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Cognition of Ontology of Open Systems
Available online at www.sciencedirect.com
ScienceDirect Procedia Computer Science 103 (2017) 339 – 346
XIIth International Symposium «Intelligent Systems», INTELS’16, 5-7 October 2016, Moscow, Russia
Cognition of ontology of Open Systems B. Fomin, T. Kachanova* Saint Petersburg Electrotechnical University “LETI”, 5, Prof. Popova street, Saint-Petersburg, 197376, Russia
Abstract Physics of Open Systems (POS) offers its own approach to cognition, scientific understanding and rational explanation of the phenomenon of complexity inherent in open natural, social and anthropogenic systems. On the basis of POS the deep analytics of systems considered in their natural scales and real complexity is being carried out. POS technologies automatically extract reliable scientific knowledge about systems from large set of heterogeneous empirical data. In this paper, a scientific review of technology of system reconstructions is given. That is a key technology of the analytical core of POS, and that provides automatic generation of scientific knowledge about ontology of open systems without resorting to expert knowledge. © 2017 The TheAuthors. Authors.Published Published Elsevier © 2017 by by Elsevier B.V.B.V. This is an open access article under the CC BY-NC-ND license Peer-review under responsibility of the scientific committee of the XIIth International Symposium «Intelligent Systems». (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the XIIth International Symposium “Intelligent Systems” Keywords: physics of open systems; knowledge generation; big data; technology of system reconstruction
1. Introduction 1.1. Physics of Open Systems Open systems possess fundamental complexity. Fundamental laws which are not yet known to science govern the organization and existence of the open systems1. Empirical science has created “Big Data” regarding open systems. Accumulated empirical material is obtained from diverse sources, it has a large volume, is heterogeneous and poorly structured. It is necessary to have a well-developed theory for generating knowledge about open systems directly from empirical data. Such theory has been proposed within the frame of interdisciplinary branch “Physics of Open Systems” (POS). Formation and development of this theory led to the appearance of a new paradigm of systemology
* Corresponding author. E-mail address: [email protected]; [email protected]
1877-0509 © 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the XIIth International Symposium “Intelligent Systems” doi:10.1016/j.procs.2017.01.119
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of the open systems2,3. Creation of a new paradigm became possible due to solving of the general problem of reconstructive analysis of open systems on the empirical descriptions. What follows below is considered as a basis of this solution4,5,6,7: x methodological foundations: logically complete system of concepts that express the cognition paradigm conception of the open systems' ontology in the context of integrity and holism; x metatechnology: conception of cognition paradigm of the open systems' ontology that is embodied in the normative language of these systems; x constructive theory: methods to generate concepts (as the formal objects of theory) of normative language of the open systems; x algorithms of mapping the objects of constructive theory into adequate concrete representations of the scientifically proven ontology. 1.2. Reconstructive analysis Idea of the solution is shown in Fig. 1. Representations of the system on different epistemological levels occur when solving dialectical contradiction “Part - Whole” is done. This contradiction is specially detailed on each turn of “cognition spiral”4. An initial empirical description of the system is given at zero epistemological level (system in data). Initial abstract representation of the system (system in relations) is being created at the first turn (“Abstraction”). Abstraction of the 1-th level has the pre-image in reality, is genetically associated with the phenomenon, and embodies (in itself) the system-wide regularities of the phenomenon being studied. Self-organization of the system is cognized and one’s inner symmetries are revealed at the second turn (“Reconstruction”). Abstraction of the 2-th level represents the system as a multiqualitative essence (system in qualities). 1 Self-expression of the system in phenomenon
Forms of implementation 3 Symmetries of doublets and triplets Implementation
Basic interactions
System in qualities Symmetry of singleton
2
Reconstruction System in relations
System-forming interaction
1
Consistency of values Abstraction Correlativity
System in data
0
0 Phenomenon and denotatum of the system
Slice of reality Pre-image of system
Fig. 1. Constructive-methodological model of the system.
It is being formed in each own qualitative definiteness as an integral whole arising from two opposites in the result of system-forming interaction. Image of phenomenon of the system considered as an integrated whole consisting of the parts (qualities) is reconstructed at the third turn (“Implementation”).
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For each system qualitative definiteness (specific feature), all variety of its manifestation forms is given by abstraction of the 3-th level. Ideal forms of system existence come into being on this level. An ability of the system to generate an actual and potential variability is related to these forms. Determining the mechanisms of generating variability in the limits of each of possible forms is being realized through basic interactions revealed in the given turn. By execution of these three spiral turns, the gnoseological level of system's cognition is being exhausted and the dialectical contradiction "One - Many" is resolved at this level. Spiral of cognition is explained by the structural-logical schema. The system is represented in three complete forms: x system in relations (substantial projection of the whole that is made up of the parts obtained independently, namely, of attributed binary relations between parameters); x system in qualities (spectrum of complete system units having main axial symmetry); x system in forms of implementation (systematics of structures and states – it reveals higher differentiation of qualitatively different forms mapping the system's variability). The common ideas about solving heterogeneities inherent in the system are expressed by predicates of harmonization, i.e. “system axioms”: x x x x
pre-image axiom (phenomenon serves as an empirical basis of the system); first axiom (states the fact of consistent variability of macro-values in the system); second axiom (establishes the role definiteness of macro-values); third axiom (sets the requirements providing an implementation of mechanisms of inner orientation in the system). Measures listed below define the properties of the system in each of its representation:
x abstraction measures (information contained in totality of macro-values of the system, about "the many" is being transformed into information about "the one", which is representing the system as a structure of binary relations with associated behavior attribute); x reconstruction measures (discovering all the variety of both qualitative definitenesses and stereotypes of behavior of the system); x implementation measures (characterization of the external forms of manifesting stereotypes of system’s behavior within the limits of reality forming them). The following symmetries are the tool of inductive inference of the system's concept: x symmetry of singletons (generates all kinds of system units of the whole); x symmetries of doublets (reveal senses of role contingency of parameters); x symmetries of triplets (establish the types of orientation of initial system units named singletons). Polyadic relations having characteristic symmetry as well as abstract forms (i.e. referents of deep system senses) act as semantic constructs of both the qualities and implementation forms of the system. Structural invariants and full set of states of the system define the following: x two-factor interaction (sets a mode of existence of phenomenon of the system); x basic interactions (produce all external forms of variability of the system and manifest higher universal mechanisms of its self-motion). The technology of ontology cognition of the system may be represented as a techno-cube (an image of this technology), see Fig. 2. The first dimension of the techno-cube represents the system as a whole, in parts and in elements. The second dimension defines the subjects of cognition (parameters, relations structures, states). The third
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dimension reveals steps of cognition (schema, type, and image).
Parameters Structures States
Whole
Part
Schema
Empirical, statistical, and structural portraits
Type
System portraits of type and type’s forms
Image
Realistic portrait
Concrete
Fig. 2. Techno-cube of system reconstructions.
The space of techno-cube is filled with elements of ontological knowledge. For them, six normative formats of representation (portraits of the system) are established. 2. A model of system reconstructions A model of system reconstructions (MSR) represents the result of system ontology cognition in concepts that are mapped onto the categories “Representation” and “Expression”, see Tab. 1. Qualities of the system are revealed as a result of the transformation of the empirical fact into the system fact. Each system quality taken separately is concrete, homogeneous and unique. The totality of the system qualities reveals the system complexity. Models of interaction describe one-factor, two-factor and multifactorial systemforming interactions. Each interaction, taken separately, refers to certain part of the system and “builds” this part. Behavior components determine semantic space of the system (space of qualities). The structure of this space is defined by the ideal states of the system and the range of their variability. Potentials of actualization evaluate the possibility of transferring the senses of certain qualities of the system onto the empirical fact. Resolved heterogeneities lead to determining the organization of space of qualities of the system. Also they lead to assessing the ability of the family of interaction models to explain multiplicity of the forms of parameters variability of the system states, and their multi-difference and evolution. System layout gives a complete image of the system being considered as a whole in all of its semantic aspects. The degree of implementation of the system senses, which are manifested in an abstract schematic system image and revealed by the behavior components, is evaluated in this layout. Table 1. Model of system reconstruction. Levels of “Expression” category
Levels of “Representation” category Whole
Whole
Whole
Initial abstract representation
Parameters of state
Empirical fact
Type
Behavior components
Models of interactions
Qualities of system
Image
Layout of system
Resolved heterogeneities
Potentials of actualization
Schema
MSR serves as a base for developing the processes, stages, key objects and main attributes of the objects of the technology of system reconstructions (TSR) of POS.
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3. Objects of TSR Objects of TSR transfer knowledge about an open system. This knowledge is obtained at the different cognitive stages of ontology of the system. The key objects of the technology are: system in data (SD); connection graph (CG); system models (SM); stratified graphs (SG); realistic singletons (RS). 3.1. System in data The concept “Variable” (empirical fact) corresponds to the object SD. The SD is a table “Object - Property”. Rows of the table (objects) are the actual states of the system being studied. Columns of the table (properties) are the parameters of the system's state and system's environment. The SD determines an attribute space of the system. The parameters of the system are the coordinates of this space. Each parameter is represented by a sampling distribution of its values. Points of the space set actual states of the system. The metric of the space is not defined. Points of the space are being perceived as unstructured entities. The SD reflects heterogeneous nature of an open system. Points of the space of attributes characterize a variety of typical and special states of the system. The aim of study of the system's complexity on the basis of its representation in data is a deep analysis of the variability of the parameters with respect to which an ability to manifest outwardly this variety should be assumed. Assessment of such ability characterizes the quality of the empirical fact. 3.2. Connection graph The concept “Schema” of a model of system reconstruction corresponds to the technology object named CG, in which an open system gets the initial abstract representation in the form of a structure of binary relationships between parameters of the SD. Each relationship in this structure has a sign. CG represents the system as an integrated and schematized whole that is manifesting outwardly hidden regularities determining the system states. All the variety of multiple large-scale intra-system correlations manifesting themselves through binary relationships of parameters is reflected in the CG. CG is a schematic representation of a heterogeneous system but it is not the system. Here the information about the system states is in itself absent. The system complexity is hidden in signed out-of-balance conditions of the CG. 3.3. System models The concept “Type” corresponds to the SM object. Through the SM and in the context of holism, the following issues occur: a multi-qualitative essence of the system is being revealed, unique qualities of the system are being expressed, and a variety of intra-system interactions forming the unity of the system whole is being defined. SM are formal descriptions of intra-system mechanisms. The mechanisms create ideal types and multi-various forms of nonideal forms of the system states. Each SM describes a system-forming mechanism of the concrete unique quality and includes the following: a determinative singleton (integral image of the given quality); a core (attraction domain of quality); factors (spread area of quality). Each SM is responsible for the self-development of qualitative definitenesses of the system. The model has a fixed structure and a fixed sense of a concrete mechanism of systemogenesis. Each SM is defined in its own subspace of the space of qualities of the system. Parameters of the determinative singleton, core and factors of the model are the coordinates of this subspace. All subspace coordinates are measured on the scale of levels of parameter values. All such scales have one and the same type. Forms of manifestation of the system in the given quality are the points of the subspace. Each point has a structure (model of a form of type) and content (multiple interactions mechanisms corresponding to this form of type). The given subspace has no metric. A complete set of SM forms a complete space of the system qualities which expresses the changing system whole. The SM reveal a complexity inherent in the system (multiplicity of qualities) through building a complete set of qualitative definitenesses of the system and a complete set of interactions models which are responsible for the self-development of the system as a whole and in each of its quality. The degree of revealing the complexity is being evaluated by the composition of the set of SM, by the completeness of each model’s organization, the measure of inner heterogeneity and the level of heterogeneity explanation by mechanisms of self-
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development. 3.4. Stratified graphs The mapping “Type → Schema” corresponds to the object of TSR named SG. An initial abstract representation of the system in each SG reveals disclosed qualities of the system. Each parameter with its structure of binary relations that is specified by the CG is represented in its own SG by a complete set of the models of particular system mechanisms which determine the variability of the parameter. Parameter variability manifested through the structure and attributes of CG is being revealed in diversity of its forms by way of a set of discovered system mechanisms participating in the formation of this variability with different intensity. The following characteristics are defined for each parameter: the number and the set of mechanisms, and the participation and role of each parameter in each mechanism. A schematic integrated representation of the system by the CG unfolds in complete set of stratified bigraphs. The integrated representations of parameters (concatenation of binary relations) in them are divided into semantic components. Each component is related to certain particular system mechanism. An aggregate of all the particular mechanisms is represented by multiple correlations of parameters. Each SG is used to evaluate the variety of system mechanisms that determine the variability of certain selected parameter for which this SG is built. For each parameter of the system, the sufficiency degree of the revealed system qualities is established through the given object of TSR in order to cognize a multiplicity of forms of the parameter variability. 3.5. Realistic singletons The mapping “Type → Variable” corresponds to the object “RS”. Feedback of the revealed unique qualitative definitenesses of the system with its empirical description is implemented through this object. A singleton, as an element of the space of qualities of the system, is associated with the points of the space of attributes of the system, herewith, providing respective objects of observation (actual states of the system) with concrete qualitative definiteness. RS has the mapping in the attribute space of the system. The inner complexity (heterogeneity) of SM expressing qualities of the system is evaluated by the level of concordance between qualities of the system and points of the attribute space. Each quality of the system is a homogeneous entity. The quality should be represented in the attribute space by all of its singletons. Each singleton of this quality should be associated with one and the same set of observation objects in the attribute space. 4. Functionality of TSR Objects of TSR represent the complex system as the whole in different forms of representation on the three stages of cognition of the system's senses (system in data, system in relations, and system in qualities), see Fig. 3. 3 System models
System in qualities
1 System in relations
2
System in data
2
Сonnection 2 graph
Stratified graphs
1 System in data
2
Realistic singletons
Fig. 3. Functional description of the technology: 1 – ascension from the fact to the sense (cognition of ontology); 2 – descent from the sense to the fact (testing of symbolic forms of the knowledge by the fact); 3 – transition to understanding.
In the first step of the ascension from the fact to the sense the system is treated as an isolated one. The limitations on the number of parameters (completeness of system description) and the number of states (representativeness of
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system description) are not imposed. The hypothesis that the system in data represents the system in its natural scale and real complexity is put forward. In the second step of the ascension, the view on the system like of a totality of actual states given in the measurements is automatically transformed into a scheme in which, through binary relations, the general, inherent in the states of the system being considered as a whole, is expressed. In such view, the system complexity is transferred through the signs of binary relations. The system gets an abstract representation of its complex whole (system in relations). In the third step of the ascension, the system is represented by a complete abstract image of an integral whole consisting of interacting homogeneous parts, each of which is both the part of the whole and the organic whole in the context of this part (system in qualities). Creation of this system image finishes the ascension from the fact to the sense, and generates symbolized knowledge of ontology of the system. In the first step of the descent from the sense to the fact, the degree of completeness of the obtained symbolized knowledge through mapping the family of SM to the initial abstract representation of the system (SG) is verified. The results of the test are: an estimate of the volume of manifested system complexity; and degree of how the complexity of the system is expressed in its ontology. In the second step of the descent, the connection of system ontology with the objects of reality from the data system (RS) is being revealed. The results are: the fact of multiplicity of qualities of the system states; evaluation of the system complexity through the set of the system qualities that are manifested in observed states; test of the adequacy of the revealed senses to the empirical fact and homogeneity of semantic parts of the system. The process of scientific understanding of the revealed system senses is implemented through mapping of the symbolized knowledge onto itself. That includes the evaluation of three forms of the system's representation (system in data, system in relations and system in qualities); analysis of the inner system organization and system-forming mechanisms; and synthesis of the sense and fact. Scientific understanding of the symbolized knowledge is the task of the technology of system examination (TSE) of POS8,9. Each TSR object is characterized by a set of attributes. Various methods of theory of reconstructive analysis, measurements theory, mathematical statistics, graph theory and visualization are used in order to build up the TSR objects and to compute their attributes. Theory of reconstructive analysis is the basis of the scientific method of POS - supports all the stages of cognition of the open system's ontology; identifies characteristic system symmetries and structures of intra-system relations (singletons, doublets, triplets, SM); determines characteristics of SM (roles of both vertices and edges; sense activity and similarity); and forms the triple predicates (RS). Methods of measurements theory, mathematical statistics and graph theory provide a construction of the initial abstract representation of the system. This representation should carry all characteristics of the system's complexity, that are sufficient to reveal it by the tools of the theory of reconstructive analysis. Visualization methods are used for representing data, information and elements of knowledge in the form of plots, diagrams, structural schemas, and tables. 5. Conclusion Cognition of the system ontology is a key stage in generating ontological knowledge based on heterogeneous empirical large-scale datasets. Fundamental complexity of the system is being overcome at the cognition, and the reliable scientific knowledge is generated (about complete space of the system qualities, complete families of the CM, and the models of system-forming interactions) 3,6,8,9. The stages of both scientific understanding and rational explanation of the system ontology; and the stage of axiology study (values, fullness, completeness) of the obtained ontological knowledge - they all follow the stage of cognition 3 7 8,9. Technology of system examination (TSE) of POS automatically implements scientific understanding of the ontology. The quality, volume, and essence of obtained knowledge are evaluated in the process of understanding. Empirical description of the system; all SM; all ideal models; mappings of all regions of qualities' space of the system into its space of attributes; and completeness of the types and forms actualization of the all qualitative definitenesses of the system - all these are the subject of system examination.
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Technology of system design (TSD) of POS automatically executes rational explanation of the ontology. The explanation covers ontological knowledge about the system as a whole, ideals and states of the system. Ontology which is cognized and scientifically understood contains the reliable scientific knowledge that includes: knowledge about the system and its emergent properties; knowledge about limitations and rules of conjugacy of various qualities of the system in its actual states. TSD explains the following: properties of the parameters in each certain state of the system; properties and actual states of the system considered as a whole; mechanisms responsible for the forming a variability of each parameter and global properties of the system. The qualimetric component of the analytical core of POS carries out the study of axiology of the ontological knowledge. Application of POS technologies for generating scientifically proven ontological knowledge about open systems, is tested and proven: in system biology 10,11, in solar-terrestrial physics 12, in security and social tensity 13, and in other fields of knowledge14,15. References 1. Klir GJ. Architecture of Systems Problem Solving. Plenum Press, New York, 1985. 2. Kachanova T, Fomin B. Physics of ыystems is a postcybernetic paradigm of systemology. In: Proc. Int. Symp. “Science 2.0 and Expansion of Science: S2ES” in the context of the 14th World-Multi-Conference on Systemics, Cybernetics and Informatics WMSCI 2010, pp 244-249. 3. Kachanova T, Fomin B. Physics of open systems: generation of system knowledge. J. Systemics, Cybernetics and Informatics, 11, No 2, 73-82, 2013. 4. Kachanova TL, Fomin BF. Fundamentals of the systemology phenomenal [in Russian], Izd. SPbGETU LETI, St. Petersburg, 1999. 5. Kachanova TL, Fomin BF. The Metatechnology of system reconstructions [in Russian], Izd. SPbGETU LETI, St. Petersburg 2002. 6. Kachanova TL, Fomin BF. An Introduction to systems language [in Russian], Nauka, St. Petersburg, 2009. 7. Kachanova TL, Fomin BF. The Technology of system reconstructions [in Russian], Politekhnika, St. Petersburg, 2003. 8. Kachanova TL, Fomin BF. Methods and technologies for generating a systemic knowledge: a manual for masters and postgraduate students [in Russian], Izd. SPbGETU LETI, St. Petersburg, 2012. 9. Kachanova TL, Fomin BF. Qualitology of system knowledge: a manual for masters and postgraduate students [in Russian], Izd. SPbGETU LETI, St. Petersburg, 2014. 10. Ageev V, Fomin B, Fomin O et al. Physics of open systems: A new approach to use genomics data in risk assessment. In The Continuum of Heath Risk Assessments, InTech", 2012, pp 135-160. 11. Ageev V, Kachanova T, Kopylev L et al. Physics of open systems: The effects of the impact of chemical stressors on differential gene expression. J. Cybernetics and Systems Analysis, 50, No. 2, 2014, pp. 218-227. 12. Fomin B, Kachanova T et al. Global system reconstructions of the models of solar activity and related geospheric and biospheric effects. In: Proc. of 39th ESLAB Symposium “Trends in Space Science and Cosmic Vision 2020”, ESTEC, 2005, pp 381-384. 13. Ageev V, Araslanov A, Kachanova T et al. Generation of system knowledge on the problems of social tensity in regions of Russia, Scientific and technical sheets SPbSPU, 147, №2-1, pp 300-308, 2012. 14. Kachanova T.L. and Fomin B. F. System ontology of classes [in Russian]. ETU "LETI" Proceedings, № 7/2015, pp. 25-36. 15. Ageev V. O., Kachanova T.L., Fomin B. F., Turalchuk K.A. Natural classification of acute poisoning with organophosphorus substances [in Russian]. ETU "LETI" Proceedings, № 8/2015, pp. 8-17.
ScienceDirect Procedia Computer Science 103 (2017) 339 – 346
XIIth International Symposium «Intelligent Systems», INTELS’16, 5-7 October 2016, Moscow, Russia
Cognition of ontology of Open Systems B. Fomin, T. Kachanova* Saint Petersburg Electrotechnical University “LETI”, 5, Prof. Popova street, Saint-Petersburg, 197376, Russia
Abstract Physics of Open Systems (POS) offers its own approach to cognition, scientific understanding and rational explanation of the phenomenon of complexity inherent in open natural, social and anthropogenic systems. On the basis of POS the deep analytics of systems considered in their natural scales and real complexity is being carried out. POS technologies automatically extract reliable scientific knowledge about systems from large set of heterogeneous empirical data. In this paper, a scientific review of technology of system reconstructions is given. That is a key technology of the analytical core of POS, and that provides automatic generation of scientific knowledge about ontology of open systems without resorting to expert knowledge. © 2017 The TheAuthors. Authors.Published Published Elsevier © 2017 by by Elsevier B.V.B.V. This is an open access article under the CC BY-NC-ND license Peer-review under responsibility of the scientific committee of the XIIth International Symposium «Intelligent Systems». (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the XIIth International Symposium “Intelligent Systems” Keywords: physics of open systems; knowledge generation; big data; technology of system reconstruction
1. Introduction 1.1. Physics of Open Systems Open systems possess fundamental complexity. Fundamental laws which are not yet known to science govern the organization and existence of the open systems1. Empirical science has created “Big Data” regarding open systems. Accumulated empirical material is obtained from diverse sources, it has a large volume, is heterogeneous and poorly structured. It is necessary to have a well-developed theory for generating knowledge about open systems directly from empirical data. Such theory has been proposed within the frame of interdisciplinary branch “Physics of Open Systems” (POS). Formation and development of this theory led to the appearance of a new paradigm of systemology
* Corresponding author. E-mail address: [email protected]; [email protected]
1877-0509 © 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the XIIth International Symposium “Intelligent Systems” doi:10.1016/j.procs.2017.01.119
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B. Fomin and T. Kachanova / Procedia Computer Science 103 (2017) 339 – 346
of the open systems2,3. Creation of a new paradigm became possible due to solving of the general problem of reconstructive analysis of open systems on the empirical descriptions. What follows below is considered as a basis of this solution4,5,6,7: x methodological foundations: logically complete system of concepts that express the cognition paradigm conception of the open systems' ontology in the context of integrity and holism; x metatechnology: conception of cognition paradigm of the open systems' ontology that is embodied in the normative language of these systems; x constructive theory: methods to generate concepts (as the formal objects of theory) of normative language of the open systems; x algorithms of mapping the objects of constructive theory into adequate concrete representations of the scientifically proven ontology. 1.2. Reconstructive analysis Idea of the solution is shown in Fig. 1. Representations of the system on different epistemological levels occur when solving dialectical contradiction “Part - Whole” is done. This contradiction is specially detailed on each turn of “cognition spiral”4. An initial empirical description of the system is given at zero epistemological level (system in data). Initial abstract representation of the system (system in relations) is being created at the first turn (“Abstraction”). Abstraction of the 1-th level has the pre-image in reality, is genetically associated with the phenomenon, and embodies (in itself) the system-wide regularities of the phenomenon being studied. Self-organization of the system is cognized and one’s inner symmetries are revealed at the second turn (“Reconstruction”). Abstraction of the 2-th level represents the system as a multiqualitative essence (system in qualities). 1 Self-expression of the system in phenomenon
Forms of implementation 3 Symmetries of doublets and triplets Implementation
Basic interactions
System in qualities Symmetry of singleton
2
Reconstruction System in relations
System-forming interaction
1
Consistency of values Abstraction Correlativity
System in data
0
0 Phenomenon and denotatum of the system
Slice of reality Pre-image of system
Fig. 1. Constructive-methodological model of the system.
It is being formed in each own qualitative definiteness as an integral whole arising from two opposites in the result of system-forming interaction. Image of phenomenon of the system considered as an integrated whole consisting of the parts (qualities) is reconstructed at the third turn (“Implementation”).
B. Fomin and T. Kachanova / Procedia Computer Science 103 (2017) 339 – 346
For each system qualitative definiteness (specific feature), all variety of its manifestation forms is given by abstraction of the 3-th level. Ideal forms of system existence come into being on this level. An ability of the system to generate an actual and potential variability is related to these forms. Determining the mechanisms of generating variability in the limits of each of possible forms is being realized through basic interactions revealed in the given turn. By execution of these three spiral turns, the gnoseological level of system's cognition is being exhausted and the dialectical contradiction "One - Many" is resolved at this level. Spiral of cognition is explained by the structural-logical schema. The system is represented in three complete forms: x system in relations (substantial projection of the whole that is made up of the parts obtained independently, namely, of attributed binary relations between parameters); x system in qualities (spectrum of complete system units having main axial symmetry); x system in forms of implementation (systematics of structures and states – it reveals higher differentiation of qualitatively different forms mapping the system's variability). The common ideas about solving heterogeneities inherent in the system are expressed by predicates of harmonization, i.e. “system axioms”: x x x x
pre-image axiom (phenomenon serves as an empirical basis of the system); first axiom (states the fact of consistent variability of macro-values in the system); second axiom (establishes the role definiteness of macro-values); third axiom (sets the requirements providing an implementation of mechanisms of inner orientation in the system). Measures listed below define the properties of the system in each of its representation:
x abstraction measures (information contained in totality of macro-values of the system, about "the many" is being transformed into information about "the one", which is representing the system as a structure of binary relations with associated behavior attribute); x reconstruction measures (discovering all the variety of both qualitative definitenesses and stereotypes of behavior of the system); x implementation measures (characterization of the external forms of manifesting stereotypes of system’s behavior within the limits of reality forming them). The following symmetries are the tool of inductive inference of the system's concept: x symmetry of singletons (generates all kinds of system units of the whole); x symmetries of doublets (reveal senses of role contingency of parameters); x symmetries of triplets (establish the types of orientation of initial system units named singletons). Polyadic relations having characteristic symmetry as well as abstract forms (i.e. referents of deep system senses) act as semantic constructs of both the qualities and implementation forms of the system. Structural invariants and full set of states of the system define the following: x two-factor interaction (sets a mode of existence of phenomenon of the system); x basic interactions (produce all external forms of variability of the system and manifest higher universal mechanisms of its self-motion). The technology of ontology cognition of the system may be represented as a techno-cube (an image of this technology), see Fig. 2. The first dimension of the techno-cube represents the system as a whole, in parts and in elements. The second dimension defines the subjects of cognition (parameters, relations structures, states). The third
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dimension reveals steps of cognition (schema, type, and image).
Parameters Structures States
Whole
Part
Schema
Empirical, statistical, and structural portraits
Type
System portraits of type and type’s forms
Image
Realistic portrait
Concrete
Fig. 2. Techno-cube of system reconstructions.
The space of techno-cube is filled with elements of ontological knowledge. For them, six normative formats of representation (portraits of the system) are established. 2. A model of system reconstructions A model of system reconstructions (MSR) represents the result of system ontology cognition in concepts that are mapped onto the categories “Representation” and “Expression”, see Tab. 1. Qualities of the system are revealed as a result of the transformation of the empirical fact into the system fact. Each system quality taken separately is concrete, homogeneous and unique. The totality of the system qualities reveals the system complexity. Models of interaction describe one-factor, two-factor and multifactorial systemforming interactions. Each interaction, taken separately, refers to certain part of the system and “builds” this part. Behavior components determine semantic space of the system (space of qualities). The structure of this space is defined by the ideal states of the system and the range of their variability. Potentials of actualization evaluate the possibility of transferring the senses of certain qualities of the system onto the empirical fact. Resolved heterogeneities lead to determining the organization of space of qualities of the system. Also they lead to assessing the ability of the family of interaction models to explain multiplicity of the forms of parameters variability of the system states, and their multi-difference and evolution. System layout gives a complete image of the system being considered as a whole in all of its semantic aspects. The degree of implementation of the system senses, which are manifested in an abstract schematic system image and revealed by the behavior components, is evaluated in this layout. Table 1. Model of system reconstruction. Levels of “Expression” category
Levels of “Representation” category Whole
Whole
Whole
Initial abstract representation
Parameters of state
Empirical fact
Type
Behavior components
Models of interactions
Qualities of system
Image
Layout of system
Resolved heterogeneities
Potentials of actualization
Schema
MSR serves as a base for developing the processes, stages, key objects and main attributes of the objects of the technology of system reconstructions (TSR) of POS.
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3. Objects of TSR Objects of TSR transfer knowledge about an open system. This knowledge is obtained at the different cognitive stages of ontology of the system. The key objects of the technology are: system in data (SD); connection graph (CG); system models (SM); stratified graphs (SG); realistic singletons (RS). 3.1. System in data The concept “Variable” (empirical fact) corresponds to the object SD. The SD is a table “Object - Property”. Rows of the table (objects) are the actual states of the system being studied. Columns of the table (properties) are the parameters of the system's state and system's environment. The SD determines an attribute space of the system. The parameters of the system are the coordinates of this space. Each parameter is represented by a sampling distribution of its values. Points of the space set actual states of the system. The metric of the space is not defined. Points of the space are being perceived as unstructured entities. The SD reflects heterogeneous nature of an open system. Points of the space of attributes characterize a variety of typical and special states of the system. The aim of study of the system's complexity on the basis of its representation in data is a deep analysis of the variability of the parameters with respect to which an ability to manifest outwardly this variety should be assumed. Assessment of such ability characterizes the quality of the empirical fact. 3.2. Connection graph The concept “Schema” of a model of system reconstruction corresponds to the technology object named CG, in which an open system gets the initial abstract representation in the form of a structure of binary relationships between parameters of the SD. Each relationship in this structure has a sign. CG represents the system as an integrated and schematized whole that is manifesting outwardly hidden regularities determining the system states. All the variety of multiple large-scale intra-system correlations manifesting themselves through binary relationships of parameters is reflected in the CG. CG is a schematic representation of a heterogeneous system but it is not the system. Here the information about the system states is in itself absent. The system complexity is hidden in signed out-of-balance conditions of the CG. 3.3. System models The concept “Type” corresponds to the SM object. Through the SM and in the context of holism, the following issues occur: a multi-qualitative essence of the system is being revealed, unique qualities of the system are being expressed, and a variety of intra-system interactions forming the unity of the system whole is being defined. SM are formal descriptions of intra-system mechanisms. The mechanisms create ideal types and multi-various forms of nonideal forms of the system states. Each SM describes a system-forming mechanism of the concrete unique quality and includes the following: a determinative singleton (integral image of the given quality); a core (attraction domain of quality); factors (spread area of quality). Each SM is responsible for the self-development of qualitative definitenesses of the system. The model has a fixed structure and a fixed sense of a concrete mechanism of systemogenesis. Each SM is defined in its own subspace of the space of qualities of the system. Parameters of the determinative singleton, core and factors of the model are the coordinates of this subspace. All subspace coordinates are measured on the scale of levels of parameter values. All such scales have one and the same type. Forms of manifestation of the system in the given quality are the points of the subspace. Each point has a structure (model of a form of type) and content (multiple interactions mechanisms corresponding to this form of type). The given subspace has no metric. A complete set of SM forms a complete space of the system qualities which expresses the changing system whole. The SM reveal a complexity inherent in the system (multiplicity of qualities) through building a complete set of qualitative definitenesses of the system and a complete set of interactions models which are responsible for the self-development of the system as a whole and in each of its quality. The degree of revealing the complexity is being evaluated by the composition of the set of SM, by the completeness of each model’s organization, the measure of inner heterogeneity and the level of heterogeneity explanation by mechanisms of self-
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development. 3.4. Stratified graphs The mapping “Type → Schema” corresponds to the object of TSR named SG. An initial abstract representation of the system in each SG reveals disclosed qualities of the system. Each parameter with its structure of binary relations that is specified by the CG is represented in its own SG by a complete set of the models of particular system mechanisms which determine the variability of the parameter. Parameter variability manifested through the structure and attributes of CG is being revealed in diversity of its forms by way of a set of discovered system mechanisms participating in the formation of this variability with different intensity. The following characteristics are defined for each parameter: the number and the set of mechanisms, and the participation and role of each parameter in each mechanism. A schematic integrated representation of the system by the CG unfolds in complete set of stratified bigraphs. The integrated representations of parameters (concatenation of binary relations) in them are divided into semantic components. Each component is related to certain particular system mechanism. An aggregate of all the particular mechanisms is represented by multiple correlations of parameters. Each SG is used to evaluate the variety of system mechanisms that determine the variability of certain selected parameter for which this SG is built. For each parameter of the system, the sufficiency degree of the revealed system qualities is established through the given object of TSR in order to cognize a multiplicity of forms of the parameter variability. 3.5. Realistic singletons The mapping “Type → Variable” corresponds to the object “RS”. Feedback of the revealed unique qualitative definitenesses of the system with its empirical description is implemented through this object. A singleton, as an element of the space of qualities of the system, is associated with the points of the space of attributes of the system, herewith, providing respective objects of observation (actual states of the system) with concrete qualitative definiteness. RS has the mapping in the attribute space of the system. The inner complexity (heterogeneity) of SM expressing qualities of the system is evaluated by the level of concordance between qualities of the system and points of the attribute space. Each quality of the system is a homogeneous entity. The quality should be represented in the attribute space by all of its singletons. Each singleton of this quality should be associated with one and the same set of observation objects in the attribute space. 4. Functionality of TSR Objects of TSR represent the complex system as the whole in different forms of representation on the three stages of cognition of the system's senses (system in data, system in relations, and system in qualities), see Fig. 3. 3 System models
System in qualities
1 System in relations
2
System in data
2
Сonnection 2 graph
Stratified graphs
1 System in data
2
Realistic singletons
Fig. 3. Functional description of the technology: 1 – ascension from the fact to the sense (cognition of ontology); 2 – descent from the sense to the fact (testing of symbolic forms of the knowledge by the fact); 3 – transition to understanding.
In the first step of the ascension from the fact to the sense the system is treated as an isolated one. The limitations on the number of parameters (completeness of system description) and the number of states (representativeness of
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system description) are not imposed. The hypothesis that the system in data represents the system in its natural scale and real complexity is put forward. In the second step of the ascension, the view on the system like of a totality of actual states given in the measurements is automatically transformed into a scheme in which, through binary relations, the general, inherent in the states of the system being considered as a whole, is expressed. In such view, the system complexity is transferred through the signs of binary relations. The system gets an abstract representation of its complex whole (system in relations). In the third step of the ascension, the system is represented by a complete abstract image of an integral whole consisting of interacting homogeneous parts, each of which is both the part of the whole and the organic whole in the context of this part (system in qualities). Creation of this system image finishes the ascension from the fact to the sense, and generates symbolized knowledge of ontology of the system. In the first step of the descent from the sense to the fact, the degree of completeness of the obtained symbolized knowledge through mapping the family of SM to the initial abstract representation of the system (SG) is verified. The results of the test are: an estimate of the volume of manifested system complexity; and degree of how the complexity of the system is expressed in its ontology. In the second step of the descent, the connection of system ontology with the objects of reality from the data system (RS) is being revealed. The results are: the fact of multiplicity of qualities of the system states; evaluation of the system complexity through the set of the system qualities that are manifested in observed states; test of the adequacy of the revealed senses to the empirical fact and homogeneity of semantic parts of the system. The process of scientific understanding of the revealed system senses is implemented through mapping of the symbolized knowledge onto itself. That includes the evaluation of three forms of the system's representation (system in data, system in relations and system in qualities); analysis of the inner system organization and system-forming mechanisms; and synthesis of the sense and fact. Scientific understanding of the symbolized knowledge is the task of the technology of system examination (TSE) of POS8,9. Each TSR object is characterized by a set of attributes. Various methods of theory of reconstructive analysis, measurements theory, mathematical statistics, graph theory and visualization are used in order to build up the TSR objects and to compute their attributes. Theory of reconstructive analysis is the basis of the scientific method of POS - supports all the stages of cognition of the open system's ontology; identifies characteristic system symmetries and structures of intra-system relations (singletons, doublets, triplets, SM); determines characteristics of SM (roles of both vertices and edges; sense activity and similarity); and forms the triple predicates (RS). Methods of measurements theory, mathematical statistics and graph theory provide a construction of the initial abstract representation of the system. This representation should carry all characteristics of the system's complexity, that are sufficient to reveal it by the tools of the theory of reconstructive analysis. Visualization methods are used for representing data, information and elements of knowledge in the form of plots, diagrams, structural schemas, and tables. 5. Conclusion Cognition of the system ontology is a key stage in generating ontological knowledge based on heterogeneous empirical large-scale datasets. Fundamental complexity of the system is being overcome at the cognition, and the reliable scientific knowledge is generated (about complete space of the system qualities, complete families of the CM, and the models of system-forming interactions) 3,6,8,9. The stages of both scientific understanding and rational explanation of the system ontology; and the stage of axiology study (values, fullness, completeness) of the obtained ontological knowledge - they all follow the stage of cognition 3 7 8,9. Technology of system examination (TSE) of POS automatically implements scientific understanding of the ontology. The quality, volume, and essence of obtained knowledge are evaluated in the process of understanding. Empirical description of the system; all SM; all ideal models; mappings of all regions of qualities' space of the system into its space of attributes; and completeness of the types and forms actualization of the all qualitative definitenesses of the system - all these are the subject of system examination.
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Technology of system design (TSD) of POS automatically executes rational explanation of the ontology. The explanation covers ontological knowledge about the system as a whole, ideals and states of the system. Ontology which is cognized and scientifically understood contains the reliable scientific knowledge that includes: knowledge about the system and its emergent properties; knowledge about limitations and rules of conjugacy of various qualities of the system in its actual states. TSD explains the following: properties of the parameters in each certain state of the system; properties and actual states of the system considered as a whole; mechanisms responsible for the forming a variability of each parameter and global properties of the system. The qualimetric component of the analytical core of POS carries out the study of axiology of the ontological knowledge. Application of POS technologies for generating scientifically proven ontological knowledge about open systems, is tested and proven: in system biology 10,11, in solar-terrestrial physics 12, in security and social tensity 13, and in other fields of knowledge14,15. References 1. Klir GJ. Architecture of Systems Problem Solving. Plenum Press, New York, 1985. 2. Kachanova T, Fomin B. Physics of ыystems is a postcybernetic paradigm of systemology. In: Proc. Int. Symp. “Science 2.0 and Expansion of Science: S2ES” in the context of the 14th World-Multi-Conference on Systemics, Cybernetics and Informatics WMSCI 2010, pp 244-249. 3. Kachanova T, Fomin B. Physics of open systems: generation of system knowledge. J. Systemics, Cybernetics and Informatics, 11, No 2, 73-82, 2013. 4. Kachanova TL, Fomin BF. Fundamentals of the systemology phenomenal [in Russian], Izd. SPbGETU LETI, St. Petersburg, 1999. 5. Kachanova TL, Fomin BF. The Metatechnology of system reconstructions [in Russian], Izd. SPbGETU LETI, St. Petersburg 2002. 6. Kachanova TL, Fomin BF. An Introduction to systems language [in Russian], Nauka, St. Petersburg, 2009. 7. Kachanova TL, Fomin BF. The Technology of system reconstructions [in Russian], Politekhnika, St. Petersburg, 2003. 8. Kachanova TL, Fomin BF. Methods and technologies for generating a systemic knowledge: a manual for masters and postgraduate students [in Russian], Izd. SPbGETU LETI, St. Petersburg, 2012. 9. Kachanova TL, Fomin BF. Qualitology of system knowledge: a manual for masters and postgraduate students [in Russian], Izd. SPbGETU LETI, St. Petersburg, 2014. 10. Ageev V, Fomin B, Fomin O et al. Physics of open systems: A new approach to use genomics data in risk assessment. In The Continuum of Heath Risk Assessments, InTech", 2012, pp 135-160. 11. Ageev V, Kachanova T, Kopylev L et al. Physics of open systems: The effects of the impact of chemical stressors on differential gene expression. J. Cybernetics and Systems Analysis, 50, No. 2, 2014, pp. 218-227. 12. Fomin B, Kachanova T et al. Global system reconstructions of the models of solar activity and related geospheric and biospheric effects. In: Proc. of 39th ESLAB Symposium “Trends in Space Science and Cosmic Vision 2020”, ESTEC, 2005, pp 381-384. 13. Ageev V, Araslanov A, Kachanova T et al. Generation of system knowledge on the problems of social tensity in regions of Russia, Scientific and technical sheets SPbSPU, 147, №2-1, pp 300-308, 2012. 14. Kachanova T.L. and Fomin B. F. System ontology of classes [in Russian]. ETU "LETI" Proceedings, № 7/2015, pp. 25-36. 15. Ageev V. O., Kachanova T.L., Fomin B. F., Turalchuk K.A. Natural classification of acute poisoning with organophosphorus substances [in Russian]. ETU "LETI" Proceedings, № 8/2015, pp. 8-17.