Advertisement

Two Kinds of Procedural Semantics for Privative Modification

  • Giuseppe Primiero
  • Bjørn Jespersen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6284)

Abstract

In this paper we present two kinds of procedural semantics for privative modification. We do this for three reasons. The first reason is to launch a tough test case to gauge the degree of substantial agreement between a constructivist and a realist interpretation of procedural semantics; the second is to extend Martin-Löf’s Constructive Type Theory to privative modification, which is characteristic of natural language; the third reason is to sketch a positive characterization of privation.

Keywords

Type Theory Elimination Rule Introduction Rule Propositional Function Empirical Property 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Duží, M., Jespersen, B., Materna, P.: Procedural Semantics for Hyperintensional Logic. Foundations and Applications of Transparent Intensional Logic. Logic, Epistemology and the Unity of Science, vol.17. Springer, Berlin (2010)Google Scholar
  2. 2.
    Jackendoff, R.: Semantic Structures. MIT Press, Cambridge (1990)Google Scholar
  3. 3.
    Jespersen, B.: Significant sententialism in Transparent Intensional Logic and Martin-Löf’s Type Theory. In: Childers, T., Majer, O. (eds.) The Logica Yearbook 2002, pp. 117–131 (2003)Google Scholar
  4. 4.
    Jespersen, B.: Explicit intensionalization, anti-actualism, and how Smith’s murderer might not have murdered Smith. Dialectica 59, 285–314 (2005)CrossRefGoogle Scholar
  5. 5.
    Jespersen, B.: Predication and extensionalization. Journal of Philosophical Logic 37, 479–499 (2008)CrossRefzbMATHGoogle Scholar
  6. 6.
    Jespersen, B.: Property modification and the rule of pseudo-detachment (in submission)Google Scholar
  7. 7.
    Jespersen, B., Carrara, M.: Two conceptions of technical malfunction (in submission)Google Scholar
  8. 8.
    Jespersen, B.: How hyper are hyperpropositions? Language and Linguistics Compass 4, 96–106 (2010)CrossRefGoogle Scholar
  9. 9.
    Jespersen, B., Duží, M., Materna, P.: The logos of semantic structure. In: Stalmaszczyk, P. (ed.) Philosophy of Language and Linguistics. The Formal Turn, vol. I, pp. 85–101. Ontos-Verlag, Farnkfurt (2010)Google Scholar
  10. 10.
    Martin-Löf, P.: Constructive mathematics and computer programming. In: Cohen, J.J., et al. (eds.) Sixth International Congress for Logic, Methodology and Philosophy of Science, pp. 153–175. North-Holland, Amsterdam (1982)CrossRefGoogle Scholar
  11. 11.
    Martin-Löf, P.: Intuitionistic Type Theory. Bibliopolis, Naples (1984)zbMATHGoogle Scholar
  12. 12.
    Martin-Löf, P.: Mathematics of infinity. In: Martin-Löf, P., Mints, G. (eds.) COLOG 1988. LNCS, vol. 417, pp. 146–197. Springer, Heidelberg (1990)CrossRefGoogle Scholar
  13. 13.
    Montague, R.: English as a formal language. In: Visentini, B., et al. (eds.) Linguaggi nella societá e nella tecnica, Milan, pp. 189–224 (1970); Reprinted in R.H. Thomasson (ed.). Formal Philosophy. Yale University Press, London (1974)Google Scholar
  14. 14.
    Nordström, B., Petersson, K., Smith, J.: Programming in Martin-Löf’s Type Theory. Oxford University Press, Oxford (1990)zbMATHGoogle Scholar
  15. 15.
    Nordström, B., Petersson, K., Smith, J.: Martin-Löf’s Type Theory. In: Abramsky, S., Gabbay, D., Maibaum, T.S.E. (eds.) Handbook of Logic in Computer Science, pp. 1–38. Oxford University Press, Oxford (2000)Google Scholar
  16. 16.
    Primiero, G.: The determination of reference in a constructive setting. Giornale di Metafisica 26, 483–502 (2004)Google Scholar
  17. 17.
    Primiero, G.: Information and Knowledge. A Constructive Type-Theoretical Approach. Logic Epistemology and the Unity of Science, vol. 10. Springer, Berlin (2008)zbMATHGoogle Scholar
  18. 18.
    Primiero, G.: Proceeding in abstraction. From concepts to types and the recent perspective on information. History and Philosophy of Logic 30, 257–282 (2009)CrossRefzbMATHGoogle Scholar
  19. 19.
    Primiero, G.: Epistemic modalities. In: Primiero, G., Rahman, S. (eds.) Acts of Knowledge: History, Philosophy and Logic, pp. 207–231. College Publications, London (2009)Google Scholar
  20. 20.
    Primiero, G.: Constructive contextual modal judgements for reasoning from open assumptions. In: Proceddings of the Computability in Europe Conference (to appear, 2010)Google Scholar
  21. 21.
    Ranta, A.: Type-Theoretical Grammar. Oxford University Press, Oxford (1990)zbMATHGoogle Scholar
  22. 22.
    Salvesen, A., Smith, J.: The strength of the subset type in Martin-Löf’s Type Theory. In: Proceedings of LICS 1988. IEEE, Edinburgh (1988)Google Scholar
  23. 23.
    Tichý, P.: The Foundations of Frege’s Logic. De Gruyter, Berlin (1988)CrossRefzbMATHGoogle Scholar
  24. 24.
    Tichý, P.: Collected Papers in Logic and Philosophy. In: Svoboda, V., Jespersen, B., Cheyne, C. (eds.) Filosofia, Czech Academy of Sciences, Prague. University of Otago Press, Dunedin (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Giuseppe Primiero
    • 1
  • Bjørn Jespersen
    • 2
  1. 1.Centre for Logic and Philosophy of ScienceGhent UniversityBelgium
  2. 2.Department of Computer ScienceTechnical University of Ostrava;, Institute of Philosophy, Department of Logic, Czech Academy of SciencesPragueCzech Republic

Personalised recommendations