Internal axioms for domain semirings

https://doi.org/10.1016/j.scico.2010.05.007Get rights and content
Under an Elsevier user license
open archive

Abstract

New axioms for domain operations on semirings and Kleene algebras are proposed. They generalise the relational notion of domain–the set of all states that are related to some other state–to a wide range of models. They are internal since the algebras of state spaces are induced by the domain axioms. They are simpler and conceptually more appealing than previous two-sorted external approaches in which the domain algebra is determined through typing. They lead to a simple and natural algebraic approach to modal logics based on equational reasoning. The axiomatisations have been developed in a new style of computer-enhanced mathematics by automated theorem proving, and the approach itself is suitable for automated systems analysis and verification. This is demonstrated by a fully automated proof of a modal correspondence result for Löb’s formula that has applications in termination analysis.

Keywords

Semiring
Kleene algebra
Modal semiring
Domain operator
Codomain operator
Antidomain operator
Algebra of domain elements
Distributive lattice
Boolean algebra
Heyting algebra
Löb’s formula
Automated theorem proving

Cited by (0)