A completeness theorem for Kleene algebras and the algebra of regular events
Papers presented at the IEEE symposium on Logic in computer science
ACM Transactions on Programming Languages and Systems (TOPLAS)
Science of Computer Programming - Special issue on mathematics of program construction (MPC 2002)
Algebras of modal operators and partial correctness
Theoretical Computer Science - Algebraic methodology and software technology
ACM Transactions on Computational Logic (TOCL)
Automated theorem proving by resolution in non-classical logics
Annals of Mathematics and Artificial Intelligence
Electronic Notes in Theoretical Computer Science (ENTCS)
Automated Reasoning in Kleene Algebra
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
RelMiCS'06/AKA'06 Proceedings of the 9th international conference on Relational Methods in Computer Science, and 4th international conference on Applications of Kleene Algebra
Using probabilistic kleene algebra for protocol verification
RelMiCS'06/AKA'06 Proceedings of the 9th international conference on Relational Methods in Computer Science, and 4th international conference on Applications of Kleene Algebra
Refinement algebra with operators for enabledness and termination
MPC'06 Proceedings of the 8th international conference on Mathematics of Program Construction
Domain and Antidomain Semigroups
RelMiCS '09/AKA '09 Proceedings of the 11th International Conference on Relational Methods in Computer Science and 6th International Conference on Applications of Kleene Algebra: Relations and Kleene Algebra in Computer Science
On automated program construction and verification
MPC'10 Proceedings of the 10th international conference on Mathematics of program construction
Partial, total and general correctness
MPC'10 Proceedings of the 10th international conference on Mathematics of program construction
Internal axioms for domain semirings
Science of Computer Programming
Unifying recursion in partial, total and general correctness
UTP'10 Proceedings of the Third international conference on Unifying theories of programming
RAMICS'11 Proceedings of the 12th international conference on Relational and algebraic methods in computer science
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A new axiomatisation for domain and codomain on semirings and Kleene algebras is proposed. It is simpler, more general and more flexible than a predecessor, and it is particularly suitable for program analysis and construction via automated deduction. Different algebras of domain elements for distributive lattices, (co-)Heyting algebras and Boolean algebras arise by adapting this axiomatisation. Modal operators over all these domain algebras can then easily be defined. The calculus of the previous axiomatisation arises as a special case. An application in terms of a fully automated proof of a modal correspondence result for Löb's formula is also presented.