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Advances in the theory of μŁΠ algebras

AuthorsMarchioni, Enrico; Spada, Luca
KeywordsReal closed fields
Free algebras
Computational complexity
Issue Date2011
PublisherOxford University Press
CitationLogic Journal of the IGPL 19: 476- 489 (2011)
AbstractRecently an expansion of ŁΠ1/2 logic with fixed points has been considered [23]. In the present work we study the algebraic semantics of this logic, namely μŁΠ algebras, from algebraic, model theoretic and computational standpoints. We provide a characterisation of free μŁΠ algebras as a family of particular functions from [0,1]n to [0,1]. We show that the first-order theory of linearly ordered μŁΠ algebras enjoys quantifier elimination, being, more precisely, the model completion of the theory of linearly ordered ŁΠ1/2 algebras. Furthermore, we give a functional representation of any ŁΠ1/2 algebra in the style of Di Nola Theorem for MV-algebras and finally we prove that the equational theory of μŁΠ algebras is in PSPACE. © The Author 2010. Published by Oxford University Press. All rights reserved.
Identifiersdoi: 10.1093/jigpal/jzp089
issn: 1367-0751
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