Internal axioms for domain semirings

  • Authors:

  • Jules Desharnais;Georg Struth

  • Affiliations:

  • Département dinformatique et de génie logiciel, Pavillon Adrien-Pouliot, 1065, avenue de la Médecine, Université Laval, Québec, QC, G1V 0A6, Canada;Department of Computer Science, University of Sheffield, Regent Court, 211 Portobello, Sheffield S1 4DP, United Kingdom

  • Venue:
  • Science of Computer Programming
  • Year:
  • 2011

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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 Lob's formula that has applications in termination analysis.