Upper and lower recursion schemes in abstract approximation spaces

Authors:
Peter Apostoli;Akira Kanda
Affiliations:
Department of Philosophy, The University of Toronto;Department of Philosophy, The University of Toronto
Venue:
RSFDGrC'03 Proceedings of the 9th international conference on Rough sets, fuzzy sets, data mining, and granular computing
Year:
2003

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Abstract

An approximation space (U, R) placed in a type-lowering retraction with 2U × U provides a model for a first order calculus of relations for computing over lists and reasoning about the resulting programs. Upper and lower approximations to the scheme of primitive recursion of the Theory of Pairs are derived from the approximation operators of an abstract approximation space (U, ⋄: u → ∪[u]R, □: u → ∩[u]R).