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Communication Dans Un Congrès Année : 2005

Completions of μ-algebras

Résumé

We define the class of algebraic models of μ-calculi and study whether every such model can be embedded into a model which is a complete lattice. We show that this is false in the general case and focus then on free modal μ-algebras, i.e. Lindenbaum algebras of the propositional modal μ-calculus. We prove the following fact: the MacNeille-Dedekind completion of a free modal μ-algebra is a complete modal algebra, hence a modal μ-algebra (i.e. an algebraic model of the propositional modal μ-calculus). The canonical embedding of the free modal μ-algebra into its Dedekind-MacNeille completion preserves the interpretation of all the terms in the class Comp(Σ1,Π1) of the alternation-depth hierarchy. The proof uses algebraic techniques only and does not directly rely on previous work on the completeness of the modal μ-calculus.
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Dates et versions

hal-01288855 , version 1 (15-03-2016)

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Luigi Santocanale. Completions of μ-algebras. 20th IEEE Symposium on Logic in Computer Science, Jun 2005, Chicago, United States. pp.219--228, ⟨10.1109/LICS.2005.11⟩. ⟨hal-01288855⟩
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