In this work we investigate bounded Lukasiewicz logics}, characterised as the intersection of the k-valued Lukasiewicz logics for k = 2, ..., n (n ≥ 2). These logics formalise a generalisation of Ulam’s game with applications in Information Theory. Here we provide an analytic proof calculus B n for each bounded Lukasiewicz logic, obtained by adding a single rule to , a hypersequent calculus for Lukasiewicz infinite-valued logic. We give a first cut-elimination proof for GL with (suitable forms of) cut rules. We then prove completeness for B n with cut and show that cut can also be eliminated in this case.


Induction Hypothesis Classical Logic Logical Rule Structural Rule Sequent Calculus 
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© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Agata Ciabattoni
    • 1
  • George Metcalfe
    • 2
  1. 1.Institut für Algebra und ComputermathematikTechnische Universität WienWienAustria
  2. 2.Department of Computer ScienceKing’s College LondonLondonUK

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