TY  - RPRT
A1  - Möller, Bernhard
A1  - Struth, Georg
T1  - Modal Kleene algebra and partial correctness
N2  - We enrich Kleene algebra by domain and codomain operators. These abstractions of relational notions give rise to four modal operators. The boxes and diamonds enjoy various symmetries via Galois connections and dualities. Lifting modal statements to modal operator semirings yields a further abstraction and thus a more elegant and concise “statefree” reasoning about modalities. We use this modal Kleene algebra for calculating soundness and completeness proofs for propositional Hoare logic. While our soundness proof is more direct than related ones, our algebraic completeness proof seems entirely novel. It uses a modal symmetry that relates the wlp predicate transformer with partial correctness assertions and that is beyond the expressibility of formalisms like propositional dynamic logic.
T3  - Reports / Technische Berichte der Fakultät für Angewandte Informatik der Universität Augsburg - 2003-08 
KW  - Kleene-Algebra
Y1  - 2006
UR  - https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/255
UR  - https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-2064
PB  - Institut für Informatik, Universität Augsburg
CY  - Augsburg
ER  -