Paraconsistent Relations as a Variant of Kleene Algebras

2025/06/06 by Cunha, Juliana, Madeira, Alexandre, Barbosa, Luís S.
#FOS: Computer and information sciences #Logic in Computer Science (cs.LO)

paper · doi:10.48550/arxiv.2506.05840

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.

Citations

• Twist structures and Nelson conuclei
• Monitoring electrical systems data-network equipment by means of Fuzzy\n and Paraconsistent Annotated Logic
• Generalising KAT to verify weighted computations
• Quantum Computing in the NISQ era and beyond
• On the Minimum Many-Valued Modal Logic over a Finite Residuated Lattice
• Paraconsistent Machines and their Relation to Quantum Computing
• Kleene algebra with tests

Related

• One-sorted Program Algebras
• Kleene Algebra With Tests for Weighted Programs
• A Coalgebraic Approach to Kleene Algebra with Tests
• Kleene Algebra with Dynamic Tests: Completeness and Complexity
• Feasibly Reducing KAT Equations to KA Equations