Logica Universalis 8 (2):141-164 (2014)

Authors
Katalin Bimbo
University of Alberta
Abstract
The decidability of the logic of pure ticket entailment means that the problem of inhabitation of simple types by combinators over the base { B, B′, I, W } is decidable too. Type-assignment systems are often formulated as natural deduction systems. However, our decision procedure for this logic, which we presented in earlier papers, relies on two sequent calculi and it does not yield directly a combinator for a theorem of ${T_\to}$. Here we describe an algorithm to extract an inhabitant from a sequent calculus proof—without translating the proof into another proof system.
Keywords Ackermann constants  combinators  decidability  inhabitation  relevance logics  sequent calculi  structurally free logics  ticket entailment  type assignment systems
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DOI 10.1007/s11787-014-0099-z
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References found in this work BETA

A Completeness Theorem in Modal Logic.Saul A. Kripke - 1959 - Journal of Symbolic Logic 24 (1):1-14.
The Undecidability of Entailment and Relevant Implication.Alasdair Urquhart - 1984 - Journal of Symbolic Logic 49 (4):1059-1073.
Combinators and Structurally Free Logic.J. Dunn & R. Meyer - 1997 - Logic Journal of the IGPL 5 (4):505-537.
Normalization as a Homomorphic Image of Cut-Elimination.Garrel Pottinger - 1977 - Annals of Mathematical Logic 12 (3):323.

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