On involutive FL e -monoids

Archive for Mathematical Logic 51 (7-8):719-738 (2012)

Hiroakira Ono
Japan Advanced Institute of Science and Technology
The paper deals with involutive FL e -monoids, that is, commutative residuated, partially-ordered monoids with an involutive negation. Involutive FL e -monoids over lattices are exactly involutive FL e -algebras, the algebraic counterparts of the substructural logic IUL. A cone representation is given for conic involutive FL e -monoids, along with a new construction method, called twin-rotation. Some classes of finite involutive FL e -chains are classified by using the notion of rank of involutive FL e -chains, and a kind of duality is developed between positive and non-positive rank algebras. As a side effect, it is shown that the substructural logic IUL plus t ↔ f does not have the finite model property
Keywords FL e -algebra  Cone representation  Twin-rotation  Structural description  Classification
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DOI 10.1007/s00153-012-0295-6
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Substructural Fuzzy Logics.George Metcalfe & Franco Montagna - 2007 - Journal of Symbolic Logic 72 (3):834 - 864.
On the Structure of Rotation-Invariant Semigroups.Sándor Jenei - 2003 - Archive for Mathematical Logic 42 (5):489-514.
On the Reflection Invariance of Residuated Chains.Sándor Jenei - 2009 - Annals of Pure and Applied Logic 161 (2):220-227.

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