Advertisement

Brief Reminder of Constructive Type Theory

  • Nicolas ClerboutEmail author
  • Shahid Rahman
Chapter
  • 436 Downloads
Part of the SpringerBriefs in Philosophy book series (BRIEFSPHILOSOPH)

Abstract

Within Per Martin-Löf’s Constructive Type Theory (CTT for short) the logical constants are interpreted through the Curry-Howard correspondence between propositions and sets. A proposition is interpreted as a set whose elements represent the proofs of the proposition. It is also possible to view a set as a problem description in a way similar to Kolmogorov’s explanation of the intuitionistic propositional calculus.

Keywords

Constructive Type Theory Intuitionistic Predicate Logic Curry-Howard Correspondence Hypothetical Judgment Elimination Rules 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Granström, J. 2011. Treatise on Intuitionistic Type Theory. Dordrecht: Springer.Google Scholar
  2. Martin-Löf, P. 1984. Intuitionistic Type Theory. Naples: Bibliopolis. Notes by Giovanni Sambin of a series of lectures given in Padua, June 1980.Google Scholar
  3. Nordström, B., K. Petersson, and J.M. Smith. 1990. Programming in Martin-Löf’s Type Theory: An Introduction. Oxford: Oxford University Press.Google Scholar
  4. Ranta, A. 1991. Constructing possible worlds. Theoria 57(1–2): 77–99.Google Scholar
  5. Ranta, A. 1994. Type-Theoretical Grammar. Oxford: Clarendon Press.Google Scholar
  6. Sundholm, G. 1997. Implicit epistemic aspects of constructive logic. Journal of Logic, Language and Information 6(2): 191–212.CrossRefGoogle Scholar
  7. Sundholm, G. 2001. A plea for logical atavism. In The Logica Yearbook 2000, ed. O. Majer, 151–162. Prague: Filosofia.Google Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.Instituto de Filosofía; CDHACSUniversidad de ValparaísoValparaísoChile
  2. 2.UMR-CNRS 8163: STLUniversity of Lille IIIVilleneuve d’AscqFrance

Personalised recommendations