TY  - JOUR
A1  - Möller, Bernhard
A1  - Struth, Georg
T1  - Algebras of modal operators and partial correctness
T2  - Theoretical Computer Science
N2  - 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.
Y1  - 2006
UR  - https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/39151
UR  - https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-391513
SN  - 0304-3975
VL  - 351
IS  - 2
SP  - 221
EP  - 239
PB  - Elsevier BV
ER  -