Operational semantics is a fundamental approach to the formalisation of programming languages and almost a standard when it comes to agent-oriented programming languages. It helps ensure the correctness of interpreters, facilitates their implementation, and supports proofs of important properties. Multi-agent oriented systems are a particular kind of distributed systems and through the semantics of agent languages, operational semantics ended up playing an important role towards ensuring their desired behaviour, even though the operational semantics becomes more involved than originally intended. This work presents a new style for the operational semantics of systems with multiple levels of abstractions (such as multi-agent systems), by providing multi-level transitions (i.e., multiple hierarchical transition systems) with vertical (i.e., inter-level) integrity constraints to ensure consistency of interrelated transitions.
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