Residuation algebras with functional duals

Wesley Fussner*, Alessandra Palmigiano

*Corresponding author for this work

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We employ the theory of canonical extensions to study residuation algebras whose associated relational structures are functional, i.e., for which the ternary relations associated to the expanded operations admit an interpretation as (possibly partial) functions. Providing a partial answer to a question of Gehrke, we demonstrate that functionality is not definable in the language of residuation algebras (or even residuated lattices), in the sense that no equational or quasi-equational condition in the language of residuation algebras is equivalent to the functionality of the associated relational structures. Finally, we show that the class of Boolean residuation algebras such that the atom structures of their canonical extensions are functional generates the variety of Boolean residuation algebras.

Original languageEnglish
Article number40
Pages (from-to)1-10
Number of pages10
JournalAlgebra Universalis
Issue number4
Early online date10 Sept 2019
Publication statusPublished - Dec 2019


FundersFunder number
Horizon 2020 Framework Programme670624


    • Canonical extensions
    • Definability of functionality
    • Residuation algebras


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