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Advances in the theory of μŁΠ algebras

Advances in the theory of μŁΠ algebras
Advances in the theory of μŁΠ algebras
Recently 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.
Algebras, Computational complexity, Free algebras, Real closed fields
1367-0751
476-489
Marchioni, Enrico
729c9984-5949-438e-8de7-0e079bdb9f96
Spada, Luca
4415d309-b8a3-45a8-a092-af076192100d
Marchioni, Enrico
729c9984-5949-438e-8de7-0e079bdb9f96
Spada, Luca
4415d309-b8a3-45a8-a092-af076192100d

Marchioni, Enrico and Spada, Luca (2011) Advances in the theory of μŁΠ algebras. Journal of IGPL, 19 (3), 476-489. (doi:10.1093/jigpal/jzp089).

Record type: Article

Abstract

Recently 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.

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More information

e-pub ahead of print date: 17 January 2010
Published date: June 2011
Keywords: Algebras, Computational complexity, Free algebras, Real closed fields

Identifiers

Local EPrints ID: 416725
URI: http://eprints.soton.ac.uk/id/eprint/416725
ISSN: 1367-0751
PURE UUID: 95fe1ca4-08f4-4a06-999a-167e264424e3

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Date deposited: 05 Jan 2018 17:30
Last modified: 06 Oct 2020 23:53

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