Monotonic versus antimonotonic exponentiation

  • Daniel F. Otth
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 664)


We investigate the relationship between the monotonic (→) and the antimonotonic exponentiation (➾) in a type system with subtyping. We present a model in which we can develop both exponentiations at the same time. In this model the monotonic and the antimonotonic exponentiation enjoy a duality, namely α➾β=∁(α→∁β) where ∁ is the type constructor complement. We give a sound and complete system of axioms for the type system with the type constructors →, ➾, ∪, ∩, ∁, ⊥, T.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Engeler, E.: Algebras and combinators. Algebra Universalis 13 (1981) 389–392Google Scholar
  2. 2.
    Otth, D.: Konsistente Operatoren. ETHZ Report(1990)Google Scholar
  3. 3.
    Otth, D.: Types and Consistency in Combinatory Algebras. Dissertation 9800, ETHZ (1992).Google Scholar
  4. 4.
    Plotkin, G.: A powerdomain construction. SIAM J. Comput. 5 (1976) 452–487Google Scholar
  5. 5.
    Schellinx, H.: Isomorphisms and nonisomorphisms of graph models. J. of Symbolic Logic, 56 (1991) 227–249Google Scholar
  6. 6.
    Scott, D.: Data types as lattices. SIAM J. Comput. 5 (1976) 522–587Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Daniel F. Otth
    • 1
  1. 1.Laboratory for Computer ScienceMassachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations