PKAT drops the law of non-contradiction and excluded middle for tests, and two examples from twisted Heyting algebras are shown to form PKATs.
Backhouse, Dexter Kozen & Bernhard M¨ oller (20 02): Applications of Kleene Algebra (Dagstuhl Seminar 01081)
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Paraconsistent Relations as a Variant of Kleene Algebras
PKAT drops the law of non-contradiction and excluded middle for tests, and two examples from twisted Heyting algebras are shown to form PKATs.