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Abstract: Preliminary Version Abstract We present a logical calculus which imposes a grading on a sequent-style calculus to account for the runtime of the programmes represented by the sequents. This system is sound for a notion of polynomial-time realizability. An extension of the grading is also considered, giving a notion of "dependant grades", which is also sound. Furthermore, we define a notion of closed graded multicategory, and show how the structure of polynomial-time realizers has that... (Update)
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BibTeX entry: (Update)
@inproceedings{ seely89graded,
author = "R. A. G. Seely",
title = "Graded Multicategories of Polynomial-time Realizers",
booktitle = "Category Theory and Computer Science",
pages = "182-197",
year = "1989",
url = "citeseer.ist.psu.edu/148561.html" }
Citations (may not include all citations):242 Linear logic (context) - Girard - 1987
146 Investigations into logical deductions (context) - Gentzen - 1969
51 Functional interpretations of feasibly constructive arithmet.. (context) - Cook, Urquhart - 1988
19 Multicategories revisited (context) - Lambek - 1987
17 Deductive systems and categories (context) - Lambek - 1968
13 Deductive systems and categories II (context) - Lambek - 1969
4 Polynomially graded logic (context) - Nerode, Remmel et al. - 1989
3 Hyperdoctrines, natural deduction, and the Beck condition (context) - Seely - 1983
2 The polynomial time hierarchy and intuitionistic bounded ari.. (context) - Buss - 1986
2 Doctoral dissertation (context) - Buss, Arithmetic - 1985
2 Proofs, programs and run-times (context) - Crossley - 1989
1 A logical calculus for polynomial time realizability - Crossley, Mathai et al. - 1989
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