Abstract
Categories with two local closed structures and factorization of maps through canonical unbalanced (epi and mono) subobjects have an internal logic close to that used in fuzzy set theory. This chapter develops a first order type theory with appropriate axioms and inference rules which can be interpreted in such categories. The theory is shown to be sound for SET(L) and the category of tolerance spaces. Unbalanced powerobject representation gives a higher order type theory for SET(L).
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© 1992 Springer Science+Business Media Dordrecht
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Stout, L.N. (1992). The Logic of Unbalanced Subobjects in a Category with Two Closed Structures. In: Rodabaugh, S.E., Klement, E.P., Höhle, U. (eds) Applications of Category Theory to Fuzzy Subsets. Theory and Decision Library, vol 14. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2616-8_4
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DOI: https://doi.org/10.1007/978-94-011-2616-8_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5156-9
Online ISBN: 978-94-011-2616-8
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