Tolerance approximation spaces
Fundamenta Informaticae - Special issue: rough sets
On Generalizing Pawlak Approximation Operators
RSCTC '98 Proceedings of the First International Conference on Rough Sets and Current Trends in Computing
Approximation Spaces of Type-Free Sets
RSCTC '00 Revised Papers from the Second International Conference on Rough Sets and Current Trends in Computing
The category-theoretic solution of recursive domain equations
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
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[4] placed an approximation space (U,≡ ) in a type-lowering retraction with its power set 2U such that the ≡ -exact subsets of U comprise the kernel of the retraction, where ≡ is the equivalence relation of set-theoretic indiscernibility within the resulting universe of exact sets. Since a concept thus forms a set just in case it is ≡ -exact, set-theoretic comprehension in (U,≡ ) is governed by the method of upper and lower approximations of Rough Set Theory. Some central features of this universe were informally axiomatized in [3] in terms of the notion of a Proximal Frege Structure and its associated modal Boolean algebra of exact sets. The present essay generalizes the axiomatic notion of a PFS to tolerance (reflexive, symmetric) relations, where the universe of exact sets forms a modal ortho-lattice. An example of this general notion is provided by the tolerance relation of “matching” over U.