### 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.

### License

BSD License

### History

July 5, 2017
  generalised extended reals to linear orders (revision b8e703159177)

### Topics

- Mathematics/Algebra

### Session Stone_Relation_Algebras

- Fixpoints
- Semirings
- Relation_Algebras
- Relation_Subalgebras
- Matrix_Relation_Algebras
- Linear_Order_Matrices
- Choose_Component

### Depends on

- Stone Algebras

### Used by

- Cardinality and Representation of Stone Relation Algebras
- Stone-Kleene Relation Algebras

### Auto-related entries

- Cardinality and Representation of Stone Relation Algebras

## Cite

×

Stone_Relation_Algebras-AFP

    @article{Stone_Relation_Algebras-AFP,
      author  = {Walter Guttmann},
      title   = {Stone Relation Algebras},
      journal = {Archive of Formal Proofs},
      month   = {February},
      year    = {2017},
      note    = {\url{https://isa-afp.org/entries/Stone_Relation_Algebras.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

Download

## Download

× Download latest

Older releases:

- Sep 13, 2023 : Isabelle2023
- Oct 27, 2022 : Isabelle2022
- Dec 14, 2021 : Isabelle2021-1
- Feb 23, 2021 : Isabelle2021
- Apr 20, 2020 : Isabelle2020
- Jun 11, 2019 : Isabelle2019
- Aug 16, 2018 : Isabelle2018
- Oct 10, 2017 : Isabelle2017
- Feb 9, 2017 : Isabelle2016-1