MENS is a bio-inspired model for higher level cognitive systems; it is an application of the Memory Evolutive Systems developed with Vanbremeersch to model complex multi-scale, multi-agent self-organized systems, such as biological or social systems. Its development resorts to an info-computationalism: first we characterize the properties of the human brain/mind at the origin of higher order cognitive processes up to consciousness and creativity, then we ‘abstract’ them in a MENS mathematical model for natural or artificial cognitive systems. The model, based on a ‘dynamic’ Category Theory incorporating Time, emphasizes the computability problems which are raised.

The aim of the paper is to compare two different approaches to the modeling of complex natural systems, in particular of their hierarchical organization with higher-order structures and their emergence processes. These approaches are, respectively, the hyperstructures (HS) of Baas and the memory evolutive systems (MES) of Ehresmann and Vanbremeersch. The HS are “structural” while MES, based on category theory, take dynamics more into account. It is shown how the dynamical organization and mechanisms developed for MES rely on simple ideas of a philosophical nature, that might be disengaged from the categorical setting and extended to the general frame of HS.

The different kinds of knowledge which were connected in Natural Philosophy (NP) have been later separated. The real separation came when Physics took its individuality and developed specific mathematical models, such as dynamic systems. These models are not adapted to an integral study of living systems, by which we mean evolutionary multi-level, multi-agent, and multi-temporality self-organized systems, such as biological, social, or cognitive systems. For them, the physical models can only be applied to the local dynamic of each co-regulator agent, but not to the global dynamic intertwining these partial dynamics. To ‘revive’ NP, we present the Memory Evolutive Systems (MES) methodology which is based on a ‘dynamic’ Category Theory; it proposes an info-computational model for living systems. Among the main results: (i) a mathematical translation of the part–whole problem (using the categorical operation colimit) which shows how the different interpretations of the problem support diverging philosophical positions, from reductionism to emergentism and holism; (ii) an explanation of the emergence, over time, of structures and processes of increasing complexity order, through successive ‘complexification processes’. We conclude that MES provides an emergentist-reductionism model and we discuss the different meanings of the concept of emergence depending on the context and the observer, as well as its relations with anticipation and creativity.

This paper presents a conceptual mathematical framework for developing rich human–machine interactions in order to improve decision-making in a social organisation, S. The idea is to model how S can create a “multi-level artificial cognitive system”, called a data analyser (DA), to collaborate with humans in collecting and learning how to analyse data, to anticipate situations, and to develop new responses, thus improving decision-making. In this model, the DA is “processed” to not only gather data and extend existing knowledge, but also to learn how to act autonomously with its own specific procedures or even to create new ones. An application is given in cases where such rich human–machine interactions are expected to allow the DA+S partnership to acquire deep anticipation capabilities for possible future changes, e.g., to prevent risks or seize opportunities. The way the social organization S operates over time, including the construction of DA, is described using the conceptual framework comprising “memory evolutive systems” (MES), a mathematical theoretical approach introduced by Ehresmann and Vanbremeersch for evolutionary multi-scale, multi-agent and multi-temporality systems. This leads to the definition of a “data analyser–MES”.