Residuation algebras with functional duals

Wesley Fussner*, Alessandra Palmigiano

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

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Abstract

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
Volume80
Issue number4
Early online date10 Sept 2019
DOIs
Publication statusPublished - Dec 2019

Funding

FundersFunder number
Horizon 2020 Framework Programme670624

    Keywords

    • Canonical extensions
    • Definability of functionality
    • Residuation algebras

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