Bibliographic Details
| Title: |
Internal axioms for domain semirings |
| Authors: |
Desharnais, Jules1 Jules.Desharnais@ift.ulaval.ca, Struth, Georg2 g.struth@dcs.shef.ac.uk |
| Source: |
Science of Computer Programming. Mar2011, Vol. 76 Issue 3, p181-203. 23p. |
| Subjects: |
Axioms, Semirings (Mathematics), Kleene algebra, Automatic theorem proving, Distributive lattices, Boolean algebra |
| Abstract: |
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. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
