Admissibility of cut in LC with fixed point combinator

Studia Logica 81 (3):399 - 423 (2005)
The fixed point combinator (Y) is an important non-proper combinator, which is defhable from a combinatorially complete base. This combinator guarantees that recursive equations have a solution. Structurally free logics (LC) turn combinators into formulas and replace structural rules by combinatory ones. This paper introduces the fixed point and the dual fixed point combinator into structurally free logics. The admissibility of (multiple) cut in the resulting calculus is not provable by a simple adaptation of the similar proof for LC with proper combinators. The novelty of our proof—beyond proving the cut for a newly extended calculus–is that we add a fourth induction to the by-and-large Gentzen-style proof.
Keywords combinatory logic  structurally free logics  substructural logics  non-classical logics  fked point combinator  (multiple) cut rule  elimination theorem
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References found in this work BETA
Gerhard Gentzen (1964). Investigations Into Logical Deduction. American Philosophical Quarterly 1 (4):288 - 306.
Lou Goble (2004). Combinator Logics. Studia Logica 76 (1):17 - 66.
J. Michael Dunn (1973). A Truth Value Semantics for Modal Logic. In Hugues Leblanc (ed.), Journal of Symbolic Logic. Amsterdam,North-Holland 87--100.

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