Calculi for symmetric generalized galois logics

• Katalin Bimbó ^[1] ; J. Michale Dunn ^[2]
  1. [1] University of Alberta

     University of Alberta

     Canadá

     
  2. [2] Indiana University
• Localización: Linguistic Analysis, ISSN 0098-9053, Vol. 36, Nº. 1-4, 2010, págs. 307-343
• Idioma: inglés
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• Resumen

  • Symmetric generalized Galois logics are motivated by proof theoretical, categorical and linguistic regularities, among others. This paper focuses on the proof theory of these logics. First, the connection between “hemi-distributivity” and the non-associative Lambek calculus with multiple right-hand sides is scrutinized. The admissibility of the single algebraic cut for the fusion-fission fragment of this calculus is proven. Next, axiomatizations are given for all the symmetric generalized Galois logics that result from the non-associative bi-Lambek calculus via an addition of a Grishin inequation. Lastly, symmetric generalized Galois logics are formalized as Belnap-style display calculi. The cut rule is proven admissible in these calculi too.