(Joint work with Peter Jipsen and Diego Valota)

Let \(\mathsf{CIdInRL}\) be the variety of commutative idempotent involutive residuated lattices. Interesting subvarieties of \(\mathsf{CIdInRL}\) include Sugihara monoids, the algebraic semantics of relevance logic \(\textsf{RM}^t\) [1]. In this talk we present some results on the structure of commutative idempotent involutive residuated lattices, resulting in a structural characterization of all finite members of \(\mathsf{CIdInRL}\).
The algebras \(\mathbf{A} \in \mathsf{CIdInRL}\) are studied by considering their monoidal reduct. For \(a, b \in A\), consider the
- A.R. Anderson and N.D. Belnap,
*Entailment. Volume I: The logic of relevance and necessity*, Princeton University Press 1975. - J. Gil-Férez and P. Jipsen and G. Metcalfe
*Structure Theorems for Idempotent Residuated Lattices*, preprint.
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