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arXiv · 2506.05840

Paraconsistent Relations as a Variant of Kleene Algebras

Juliana Cunha·Alexandre Madeira·Luís S. Barbosa
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Abstract

Kleene algebras (KA) and Kleene algebras with tests (KAT) provide an algebraic framework to capture the behavior of conventional programming constructs. This paper explores a broader understanding of these structures, in order to enable the expression of programs and tests yielding vague or inconsistent outcomes. Within this context, we introduce the concept of a paraconsistent Kleene Algebra with tests (PKAT), capable of capturing vague and contradictory computations. Finally, to establish the semantics of such a structure, we introduce two algebras parametric on a class of twisted structures. We believe this sort of structures, for their huge flexibility, have an interesting application potential.

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Juliana Cunha, Alexandre Madeira, Luís S. Barbosa. 2025-06-06. Paraconsistent Relations as a Variant of Kleene Algebras. https://doi.org/10.4204/eptcs.421.8

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