Hostname: page-component-599cfd5f84-v8j7l Total loading time: 0 Render date: 2025-01-07T07:08:35.263Z Has data issue: false hasContentIssue false
  • English
  • Français

Reductions in Intuitionistic Linear Logic

Published online by Cambridge University Press:  04 March 2009

Sergei Soloviev
Sergei Soloviev
Affiliation:
St.Petersburg Institute for Informatics of the Russian Academy of Sciences (SPIIRAN), 199178, St.Petersburg, 14-th line, 39, Email [email protected] or [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this work we show how some useful reductions known from ordinary intuitionistic propositional calculus can be modified for Intuitionistic Linear Logic (without modalities). The main reductions we consider are: (1) the reduction of the depth of formulas in the sequents by addition of new variables, and (2) the elimination of linear disjunction, tensor and constant F. Both transformations preserve deducibility, that is, a transformed sequent is deducible if and only if the initial one was deducible. The size of the sequent grows linearly in case (1) and ≤ On8 in case (2).

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 5 , Issue 4 , December 1995 , pp. 483 - 499
Copyright
Copyright © Cambridge University Press 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Rose, G. (1953) Prepositional calculus and readability. Transactions AMS. 75 1–19.CrossRefGoogle Scholar
Soloviev, S. (1979) Preservation of equivalence of derivations under reduction of depth of formulas. (English translation) J. of Sov. Math. 20 2370–2376.CrossRefGoogle Scholar
Soloviev, S. (1990) On the conditions of full coherence in closed categories. J. of Pure and Applied Algebra 69 301–329. (Communicated by S. Mac Lane)CrossRefGoogle Scholar
Volozh, B., Matskin, M., Mints, G. and Tyugu, E. (1983) The PRIZ system and propositional calculus. (English translation) Cybernetics 18 777–788.CrossRefGoogle Scholar
Girard, G.-Y. and Lafont, Y. (1987) Linear logic and lazy computation. In: Proc. TAPSOFT ‘87 (Pisa) 2. Springer-Verlag Lecture Notes in Computer Science 250 52–66.CrossRefGoogle Scholar
Engberg, U. and Winskel, G. (1992) Petri Nets as Models of Linear Logic.Google Scholar
Lambek, J. (1968) Deductive systems and categories, I. Math. Systems Theory 2 287–318.CrossRefGoogle Scholar
Szabo, M. (1978) Algebra of Proofs. Studies in Logic and the Foundations of Mathematics 88, North-Holland.Google Scholar