# Stone Relation Algebras

 Title: Stone Relation Algebras Author: Walter Guttmann Submission date: 2017-02-07 Abstract: We develop Stone relation algebras, which generalise relation algebras by replacing the underlying Boolean algebra structure with a Stone algebra. We show that finite matrices over extended real numbers form an instance. As a consequence, relation-algebraic concepts and methods can be used for reasoning about weighted graphs. We also develop a fixpoint calculus and apply it to compare different definitions of reflexive-transitive closures in semirings. Change history: [2017-07-05]: generalised extended reals to linear orders (revision b8e703159177) BibTeX: @article{Stone_Relation_Algebras-AFP, author = {Walter Guttmann}, title = {Stone Relation Algebras}, journal = {Archive of Formal Proofs}, month = feb, year = 2017, note = {\url{https://isa-afp.org/entries/Stone_Relation_Algebras.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License Depends on: Stone_Algebras Used by: Stone_Kleene_Relation_Algebras Status: [ok] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.