Studia Logica

, Volume 54, Issue 2, pp 149–171 | Cite as

Connectification forn-contraction

  • Andreja Prijatelj


In this paper, we introduce connectification operators for intuitionistic and classical linear algebras corresponding to linear logic and to some of its extensions withn-contraction. In particular,n-contraction (n≥2) is a version of the contraction rule, wheren+1 occurrences of a formula may be contracted ton occurrences. Since cut cannot be eliminated from the systems withn-contraction considered most of the standard proof-theoretic techniques to investigate meta-properties of those systems are useless. However, by means of connectification we establish the disjunction property for both intuitionistic and classical affine linear logics withn-contraction.


Mathematical Logic Linear Algebra Computational Linguistic Linear Logic Disjunction Property 
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  1. Došen, K., P. Schroeder-Heister (eds.), 1993,Substructural Logics, Studies in Logic and Computation, D. Gabbay (ed.), Clarendon Press, Oxford.Google Scholar
  2. Girard, J. Y., 1987, ‘Linear Logic’,Theoretical Computer Science 50.Google Scholar
  3. Hori, R., H. Ono and H. Schellinx, 199x, ‘Extending Intuitionistic Linear Logic with Knotted Structural Rules’, to appear inNotre Dame Journal of Formal Logic.Google Scholar
  4. Kanazawa, M., 1992, ‘The Lambek Calculus Enriched by Additional Connectives’,Journal of Logic, Language and Information (1).Google Scholar
  5. Moerdijk, I., 1982, ‘Glueing Topoi and Higher Order Disjunction and Existence’,The L. E. J. Brouwer Centenary Symposium, A. S. Troelstra and D. van Dalen (eds), North-Holand.Google Scholar
  6. Moerdijk, I., 1983, ‘On the Freyd Cover of a Topos’,Notre Dame Journal of Formal Logic, vol.24, num. 4.Google Scholar
  7. Prijatelj, A., 1993, ‘Bounded Contraction and Many-Valued Semantics’,ILLC Prepublication Series for Mathematical Logic and Foundations ML-93-04, University of Amsterdam.Google Scholar
  8. Prijatelj, A., 1994, ‘Free Algebra Corresponding to Multiplicative Classical Linear Logic and some Extensions’,ILLC Prepublication Series for Mathematical Logic and Foundations ML-94-08, University of Amsterdam.Google Scholar
  9. Scedrov, A., P. J. SCOTT, 1982, ‘A Note on the Friedman Slash and Freyd Covers’,The L. E. J. Brouwer Centenary Symposium, A. S. Troelstra and D. van Dalen (eds), North-Holand.Google Scholar
  10. Smorynski, C. A., 1973, ‘Applications of Kripke Models’,Metamathematical Investigations of Intuitionistic Arithmetic and Analysis, A. S. Troelstra (ed), Springer-Verlag, Berlin.Google Scholar
  11. Troelstra, A. S., 1992,Lectures on Linear Logic, CSLI Lecture Notes, No. 29, Center for the Study of Language and Information, Stanford.Google Scholar
  12. Troelstra, A. S. and D. van Dalen, 1988,Constructivism in Mathematics, vol. I., vol. II, North-Holland Publishing Company, Amsterdam.Google Scholar

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Andreja Prijatelj
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of AmsterdamThe Netherland

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