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A New Machinechecked Proof of Strong Normalisation for Display Logic
 Electronic Notes in Theoretical Computer Science
, 2002
"... We use a deep embedding of the display calculus for relation algebras #RA in the logical framework Isabelle/HOL to formalise a new, machinechecked, proof of strong normalisation and cutelimination for #RA which does not use measures on the size of derivations. Our formalisation generalises easily ..."
Abstract

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We use a deep embedding of the display calculus for relation algebras #RA in the logical framework Isabelle/HOL to formalise a new, machinechecked, proof of strong normalisation and cutelimination for #RA which does not use measures on the size of derivations. Our formalisation generalises easily to other display calculi and can serve as a basis for formalised proofs of strong normalisation for the classical and intuitionistic versions of a vast range of substructural logics like the Lambek calculus, linear logic, relevant logic, BCKlogic, and their modal extensions. We believe this is the first full formalisation of a strong normalisation result for a sequent system using a logical framework.
A New Machinechecked Proof of Strong Normalisation for Display Logic
"... 1 Introduction Sequent calculi provide a rigorous basis for metatheoretic studies of logics. The central theorem is cutelimination which states that detours through lemmata can be avoided, and it can be used to show many important logical properties like consistency, interpolation, and Beth defina ..."
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1 Introduction Sequent calculi provide a rigorous basis for metatheoretic studies of logics. The central theorem is cutelimination which states that detours through lemmata can be avoided, and it can be used to show many important logical properties like consistency, interpolation, and Beth definability. Cutfree sequent calculi are also useful for automated deduction [14], nonclassical extensions of logic programming [22], and studying deep connections between cut elimination, lambda calculi and functional programming. Sequent calculi, and their extensions, therefore play an important role in theoretical computer science.
Abstract A New Machinechecked Proof of Strong Normalisation for Display Logic
"... We use a deep embedding of the display calculus for relation algebras δRA in the logical framework Isabelle/HOL to formalise a new, machinechecked, proof of strong normalisation and cutelimination for δRA which does not use measures on the size of derivations. Our formalisation generalises easily ..."
Abstract
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(Show Context)
We use a deep embedding of the display calculus for relation algebras δRA in the logical framework Isabelle/HOL to formalise a new, machinechecked, proof of strong normalisation and cutelimination for δRA which does not use measures on the size of derivations. Our formalisation generalises easily to other display calculi and can serve as a basis for formalised proofs of strong normalisation for the classical and intuitionistic versions of a vast range of substructural logics like the Lambek calculus, linear logic, relevant logic, BCKlogic, and their modal extensions. We believe this is the first full formalisation of a strong normalisation result for a sequent system using a logical framework. 1