Algebras of modal operators and partial correctness
- Modal Kleene algebras are Kleene algebras enriched by forward and backward box and diamond operators. We formalise the symmetries of these operators as Galois connections, complemetarities and dualities. We study their properties in the associated operator algebras and show that the axioms of relation algebra are theorems at the operator level. Modal Kleene algebras provide a unifying semantics for various program calculi and enhances efficient cross-theory reasoning in this class, often in a very concise pointfree style. This claim is supported by novel algebraic soundness and completeness proofs for Hoare logic and by connecting this formalism with an algebraic decision procedure.
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| Author: | Bernhard MöllerGND, Georg StruthGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-391513 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/39151 |
| ISSN: | 0304-3975OPAC |
| Parent Title (English): | Theoretical Computer Science |
| Publisher: | Elsevier BV |
| Type: | Article |
| Language: | English |
| Year of first Publication: | 2006 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2018/08/01 |
| Volume: | 351 |
| Issue: | 2 |
| First Page: | 221 |
| Last Page: | 239 |
| DOI: | https://doi.org/10.1016/j.tcs.2005.09.069 |
| Institutes: | Fakultät für Angewandte Informatik |
| Fakultät für Angewandte Informatik / Institut für Informatik | |
| Fakultät für Angewandte Informatik / Institut für Informatik / Professur für Programmiermethodik und Multimediale Informationssysteme | |
| Dewey Decimal Classification: | 0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik |
| Licence (German): |  CC-BY-NC-ND 4.0: Creative Commons: Namensnennung - Nicht kommerziell - Keine Bearbeitung (mit Print on Demand) |
