NDLI: Completions of /spl mu/-algebras

Content Provider	IEEE Xplore Digital Library
Author	Santocanale, L.
Copyright Year	2005
Description	Author affiliation: LIF, Univ. de Provence, Marseille, France (Santocanale, L.)
Abstract	We define the class of algebraic models of /spl mu/-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 /spl mu/-algebras, i.e. Lindenbaum algebras of the propositional modal /spl mu/-calculus. We prove the following fact: the MacNeille-Dedekind completion of a free modal /spl mu/-algebra is a complete modal algebra, hence a modal /spl mu/-algebra (i.e. an algebraic model of the propositional modal /spl mu/-calculus). The canonical embedding of the free modal /spl mu/-algebra into its Dedekind-MacNeille completion preserves the interpretation of all the terms in the class Comp(/spl Sigma//sub 1//spl Pi//sub 1/) 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 /spl mu/-calculus.
Starting Page	219
Ending Page	228
File Size	310595
Page Count	10
File Format	PDF
ISBN	0769522661
ISSN	10436871
DOI	10.1109/LICS.2005.11
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2005-06-26
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Lattices Equations Electronic mail Concrete Computer science Logic functions Boolean algebra
Content Type	Text
Resource Type	Article
Subject	Mathematics Software

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