Categorical logics for contravariant simulations, partial bisimulations, modal refinements and mixed transition systems

Covariant-contravariant simulation and conformance simulation generalize plain simulation and try to capture the fact that it is not always the case that “the larger the number of behaviors, the better”. We have previously studied some of their properties, showing that they can be presented as particular instances of the general notion of categorical simulation developed by Hughes and Jacobs and constructing the axiomatizations of the preorders defined by the simulation relations and their induced equivalences. We have also studied their logical characterizations and in this paper we continue with that study, presenting them as instantiations of the categorical results on simulation logics by Cı̂rstea. In addition, we continue exploring, now in this categorical framework, the relationship between covariant-contravariant simulation, partial bisimulation over labeled transition systems, refinement over modal transition systems and mixed transition systems.