The structural operational semantics approach to the dynamic meaning of formal models has been immensely influential as a foundation of both theoretical calculi and practical programming languages, and is a viable alternative to automata-oriented approaches. We report on an effort to apply the approach to cellular automata, in particular of the two-dimensional, regular finite grid kind that underlies many agent-based simulation models. We summarize previous, intensively category-theoretic work in more general terms, and discuss how various interesting properties are made (more) explicit by the semantical analysis of cellular automata in terms of novel mathematical structures.
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