Abstract
Often referred to as ‘the mathematics of dynamical, state-based systems’, Coalgebra claims to provide a compositional and uniform framework to specify, analyse and reason about state and behaviour in computing. This paper addresses this claim by discussing why Coalgebra matters for the design of models and logics for computational phenomena. To a great extent, in this domain one is interested in properties that are preserved along the system’s evolution, the so-called ‘business rules’ or system’s invariants, as well as in liveness requirements, stating that e.g. some desirable outcome will be eventually produced. Both classes are examples of modal assertions, i.e. properties that are to be interpreted across a transition system capturing the system’s dynamics. The relevance of modal reasoning in computing is witnessed by the fact that most university syllabi in the area include some incursion into modal logic, in particular in its temporal variants. The novelty is that, as it happens with the notions of transition, behaviour, or observational equivalence, modalities in Coalgebra acquire a shape. That is, they become parametric on whatever type of behaviour, and corresponding coinduction scheme, seems appropriate for addressing the problem at hand. In this context, the paper revisits Coalgebra from a computational perspective, focussing on three topics central to software design: how systems are modelled, how models are composed, and finally, how properties of their behaviours can be expressed and verified. © 2022, College Publications. All rights reserved.

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
This paper introduces a class of automata and associated languages, suitable to model a computational paradigm of fuzzy systems, in which both vagueness and simultaneity are taken as first-class citizens. This requires a weighted semantics for transitions and a precise notion of a synchronous product to enforce the simultaneous occurrence of actions. The usual relationships between automata and languages are revisited in this setting, including a specific Kleene theorem.

Abstract

Abstract
Finite-State Automata (FSA) are foundations for modelling, synthesis, verification, and implementation of controllers for manufacturing systems. However, FSA are limited to represent emerging features in manufacturing, such as the ability to recognise and switch contexts. One option is to enrich FSA with parameters that carry details about the manufacturing, which may favour design and control. A parameter can be embedded either on transitions or states of an FSA, and each approach defines its own modelling framework, so that their comparison and integration are not straightforward, and they may lead to different control solutions, modelled, processed and implemented distinctly. In this paper, we show how to combine advantages from parameters in manufacturing the modelling and control. We initially present a background that allows to understand each parameterisation strategy. Then, we introduce a conversion method that translates a design-friendly model into a synthesis-efficient structure. Finally, we use the converted models is synthesis, highlighting their advantages. Examples are used throughout the paper to illustrate and compare our results and tooling support is also provided.

Abstract
Embedding CRDT counters has shown to be a challenging topic, since their introduction in Riak Maps. The desire for obliviousness, where all information about a counter is fully removed upon key removal, faces problems due to the possibility of concurrency between increments and key removals. Previous state-based proposals exhibit undesirable reset-wins semantics, which lead to losing increments, unsatisfactorily solved through manual generation management in the API. Previous operation-based approaches depend on causal stability, being prone to unbounded counter growth under network partitions. We introduce a novel embeddable operation-based CRDT counter which achieves both desirable observed-reset semantics and obliviousness upon resets. Moreover, it achieves this while merely requiring FIFO delivery, allowing a tradeoff between causal consistency and faster information propagation, being more robust under network partitions.