин, ‘Интyициoнистская логика и ℰ-символ Гильбета,’Исторпя и методология естественных наук, вьіп. XУI, Математика, меҳаника. МГУ, 1974.

    Google Scholar 

  • A. C. Leisenring, Mathematical logic and Hilbert’s ℰ-symbol, London, 1969.

    Google Scholar 

  • Г. E .МиIIп,, Гейтнговское исчисление предикатов с зпсилонсимволом,, Записки ІІаучпыҳ семипаров ЛОМИ, т.40. Исследования по конструктивной математике и математической логике ,УІ.Лепипград,1974.

    Google Scholar 

  • B. H. Opeвков,,Злимипация функциопалъныҳ знаков без условия единственностии конструктивые исчисления предикатов c 2130-символом’, Теория логического вывода ( тезисы докладов Всесоюзного симпозиума, Москва, март) 25–27, 1974), ч.I, M., 1974.

    Google Scholar 

  • E. Слупецкий Л. Борковский, Элементы математической логики и теория мношсеств, M., 1965 (перевод с польского, 1963).

    Google Scholar 

  • V. A. Smirnov, ‘Elimination des termes ℰ dans la logique intuitioniste’, Revue International de Philosophie 98, 1971.

    Google Scholar 

  • B. A. Смирпов Формальный вывод и логические исчиления , M., 1972.

    Google Scholar 

  • D. Leivant, ‘Existential instantiation in a system of natural deduction for intuitionistic arithmetic’, Stichting Mathematisch Centrum, Amsterdam, 1973.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1979 D. Reidel Publishing Company, Dordrecht, Holland

About this chapter

Cite this chapter

Smirnov, V.A. (1979). Theory of Quantification and ‰-Calculi. In: Hintikka, J., Niiniluoto, I., Saarinen, E. (eds) Essays on Mathematical and Philosophical Logic. Synthese Library, vol 122. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9825-4_3

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-9825-4_3

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-009-9827-8

  • Online ISBN: 978-94-009-9825-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics