Modal MTL-algebras

Authors:
W. Morton;C. J. Van Alten
Affiliations:
Department of Mathematics, University of Johannesburg, PO Box 524, Auckland Park 2006, South Africa;School of Computer Science, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050, South Africa
Venue:
Fuzzy Sets and Systems
Year:
2013

Citing 4
Cited 0

Linear logic

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Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Volume 151

Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Volume 151
Algebraic and proof-theoretic characterizations of truth stressers for MTL and its extensions

Fuzzy Sets and Systems

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Abstract

A modal MTL-algebra is an algebra in the variety generated by the modal MTL-chains-linearly ordered commutative, bounded, integral, residuated lattices equipped with a unary order-preserving operation. Reverse modal MTL-algebras can be defined similarly by equipping a unary order-reversing operation instead. We axiomatize the variety of (reverse) modal MTL-algebras. Two constructions are considered on (reverse) modal MTL-chains: the MacNeille completion of the underlying order and a finite embeddability construction. In both cases we define a suitable extension of the unary order-preserving (-reversing) operation. Properties preserved via these constructions are investigated using approximations. In particular, a large class of identities preserved by each of the constructions is described syntactically.