Paraconsistent Relations as a Variant of Kleene Algebras
Juliana Cunha, Alexandre Madeira, Luís Soares Barbosa · Electronic Proceedings in Theoretical Computer Science · 2025
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, Set P (T ) and Rel P (K, T ), parametric on a class of twisted structures K and T .We believe this sort of structures, for their huge flexibility, have an interesting application potential.