A Hierarchy of Algebras for Boolean Subsets


Title: A Hierarchy of Algebras for Boolean Subsets
Authors: Walter Guttmann and Bernhard Möller
Submission date: 2020-01-31
Abstract: We present a collection of axiom systems for the construction of Boolean subalgebras of larger overall algebras. The subalgebras are defined as the range of a complement-like operation on a semilattice. This technique has been used, for example, with the antidomain operation, dynamic negation and Stone algebras. We present a common ground for these constructions based on a new equational axiomatisation of Boolean algebras.
  author  = {Walter Guttmann and Bernhard Möller},
  title   = {A Hierarchy of Algebras for Boolean Subsets},
  journal = {Archive of Formal Proofs},
  month   = jan,
  year    = 2020,
  note    = {\url{https://isa-afp.org/entries/Subset_Boolean_Algebras.html},
            Formal proof development},
  ISSN    = {2150-914x},
License: BSD License
Depends on: Stone_Algebras
Used by: Correctness_Algebras