Cut elimination for entailment relations

Archive for Mathematical Logic:1-21 (forthcoming)
Entailment relations, introduced by Scott in the early 1970s, provide an abstract generalisation of Gentzen’s multi-conclusion logical inference. Originally applied to the study of multi-valued logics, this notion has then found plenty of applications, ranging from computer science to abstract algebra. In particular, an entailment relation can be regarded as a constructive presentation of a distributive lattice and in this guise it has proven to be a useful tool for the constructive reformulation of several classical theorems in commutative algebra. In this paper, motivated by these concrete applications, we state and prove a cut-elimination result for inductively generated entailment relations. We analyse some of its consequences and describe the existing connections with analogous results in the literature.
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DOI 10.1007/s00153-018-0653-0
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References found in this work BETA

Inductively Generated Formal Topologies.Thierry Coquand, Giovanni Sambin, Jan Smith & Silvio Valentini - 2003 - Annals of Pure and Applied Logic 124 (1-3):71-106.
Structural Proof Theory.Jan von Plato & Sara Negri - 2006 - Philosophical Review 115 (2):255-258.
Cut Elimination in the Presence of Axioms.Sara Negri & Jan Von Plato - 1998 - Bulletin of Symbolic Logic 4 (4):418-435.
On Engendering an Illusion of Understanding.Dana Scott - 1971 - Journal of Philosophy 68 (21):787-807.
On Preserving.Gillman Payette & Peter K. Schotch - 2007 - Logica Universalis 1 (2):295-310.

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