# Relation algebras of Sugihara, Belnap, Meyer, and Church

## TL;DR

This paper explores the relation algebras associated with Sugihara, Belnap, Meyer, and Church, showing their representability as relation algebras and their application to provide semantics for R-mingle.

## Contribution

It demonstrates that these algebras are definitional reducts or subreducts of proper relation algebras, establishing their representability and semantic significance.

## Key findings

- Sugihara matrices are representable as relation algebras.
- Representability provides sound and complete semantics for R-mingle.
- Algebras are reducts or subreducts of proper relation algebras.

## Abstract

Algebras introduced by, or attributed to, Sugihara, Belnap, Meyer, and Church are representable as algebras of binary relations with set-theoretically defined operations. They are definitional reducts or subreducts of proper relation algebras. The representability of Sugihara matrices yields sound and complete set-theoretical semantics for R-mingle.