We propose a mathematical semantics for event-based architectures that serves two main purposes: to characterise the modularisation properties that result from the algebraic structures induced on systems by this discipline of coordination; and to further validate and extend the categorical approach to architectural modelling that we have been building around the language CommUnity with the 'implicit invocation', also known as 'publish/subscribe' architectural style. We then use this formalisation to bring together synchronous and asynchronous interactions within the same modelling approach. We see this effort as a first step towards a form of engineering of architectural styles. Our approach adopts transition systems extended with events as a mathematical model of implicit invocation, and a family of logics that support abstract levels of modelling.
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