Paraconsistent Relations as a Variant of Kleene Algebras
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915330844000256 |
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| author | Cunha, Juliana Madeira, Alexandre Barbosa, Luís S. |
| author_facet | Cunha, Juliana Madeira, Alexandre Barbosa, Luís S. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_05840 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Paraconsistent Relations as a Variant of Kleene Algebras Cunha, Juliana Madeira, Alexandre Barbosa, Luís S. Logic in Computer Science 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. |
| title | Paraconsistent Relations as a Variant of Kleene Algebras |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2506.05840 |