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.

The need for more flexible and robust models to reason about systems in the presence of conflicting information is becoming more and more relevant in different contexts. This has prompted the introduction of paraconsistent transition systems, where transitions are characterized by two pairs of weights: one representing the evidence that the transition effectively occurs and the other its absence. Such a pair of weights can express scenarios of vagueness and inconsistency. This paper establishes a foundation for a compositional and structured specification approach of paraconsistent transition systems, framed as paraconsistent institution. The proposed methodology follows the stepwise implementation process outlined by Sannella and Tarlecki.