Abstract
In this paper we describe a solution to the problem of proving cut-elimination for FILL, a variant of exponential-free and multiplicative Linear Logic originally introduced by Hyland and de Paiva. In the work of Hyland and de Paiva, a term assignment system is used to describe the intuitionistic character of FILL and a proof of cut-elimination is barely sketched. In the present paper, as well as correcting a small mistake in their work and extending the system to deal with exponentals, we introduce a different formal system describing the intuitionistic character of FILL and we provide a full proof of the cut-elimination theorem. The formal system is based on a dependency-relation between formulae occurrences within a given proof and seems of independent interest. The procedure for cut-elimination applies to (multiplicative and exponential) Classical Linear Logic, and we can (with care) restrict our attention to the subsystem FILL. The proof, as usual with cut-elimination proofs, is a little involved and we have not seen it published anywhere.
The work presented here was partially carried out while this author was employed by BRIGS, Aarhus University. The author is presently supported by the Danish Natural Science Research Council.
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References
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Braüner, T., de Paiva, V. (1998). A formulation of linear logic based on dependency-relations. In: Nielsen, M., Thomas, W. (eds) Computer Science Logic. CSL 1997. Lecture Notes in Computer Science, vol 1414. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028011
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DOI: https://doi.org/10.1007/BFb0028011
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