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Paraconsistent transition structures: compositional principles and a modal logic

Published online by Cambridge University Press:  04 July 2025

Juliana Cunha ,
Alexandre Madeira Open the ORCID record for Alexandre Madeira [Opens in a new window]  and
Luis S. Barbosa
Juliana Cunha
Affiliation:
CIDMA, University of Aveiro, Aveiro, Portugal HASLab INESC-TEC, University of Minho, Braga, Portugal
Alexandre Madeira*
Affiliation:
CIDMA, University of Aveiro, Aveiro, Portugal
Luis S. Barbosa
Affiliation:
HASLab INESC-TEC, University of Minho, Braga, Portugal
*
Corresponding author: Alexandre Madeira; Email: madeira@ua.pt
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Abstract

Often in Software Engineering, a modeling formalism has to support scenarios of inconsistency in which several requirements either reinforce or contradict each other. Paraconsistent transition systems are proposed in this paper as one such formalism: states evolve through two accessibility relations capturing weighted evidence of a transition or its absence, respectively. Their weights come, parametrically, from a residuated lattice. This paper explores both i) a category of these systems, and the corresponding compositional operators and ii) a modal logic to reason upon them. Furthermore, two notions of crisp and graded simulation and bisimulation are introduced in order to relate two paraconsistent transition systems. Finally, results of modal invariance, for specific subsets of formulas, are discussed.

Keywords

Paraconsistent transition systemsparaconsistent logicmodal logicsimulationbisimulation

Information

Type
Special issue: LSFA 2021 and LSFA 2022
Information
Mathematical Structures in Computer Science , Volume 35 , 2025 , e14
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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