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Non-commutative logic II: sequent calculus and phase semantics

Published online by Cambridge University Press:  01 April 2000

PAUL RUET
Affiliation:
Institut de Mathématiques de Luminy, 163 avenue de Luminy, Case 907, 13288 Marseille Cedex 9, France. Email: ruet@iml.univ-mrs.fr

Abstract

Non-commutative logic, which is a unification of commutative linear logic and cyclic linear logic, is extended to all linear connectives: additives, exponentials and constants. We give two equivalent versions of the sequent calculus (directly with the structure of order varieties, and with their presentations as partial orders), phase semantics and a cut-elimination theorem. This involves, in particular, the study of the entropy relation between partial orders, and the introduction of a special class of order varieties: the series–parallel order varieties.

Type
Research Article
Copyright
© 2000 Cambridge University Press

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