International Colloquium on Automata, Languages and Programming on Automata, languages and programming
Introduction to higher order categorical logic
Introduction to higher order categorical logic
On Kleene algebras and closed semirings
MFCS '90 Proceedings on Mathematical foundations of computer science 1990
Action logic and pure induction
JELIA '90 Proceedings of the European workshop on Logics in AI
Complete systems of B -rational identities
Theoretical Computer Science
A completeness theorem for Kleene algebras and the algebra of regular events
Papers presented at the IEEE symposium on Logic in computer science
Duality and the completeness of the modal &mgr;-calculus
Selected papers of the workshop on Topology and completion in semantics
Completeness of Park induction
MFPS '94 Proceedings of the tenth conference on Mathematical foundations of programming semantics
Equational properties of iteration in algebraically complete categories
MFCS '96 Selected papers from the 21st symposium on Mathematical foundations of computer science
The modal mu-calculus alternation hierarchy is strict
Theoretical Computer Science
Duality for modal &mgr;-logics
Theoretical Computer Science
Information and Computation
Two Complete Axiom Systems for the Algebra of Regular Events
Journal of the ACM (JACM)
Completeness of Kozen's axiomatisation of the propositional &mgr;-calculus
Information and Computation
Dynamic Logic
A Hierarchy Theorem for the µ-Calculus
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
Complete Axioms for Categorical Fixed-Point Operators
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
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We propose a method to axiomatize by equations the least prefixed point of an order preserving function. We discuss its domain of application and show that the Boolean modal µ-calculus has a complete equational axiomatization. The method relies on the existence of a "closed structure" and its relationship to the equational axiomatization of Action Logic is made explicit. The implication operation of a closed structure is not monotonic in one of its variables; we show that the existence of such a term that does not preserve the order is an essential condition for defining by equations the least prefixed point. We stress the interplay between closed Structures and fixed point operators by showing that the theory of Boolean modal µ-algebras is not a conservative extension of the theory of modal µ-algebras. The latter is shown to lack the finite model property.