On involutive FLe-monoids

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

The paper deals with involutive FLe-monoids, that is, commutative residuated, partially-ordered monoids with an involutive negation. Involutive FLe-monoids over lattices are exactly involutive FLe-algebras, the algebraic counterparts of the substructural logic IUL. A cone representation is given for conic involutive FLe-monoids, along with a new construction method, called twin-rotation. Some classes of finite involutive FLe-chains are classified by using the notion of rank of involutive FLe-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.

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Hiroakira Ono
Japan Advanced Institute of Science and Technology