Cut Elimination For Classical Bilinear Logic

Authors:
J. Lambek
Affiliations:
Mathematics Department, McGill University, Montreal, Quebec, Canada, H3A 2K6
Venue:
Fundamenta Informaticae
Year:
1995

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Abstract

In this paper a cut elimination theorem is proved for classical non-commutative linear logic without exponentials, presented as a dual Schütte style deductive system. The notion of equality between deductions is sketched and they are interpreted as relations, in the spirit of the formulas as types paradigm. (The author acknowledges support from the Social Sciences and Humanities Research Council of Canada.)