The Logic of Unbalanced Subobjects in a Category with Two Closed Structures

@inproceedings{Stout1992TheLO,
  title={The Logic of Unbalanced Subobjects in a Category with Two Closed Structures},
  author={Lawrence Neff Stout},
  year={1992}
}
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).