A System of Interaction and Structure

Details A System of Interaction and Structure A System of Interaction and Structure

1999-10-28

arxiv.org/abs/cs/9910023v4

ACM Transactions on Computational Logic, Vol. 8 (1:1), 2007, pp. 1-64

Computer Science

Logic in Computer Science

This is the authoritative version of the article, with readable pictures, in colour, also available at <http://cs.bath.ac.uk

Scientific paper

10.1145/1182613.1182614

This paper introduces a logical system, called BV, which extends multiplicative linear logic by a non-commutative self-dual logical operator. This extension is particularly challenging for the sequent calculus, and so far it is not achieved therein. It becomes very natural in a new formalism, called the calculus of structures, which is the main contribution of this work. Structures are formulae submitted to certain equational laws typical of sequents. The calculus of structures is obtained by generalising the sequent calculus in such a way that a new top-down symmetry of derivations is observed, and it employs inference rules that rewrite inside structures at any depth. These properties, in addition to allow the design of BV, yield a modular proof of cut elimination.

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