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Hypersequents, logical consequence and intermediate logics for concurrency

  • Arnon Avron
Article

Abstract

The existence of simple semantics and appropriate cut-free Gentzen-type formulations are fundamental intrinsic criteria for the usefulness of logics. In this paper we show that by using hypersequents (which are multisets of ordinary sequents) we can provide such Gentzen-type systems to many logics. In particular, by using a hypersequential generalization of intuitionistic sequents we can construct cut-free systems for some intermediate logics (including Dummett's LC) which have simple algebraic semantics that suffice, e.g., for decidability. We discuss the possible interpretations of these logics in terms of parallel computation and the role that the usual connectives play in them (which is sometimes different than in the sequential case).

Keywords

Neural Network Artificial Intelligence Complex System Nonlinear Dynamics Parallel Computation 
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.

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Copyright information

© J.C. Baltzer A.G. Scientific Publishing Company 1991

Authors and Affiliations

  • Arnon Avron
    • 1
  1. 1.Department of Computer Science, Raymond and Beverly Sackler Faculty of Exact SciencesUniversity of Tel AvivTel AvivIsrael

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