6 papers
Representability for distributive quasi relation algebras via nested sums
Andrew Craig, Claudette Robinson, Wilmari Morton
We extend the work of Galatos (2004) on nested sums, originally called generalised ordinal sums, of residuated lattices. We show that the nested sum of an odd quasi relation algebr…
Duality theory and representations for distributive quasi relation algebras and DInFL-algebras
Andrew Craig, Peter Jipsen, Claudette Robinson
We develop dualities for complete perfect distributive quasi relation algebras and complete perfect distributive involutive FL-algebras. The duals are partially ordered frames with…
Pregroup representable expansions of residuated lattices
Andrew Craig, Claudette Robinson
Group representable relation algebras play an important role in the study of representable relation algebras. The class of distributive involutive FL-algebras (DInFL-algebras) gene…
Contractions of quasi relation algebras and applications to representability
Andrew Craig, Wilmari Morton, Claudette Robinson
Quasi relation algebras (qRAs) were first described by Galatos and Jipsen in 2013. They are generalisations of relation algebras and can also be viewed as certain residuated lattic…
Representing Sugihara monoids via weakening relations
Andrew Craig, Claudette Robinson
We show that all Sugihara monoids can be represented as algebras of binary relations, with the monoid operation given by relational composition. Moreover, the binary relations are…
Representable distributive quasi relation algebras
Andrew Craig, Claudette Robinson
We give a definition of representability for distributive quasi relation algebras (DqRAs). These algebras are a generalisation of relation algebras and were first described by Gala…