Closing the Loop: How Semantic Closure Enables Open-Ended Evolution

This manuscript explores the evolutionary emergence of semantic closure -- the self-referential mechanism through which symbols actively construct and interpret their own functional contexts -- by integrating concepts from relational biology, physical biosemiotics, and ecological psychology into a unified computational enactivism framework. By extending Hofmeyr's (F, A)-systems -- a continuation of Rosen's (M, R)-systems -- with temporal parametrization and multiscale causality, we develop a model capable of capturing critical life properties, including autopoiesis, anticipation, and adaptation. We then establish a formal equivalence between our extended (F, A)-systems and swarms of communicating automata, resolving self-referential challenges concerning the realizability of relational models. Our stepwise model traces the evolution of semantic closure from simple reaction networks that recognize regular languages to self-replicating chemical systems with memory and anticipatory capabilities, identifying self-reference as necessary for robust self-replication and open-ended evolution. Such a computational enactivist perspective underscores the essential necessity of implementing symbol-matter transformations into computing architectures, providing a cohesive theoretical basis for a recently proposed trialectic between autopoiesis, anticipation, and adaptation to solve the problem of relevance realization. Thus, our work opens pathways to new models of computation for life, agency and cognition, offering fundamental principles underlying biological information processing.