Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
An Algorithm Defining the Choice of ‘Active~Passive’ Formal Paradigms in Georgian Read chapter Read first chapter

2017 | OriginalPaper | Chapter

Subintuitionistic Logics with Kripke Semantics

Authors : Dick de Jongh, Fatemeh Shirmohammadzadeh Maleki

Published in: Logic, Language, and Computation

Publisher: Springer Berlin Heidelberg

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

The subintuitionistic logics introduced by Corsi and Restall are developed in a uniform manner. In this way Restall’s contributions are clarified. Hilbert type proof systems are given for derivations without and with assumptions. The results are applied to give conservation theorems for intuitionistic logic IPC over Corsi’s system F. For Visser’s basic logic additional conservation results are obtained.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Quasi-Realization
Footnotes
1
Neither is it the case that the class of NNIL-formulas is locally finite in BPC as it is in IPC, the fact that \(\nvdash _\mathsf{BPC} (p\rightarrow (p\rightarrow q))\leftrightarrow (p\rightarrow q)\) quickly leads to infinitely many non-equivalent NNIL-formulas in two variables.
 
Literature
1.
Aghaei, M., Ardeshir, M.: A bounded translation of intuitionistic propositional logic into basic propositional logic. Math. Logic Q. 46(2), 195–206 (2000)MathSciNetCrossRefMATH
2.
3.
4.
Došen, K.: Modal translations in K and D. In: de Rijke, M. (ed.) Diamonds and Defaults. Synthese Library, vol. 229, pp. 103–127. Springer, Dordrecht (1994)
5.
Kleene, S.C.: Disjunction and Existence under Implication in elementary Intuitionistic formalisms. J. Symbolic Logic 27, 11–18 (1962)MathSciNetCrossRefMATH
6.
7.
Sano, K., Ma, M.: Alternative semantics for visser’s propositional logics. In: Aher, M., Hole, D., Jeřábek, E., Kupke, C. (eds.) TbiLLC 2013. LNCS, vol. 8984, pp. 257–275. Springer, Heidelberg (2015). doi:10.​1007/​978-3-662-46906-4_​15
8.
9.
Suzuki, Y., Ono, H.: Hilbert-style proof system for BPL. Technical report, IS-RR-97-0040F. Japan Advanced Institute of Science and Technology (1997)
10.
11.
Visser, A., van Benthem, J., de Jongh, D., Renardel de Lavalette, G.: NNIL, a study in intuitionistic propositional Logic. In: Ponse, A., de Rijke, M., Venema, Y. (eds.) Modal Logics and Process Algebra, a Bisimulation Perspective, pp. 289–326 (1995)
Metadata
Title
Subintuitionistic Logics with Kripke Semantics
Authors
Dick de Jongh
Fatemeh Shirmohammadzadeh Maleki
Copyright Year
2017
Publisher
Springer Berlin Heidelberg
Book
Logic, Language, and Computation

Print ISBN: 978-3-662-54331-3

Electronic ISBN: 978-3-662-54332-0

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-662-54332-0_18

Premium Partner

    Image Credits