Formalization of the conceptual framework of spatial systems

The work formalizes the phenomenon of Conceptual Frameworks of Spatial Systems. It is preceded by the conceptualization of the same phenomenon, but for a narrower class of classical Atlas Systems. Formalization is needed for several reasons. The first is the use of Conceptual Frameworks in the creation of System Cartography and, in particular, Model-Based Cartography as a new system paradigm of cartography and as a specialization of Model-Based Engineering. The second is the simplification of implementation, since formalized designs are easier to implement by means of informatics. The third is the possibility of using inductive inferences by researchers with experience different from ours. This article first describes the formalized constructions of levels and strata of the Conceptual Framework of Spatial Systems. At the same time, to formalize the concept of strata, the concept is used even more widely than Spatial Systems. This is the so-called Science of information systems, which is of great importance for understanding the essence of both research and design of system subjects X. After that, the practically applicable constructions of the layers of the Conceptual Framework of Atlas or Spatial Systems are obtained by analogy. The indicated three reasons are satisfied by considering the formalizations of the Conceptual Framework relevant today from the point of view of three disciplines: 1) cartography, 2) computer science, 3) systemology. In cartography, analogies important for modern practice are made with the formal model of the McKinney-Schneider Carto-Framework map in the 2016 monograph. In computer science - with Concepts of software stability in the presentation of the 2015 monograph. In systemology - with Clear's Universal System Problem Solver, which is still relevant in our time. At the end, opinions are expressed regarding the applicability of the Conceptual Framework of subjects X to the classification of Spatial Activity Systems, if Cartography in general or System Cartography in particular are presented as such. Keywords: Conceptual Framework of Atlas or Spatial Systems (AtS/PrS) in the extended sense (AtSsh/PrSsh), Infrastructure of AtSh/PrSsh (PrS/PrSsh), formalization of the AtSsh/PrSsh Conceptual Framework.