In the last decades, dynamic logics have been used in different domains as a suitable formalism to reason about and specify a wide range of systems. On the other hand, logics with many-valued semantics are emerging as an interesting tool to handle devices and scenarios where uncertainty is a prime concern. This paper contributes towards the combination of these two aspects through the development of a method for the systematic construction of many-valued dynamic logics. Technically, the method is parameterised by an action lattice that defines both the computational paradigm and the truth space (corresponding to the underlying Kleene algebra and residuated lattices, respectively).

The original purpose of component-based development was to provide techniques to master complex software, through composition, reuse and parametrisation. However, such systems are rapidly moving towards a level in which software becomes prevalently intertwined with (continuous) physical processes. A possible way to accommodate the latter in component calculi relies on a suitable encoding of continuous behaviour as (yet another) computational effect.This paper introduces such an encoding through a monad which, in the compositional development of hybrid systems, may play a role similar to the one played by 1+, powerset, and distribution monads in the characterisation of partial, nondeterministic and probabilistic components, respectively. This monad and its Kleisli category provide a universe in which the effects of continuity over (different forms of) composition can be suitably studied.

Abstract. This paper introduces a method to build dynamic logics with a graded semantics. The construction is parametrized by a structure to support both the spaces of truth and of the domain of computations. Possible instantiations of the method range from classical (assertional) dynamic logic to less common graded logics suitable to deal with programs whose transitional semantics exhibits fuzzy or weighted behaviour. This leads to the systematic derivation of program logics tailored to specific program classes

Motivated by the need to reason about hybrid systems, we study limits in categories of coalgebras whose underlying functor is a Vietoris polynomial one -intuitively, the topological analogue of a Kripke polynomial functor. Among other results, we prove that every Vietoris polynomial functor admits a final coalgebra if it respects certain conditions concerning separation axioms and compactness.When the functor is restricted to some of the categories induced by these conditions the resulting categories of coalgebras are even complete.As a practical application, we use these developments in the specification and analysis of nondeterministic hybrid systems, in particular to obtain suitable notions of stability, and behaviour.

Abstract. Adding to the modal description of transition structures the ability to refer to specific states, hybrid(ised) logics provide an interesting framework for the specification of reconfigurable systems. The qualifier 'hybrid(ised)' refers to a generic method of developing, on top of whatever specification logic is used to model software configurations, the elements of an hybrid language, including nominals and modalities. In such a context, this paper shows how a calculus for a hybrid(ised) logic can be generated from a calculus of the base logic and that, moreover, it preserves soundness and completeness. A second contribution establishes that hybridising a decidable logic also gives rise to a decidable hybrid(ised) one. These results pave the way to the development of dedicated proof tools for such logics used in the design of reconfigurable systems.

Hybrid computation harbours discrete and continuous dynamics in the form of an entangled mixture, inherently present in various natural phenomena and in applications ranging from control theory to microbiology. The emergent behaviours bear signs of both computational and physical processes, and thus present difficulties not only in their analysis, but also in describing them adequately in a structural, well-founded way.In order to tackle these issues and, more generally, to investigate hybridness as a dedicated computational phenomenon, we introduce a while-language for hybrid computation inspired by the fine-grain call-by-value paradigm. We equip it with operational and computationally adequate denotational semantics. The latter crucially relies on a hybrid monad supporting an (Elgot) iteration operator that we developed elsewhere. As an intermediate step, we introduce a more lightweight duration semantics furnished with analogous results and based on a new duration monad that we introduce as a lightweight counterpart to the hybrid monad. CCS CONCEPTS• Theory of computation → Timed and hybrid models.

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