Montague-Gallin’s Intensional Logic, Structured Meanings and Scott’s Domains

  • Serge Lapierre
Part of the Synthese Library book series (SYLI, volume 236)


In this paper we present an extension of Montague-Gallin’s Intensional Logic, called Hyperintensional Logic (HL), which includes both the notion of structured meaning and the notion of Scott’s domain. On the one hand, structured meanings solve the problem of the failure of substitutivity of logically equivalent sentences in propositional attitude contexts. On the other hand, Scott’s domains solve in a general and natural way the set-theoretical problem of the reiteration of hyperintensional functors,which are functors denoting functions taking structured meanings (or intensional structures) as arguments. HL has many advantages on a similar, but in many respects different system already suggested by the author1. First, the logical connectives and the quantifiers are easier to define; secondly, we need to define only one system of inverse limits instead of two; finally, it is a natural conservative extension of a well known formal system. In what follows an acquaintance with Montague-Gallin’s Intensional Logic (see [1], [7]), Structured Meanings Semantics (see [3], [4]) and Domain Theory (see [2], [8], [9], [10]) is presupposed.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    D. Gallin, Intensional and Higher-Order Modal Logic, North-Holland Publishing Company, 1975.Google Scholar
  2. [2]
    H.P. Barendreght, The Lambda Calculus: Its Syntax and Semantics, Studies in Logic and the Foundations of Mathematics, vol. 103, North-Holland, 1981.Google Scholar
  3. [3]
    M.J. Cresswell, “Hyperintensional Logic”, Studia Logica 34 (1975): 25–38.CrossRefGoogle Scholar
  4. [4]
    M.J. Cresswell, Structured Meanings: The Semantics of Propositional Attitudes, Cambridge, Mass., M.I.T. Press, 1985.Google Scholar
  5. [5]
    S.Lapierre, Logique intensionnelle, attitudes propositionnelles et compétence sémantique, Ph.D dissertation, Université du Québec à Trois-Rivières, Trois-Rivières, 1989.Google Scholar
  6. [6]
    S. Lapierre, “Structured Meanings and Reflexive Domains”, Studia Logica 51 (1992): 215–239.CrossRefGoogle Scholar
  7. [7]
    R. Montague, “Universal Grammar”, Theoria 36 (1970): 373–398.CrossRefGoogle Scholar
  8. [8]
    D. Scott, “Continuous Lattices”, in F.W. Lawere (ed.), Toposes, algebraic geometry and logic, Lecture Notes in Mathematics, vol. 274, Springer-Verlag, 1972, pp. 97–136.Google Scholar
  9. [9]
    D. Scott, “Models for Various Type-free Calculi”, in P. Suppes, L. Henkin, J. Athanase and GR. C. Moisil (eds.), Logic, Methodology and Philosophy of Science IV, North-Holland, 1973, pp. 157–187.Google Scholar
  10. [10]
    J.E. Stoy, Denotational Semantics: The Scott-Strachey Approach to programming Language Theory, Cambridge, Mass., London, England, M.I.T Press, 1977.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1994

Authors and Affiliations

  • Serge Lapierre
    • 1
  1. 1.University of MontrealUSA

Personalised recommendations