Abstract
In this paper we discuss the incompatibility between the notions of validity and impreciseness in the context of Dynamic Logics. To achieve that we consider the Lukasiewicz action lattice and its interval counterpart, we show how some validities fail in the context of intervals. In order to capture the properties of action lattices that remain valid for intervals we propose a new structure called Quasi-action Lattices which generalizes action lattices and is able to model both: The Lukasiewicz action lattice, L, and its interval counterpart, (sic). The notion of graded satisfaction relation is extended to quasi-action lattices. We demonstrate that, in the case of intervals, the relation of graded satisfaction is correct (cf. Theorem 3) with respect to the graded satisfaction relation on the Lukasiewicz action lattice. Although this theorem guarantees that satisfiability is preserved on intervals, we show that validity is not. We propose, then, to weaken the notion of validity on action lattices to designated validity on quasi-action lattices. In this context, Theorem 4 guarantees that the dynamic formula which are valid with respect to L will be designated valid with respect to (sic).

Abstract
Multi-agent Dynamic Epistemic Logic, as a suitable modal logic to reason about knowledge evolving systems, has emerged in a number of contexts and scenarios. The agents knowledge in this logic is simply characterised by valuations of propositions. This paper discusses the adoption of other richer structures to make these representations, as graphs, algebras or even epistemic models. This method of building epistemic logics over richer structures is called "Epistemisation". On this view a parametric method to build such Epistemic Logics with Public Announcements is introduced. Moreover, a parametric notion of bisimulation is presented, and the modal invariance of the proposed logics, with respect to this relation, are proved. Some interesting application horizons opened with this construction are stated.

Abstract
We propose (formula presented) -logic as a formal foundation for the specification and development of event-based systems with local data states. The logic is intended to cover a broad range of abstraction levels from abstract requirements specifications up to constructive specifications. Our logic uses diamond and box modalities over structured actions adopted from dynamic logic. Atomic actions are pairs where e is an event and (formula presented) a state transition predicate capturing the allowed reactions to the event. To write concrete specifications of recursive process structures we integrate (control) state variables and binders of hybrid logic. The semantic interpretation relies on event/data transition systems; specification refinement is defined by model class inclusion. For the presentation of constructive specifications we propose operational event/data specifications allowing for familiar, diagrammatic representations by state transition graphs. We show that (formula presented) -logic is powerful enough to characterise the semantics of an operational specification by a single (formula presented) -sentence. Thus the whole development process can rely on (formula presented) -logic and its semantics as a common basis. This includes also a variety of implementation constructors to support, among others, event refinement and parallel composition. © The Author(s) 2019.

Abstract
Fuzziness, as a way to express imprecision, or uncertainty, in computation is an important feature in a number of current application scenarios: from hybrid systems interfacing with sensor networks with error boundaries, to knowledge bases collecting data from often non-coincident human experts. Their abstraction in e.g. fuzzy transition systems led to a number of mathematical structures to model this sort of systems and reason about them. This paper adds two more elements to this family: two modal logics, framed as institutions, to reason about fuzzy transition systems and the corresponding processes. This paves the way to the development, in the second part of the paper, of an associated theory of structured specification for fuzzy computational systems.

Abstract
Modelling complex information systems often entails the need for dealing with scenarios of inconsistency in which several requirements either reinforce or contradict each other. In this kind of scenarios, arising e.g. in knowledge representation, simulation of biological systems, or quantum computation, inconsistency has to be addressed in a precise and controlled way. This paper generalises Belnap-Dunn four-valued logic, introducing paraconsistent transition systems (PTS), endowed with positive and negative accessibility relations, and a metric space over the lattice of truth values, and their modal logic.

Abstract
We extend hybrid dynamic logic with binders (for state variables) by distinguishing between observable and silent transitions. This differentiation gives rise to two kinds of observational interpretations: The first one relies on observational abstraction from the ordinary model class of a specification Sp by considering its closure under weak bisimulation. The second one uses an observational satisfaction relation for the axioms of the specification Sp, which relaxes the interpretation of state variables and the satisfaction of modal formulae by abstracting from silent transitions. We establish a formal relationship between both approaches and show that they are equivalent under mild conditions. For the proof we instantiate the previously introduced concept of a behaviour-abstractor framework to the case of dynamic logic with binders and silent transitions. As a particular outcome we provide an invariance theorem and show the Hennessy-Milner property for weakly bisimilar labelled transition systems and observational satisfaction. In the second part of the paper we integrate our results in a development methodology for reactive systems leading to two versions of observational refinement. We provide conditions under which both kinds of refinement are semantically equivalent, involving implementation constructors for relabelling, hiding, and parallel composition.