Abstract

[4] placed an approximation space (U,≡ ) in a type-lowering retraction with its power set 2 U 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.

Keywords

Modal Logic Approximation Space Tolerance Relation Complete Boolean Algebra Proximity Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Peter John Apostoli
    • 1
  • Akira Kanda
    • 1
  1. 1.Department of PhilosophyThe University of PretoriaPretoriaSouth Africa

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