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Admissibility of Cut in LC with Fixed Point Combinator

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Abstract

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.

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  1. School of Informatics, Indiana University Bloomington, IN, 47408-3912, USA

    Katalin Bimbó

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  1. Katalin Bimbó
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Correspondence to Katalin Bimbó.

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Bimbó, K. Admissibility of Cut in LC with Fixed Point Combinator. Stud Logica 81, 399–423 (2005). https://doi.org/10.1007/s11225-005-4651-y

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  • DOI: https://doi.org/10.1007/s11225-005-4651-y

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