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Labelled Deduction over Algebras of Truth-Values*

  • João Rasga
  • Amílcar Sernadas
  • Cristina Sernadas
  • Luca Viganò
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2309)

Abstract

We introduce a framework for presenting non-classical logics in a modular and uniform way as labelled natural deduction systems. The use of algebras of truth-values as the labelling algebras of our systems allows us to give generalized systems for multiple-valued logics. More specifically, our framework generalizes previous work where labels represent worlds in the underlying Kripke structure: since we can take multiple-valued logics as meaning not only finitely or infinitely many-valued logics but also power-set logics, our framework allows us to present also logics such as modal, intuitionistic and relevance logics, thus providing a first step towards fibring these logics with many-valued ones.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • João Rasga
    • 1
  • Amílcar Sernadas
    • 1
  • Cristina Sernadas
    • 1
  • Luca Viganò
    • 2
  1. 1.CLC, Dep. de MatemáticaISTLisbonPortugal
  2. 2.Institut für InformatikUniversität FreiburgFreiburgGermany

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