Domain and Antidomain Semigroups

Abstract

Abstract. We axiomatise and study operations for relational domain and antidomain on semigroups and monoids. We relate this approach with previous axiomatisations for semirings, partial transformation semigroups and dynamic predicate logic.

Taming Multirelations

“…Depending on the order-dual interpretations of sequential composition as join or meet, 1 σ becomes the least or greatest semilattice element. As similar result has been established in [6], but the proof does not transfer due to the lack of associativity of sequential composition. Next we derive three interaction laws.…”

“…We define a domain operation explicitly on these c-monoids and show that the domain elements form a sub-semilattice in which sequential and parallel composition coincide. We show that previous domain axioms for sequential monoids [6] and concurrent monoids [10] are derivable in this setting.…”

“…which has been verified in the multirelational model, to derive domain axioms similar to those for domain monoids [6], and to verify some properties of the M (X), S (X), T (X) triangle.…”

A Hierarchy of Algebras for Boolean Subsets

“…Axioms for domain and antidomain in idempotent semirings and weaker semiring structures have been studied, for example, in [ 9 – 12 ]. Axioms for these operations in semigroups and monoids have been studied, for example, in [ 7 , 23 ].…”

Ordered domain algebras

“…The algebraic behaviour of domain algebras have been investigated, e.g. in [DJS09a,DJS09b]. Their primary models are algebras of relations, viz.…”