ПРИКЛАДНОЙ ПОДХОД К ПРЕДСТАВЛЕНИЮ КОНЦЕПТУАЛЬНОЙ ВИЗУАЛИЗАЦИИ

Исмаилова Л.Ю.¹, Косиков С.В.²

¹Кандидат технических наук,

НИЯУ МИФИ,

² Институт Актуального образования ЮрИнфоР-МГУ

ПРИКЛАДНОЙ ПОДХОД К ПРЕДСТАВЛЕНИЮ КОНЦЕПТУАЛЬНОЙ ВИЗУАЛИЗАЦИИ

Аннотация

В статье представлен прикладной подход к способам концептуальной визуализации, осуществляемой при помощи компьютера. Мы используем термин «концептуальная визуализация» для обозначения концептуальной информации визуально-графического представления данных в форме структурированных и неструктурированных описаний доменных объектов и их отношений с целью эргономики и удобства пользователя. Представлен анализ широкого класса электронных инструментов для обработки подобной концептуальной информации. Построена прикладная вычислительная модель основанная на лямбда-исчислении и предоставлены способы ее поддержки в  виде набора специализированных комбинаторов, которые представляют и обрабатывают графически-ориентированные концептуальные данные. Прикладной характер вычислительной модели позволяет предложить метод ее выполнения с использованием инструментов прикладного характера.

Ключевые слова: доменная модель, концепт, зависимости концепта, концептуальное проектирование, концептуальный домен, теория типа, графический формат, графические объекты, построение диаграмм, вычислительная среда, концептуальная визуализация.

Ismailova L.Y.¹, Kosikov S.V.²

¹PhD, Department of cybernetics,

National Research Nuclear University MEPhI(Moscow Engineering Physics Institute),

²Institute of contemporary education JurInfoR-MSU

APPLICATIVE APPROACH TO PROVIDING A CONCEPTUAL VISUALIZATION

Abstract

Applicative approach for getting means for a computer-aided conceptual visualization is presented.  We use a term “conceptual visualization” for presenting conceptual information for a visual graphical representation of data in a form of structured and unstructured descriptions of a domain objects and their relations for the best ergonomics and usability. An analysis of wide classes of computer-aided tools for such conceptual information processing is given. The applicative computational model based on a lambda calculus is constructed and means of its support in a form of a set of the specialized combinators providing representation and processing of graphically oriented conceptual data are offered. Applicative character of this computational model allows to offer a method of its further implementation with use of tools of applicative type.

Keywords: domain model, concept, concept dependences, conceptual construction, conceptual domain, type theory, graphical format, graphical objects, diagramming, computational environment, conceptual visualization.

INTRODUCTION

In the present paper we define the term “conceptual model” as a set of constructions for presenting structured and unstructured descriptions of a domain objects and their relations for the given problem domain. Then we define the term “conceptual visualization” as a visual graphical representation of conceptual model constructions for the best ergonomics and usability. The computer-aided conceptual visualization requires separation of kinds of conceptual information and ways of manipulations with it.

Using а conceptual information in the practical information systems assumes development of the appropriate means of processing. These means must be coordinated with the proposed conceptual structure. The coordination can be achieved by creation of a computational model of graphically oriented conceptual data and the following development the applicative means based on the model. This way of the development, in turn, demands determination of the specialized language and tools. Actually the range of such means is rather wide: from conceptual systems of interpretation to the appropriate abstract machines (Ismailova and Kosikov, 2010).

The considered task requires the support of extensibility of modeling tools. The extensibility is reached primarily due to computing nature of model. The convenient formalisms for this purpose are applicative computing systems (ACS) (Wolfengagen, 2010, Ismailova, 2014). At the level of fixing of objects of data domain we propose to use the lambda calculus. It provides the most compact description of abstraction which is one of the main operations of conceptualization. At the level of the description of the supporting mechanisms we prefer to use the methods of the combinator theory. It provides a construction of a computational environment which is free from variables. The set of combinators can be directly transformed further to command set of the abstract machine (Ismailova and Kosikov, 2010).

Important advantage of applicative computing systems is the possibility of support of flexible schemes of object typing. The methods of typing accepted in the simple type theory are convenient for the description of types of basic graphic objects. Using of the different types of the? polymorphism enables determination of generalized (generic) types. These types allow to give uniform definitions of the processing methods for uniformly constructed data classes.

In this article we will construct the basic level of a computational model. This level is used for the transition from the description of objects to the appropriate data representation and the supporting a computation over them by the abstract machine of an applicative type.

RELATED WORK

Well known approaches to processing of the conceptualized graphic information were investigated by many authors under different point of view (Kirkpatrick, 2015). So, possibilities of support of processing of the conceptualized objects can be collocated both to features of different graphic formats, and to classes of graphic processing supporting tools.

It is natural to correlate methods of processing of graphically oriented conceptual data first of all to the existing formats of graphic data representation. It is known that there are two large classes of graphic formats – raster and vector (Coquand, Thierry; and Huet, Gérard., 1988). However in the context of this article vector formats are of interest first of all. It is connected to that the existing methods of processing of raster formats, as a rule, are oriented on the local information contained in a raster format and, as a result, aren't adjusted for separation conceptualized information. Filters of the Adobe Photoshop program and similar to it can be considered as a common example of use of raster formats. It is necessary to mark that even separation of boundary between two areas which are differently colored in case of such approach is a problem.

The analysis existing attempts of conceptualization of raster information (Novak and Canas, 2008) lead to approach based to a separation of an objects (monophonic areas of the image, boundaries of areas, graduated fills, etc.) which are indeed poorly connected to objects of data domain. Besides, establishment of such link usually happens on the basis of the separation of the intermediate level of the abstraction based on a separation of fragments of the image and describing rules of a separation of fragments of the bitmap image, and also their linking with objects of data domain. Such intermediate level can be considered as a peculiar vector format and by that joins in a context of this article.

Reviewing of the existing vector formats shows that they provide the graphic information or as a set of separate graphic elements (DXF), or as hierarchical nested structure (SVG). More developed means of operation with vector graphics (PostScript) also use model of graphical representation in the form of a set of graphic elements (Postscript). The list representation accepted, in particular, in AutoCAD system which potentially is capable to provide the computed variability of graphic representations, and appropriate tools – list processing languages such as Lisp (Ismailova, 2014) appears natural representation of a set of graphic elements.

One of the ways of graphic informational processing which can be considered as conceptualization, is used in pattern recognition systems (Alkoffash et al, 2014). Such systems on the basis of the analysis of low level graphic primitives of the given object carry out its interpretation in terms of higher level. It is necessary to mark, however, that the selected images usually have standard character (letters and other characters of a font, the conventional signs, etc.). Besides, conceptualization is carried out only in one direction – from the low level to high, the reverse transition usually isn't supported.

General purpose conceptual modeling systems (including ontology supporting systems (Horrocks I. et al., 2005), on the contrary, are oriented on operation with conceptual information, including in applicative style. However the supporting mechanisms of such systems aren't oriented on processing of a graphic  information that leads to bulky decisions when somebody attempts to integrate a graphic subsystem into the abstract machine of general purpose. Systems of a little lower level (such as Java-machine) can provide the best integration with the graphic component (presented, as a rule, abstractly in the interface to some graphic library like OpenGL) due to lowering of the abstraction layer during conceptual construction processing.

One of the most elaborated approaches to conceptual modeling is based on UML (UML, 2011). UML is a general purpose modeling language. So it can be used for modeling of conceptual graphic information, but this is not its main purpose. Primarily UML is used in the field of software engineering for the visualization of the design of program systems. So the presented approach to conceptual visualization can be used for representing UML diagrams. This is one of the interesting directions of future work.

The intermediate level is occupied by Computer-Aided Design systems like CAD. In such systems rather high level of conceptualization is combined with developed opportunities of graphic processing. However such systems are, as a rule, oriented on rather specific areas of applications (mechanical engineering, architecture, etc.) that complicates their use in the other domains.

Interesting approach is shown by systems of a schematization (scheme diagramming Bounford, Trevor, 2000) like concept maps (Cañas et al., 2003; Beel and Langes, 2013). In such systems creation of specialized graphic descriptions with use enough rich graphic means is possible. In particular, display of different types of conceptual structure, the description of hierarchies, classifications, etc. is possible. Though such systems can be considered as the universal for the given class of data domains, usually they badly provide extensibility of the used graphic means (especially methods of composition of means) and methods of their communication with semantic information in need of specification of the description of data domain.

Another interesting approach is connected with social network aggregation systems like FlipBoard. These systems collect content from different sources and arrange it. The presented approach can be used together with network aggregation tools as a part of the internal model of the aggregation.

The approach offered in this article is oriented on the description of graphically oriented conceptual information at higher level, than it is provided in formats of graphic data or pattern recognition systems. At the same time more detail description of graphic primitives, than is provided in systems of conceptualization of general purpose.

CONCEPTUAL DOMAINS

Let use an object containing the set of properties represented as an ordered pair of property type and it’s a value as an idealized representation of the graphic environment object. Further such object will name conceptual construction. Such structure of an object rather well corresponds to real formats of graphic data (SVG, DXF) and at the same time allows distracting from representation details which are not essential in the context of this paper. The ordered pair consisting of a property type and a value of the property we will consider as a main unit of the conceptualization and will name conceptualizator of graphic objects.

We will introduce necessary classes of expressions in the form of semantic domains (Wolfengagen, 2013) for the formal representation of conceptualizers of graphic objects. The conceptual domains can be constructed with general technique of the variable domains. The variable domains are functors from a suitable category Asg of assignment points to the category of sets. An object of the category Asg corresponds to the state of the problem domain. The value of the functor is defined as

 H_U (A) = {h | h : A → U},

where A and U are objects of the category Asg.

An arrow of the category Asg corresponds to the transition from one state to another. The value of the functor (variable domain) is defined as

 H_U (f) (h) = h ◦ f,

where f : B → A is an arrow of category Asg.

Use of semantic domains provides on the one hand, possibility of an elementary description of data based on their structural features within the theory of sets and, on the other hand, possibility of transition to powerful technique of the lattice theory and other richer structures (the continuous lattice, etc.) that allows to use developed methods of handling such structures, including algebraic type structures.

We will use as basic the following semantic domains:

CGIType – types of conceptual constructions of graphic objects;

CGIVal – values of conceptual constructions of graphic objects.

Further we will introduce GCIBag - semantic domain of sets (baskets) of conceptual constructions of the graphic objects attributed to concrete conceptual construction at a stage of determination of representations of objects,  CBag - semantic domain of baskets of conceptual constructions, and also  GValBag  - semantic domain of baskets of values of conceptual constructions. These domains are intended to represent sets of corresponding constructions for different parts of conceptual model.

The semantic domain of conceptual constructions of the graphic objects attributed to concrete to conceptual construction can be described by GCIBag in the form of the inductive class as follows:

• { } ε GCIBag
• If t ε CGIType, v ε CGIVal, b ε CGIBag, then (t, v) + b ε

The semantic domain of baskets of conceptual constructions CBag describes possible statuses of sets of conceptual constructions. It can be described in the form of the inductive class as follows:

• { } ε CBag
• If c ε CGIBag, b ε CBag, then c + b ε

The introduced semantic domain CBag describes initial data for computation of specialized conceptual operations. Further it is necessary to describe result of computation which represents a basket of values of the conceptual constructions. The semantic domain of baskets of values of conceptualizator CValBag can be described in the form of the inductive class as follows:

• { } ε CValBag
• If v ε CGIVal, b ε CValBag, then v + b ε

Further we will use constructions "value belongs to the appropriate type" and "value is an element of the appropriate domain" as synonyms.

CONCEPTUAL OPERATIONS

Let consider some set of operations. We will suppose that this set has an enough general form for building practically useful systems of describing graphically oriented conceptual information and ways for the manipulation with it. It seems that such set has to involve: search operations, operations for DB modification and specialized conceptual operations.  It is supposed that in a case of execution of specialized operations as an extensional of argument of operation the full set of conceptual constructions received at a certain stage of the domain description is used. Computation of an extensional of such operations happens according to the uniform scheme provided below.

1. Search operation may be viewed differently. We have to note that to different operations in the conceptual model correspond, generally speaking, different quantifiers though interpretation of operations isn't reduced to interpretation of quantifiers.

The most typical operation of search is considered as having the following type: CBag → CBag where the argument of an operation represents a DB status, and result of it is interpreted as a set of the selected conceptual constructions.

It is set by the function:

fs: CGIType → B (function of a search criterion)

where B = {true, false } – the semantic domain of truth values. Computation of an eхtensional of operation is made as follows

F ({}) = { }

F (с + b) = if Fs (c) then c + F (b) else F(b)

where function of selection of conceptual constructions Fs: GCIBag → B is defined as follows:

Fs ({}) = false

Fs ((t, v) + b) = if fs (t) = true, then true, else Fs (b).

It is possible to carry out synthesis of determination for involving in to reviewing more difficult search criterions.

1. Operation of modification is considered as having a type CBag → CBag, where an argument of an operation of modification is an initial state of database and a result is interpreted as modified state of the data base. This operation is defined by the couple of function.

f_s : CGIType → B (function of type selection)

f_v : CGIVal → CGIVal (modification value function)

A computing of an extensional of an operation may be done by the function

F : CBag → CValBag. It is defined as follows:

F ({}) = {}

F (c + b) = Fv (c) + F (b),

where function of modification of a conceptual construction Fv : GCIBag → CGIBag is defined as follows:

Fv ({}) = {}

Fv ((t, v) + b) = if f_s (t) = true, then (t, f_v (v)) + Fv (b), else Fv (b).

1. Specialized conceptual operation is considered as having a type CBag → CValBag. It defined by the couple of functions

f_s : CGIType → B (type checking function)

f_v : CGIVal → CGIVal (function of value).

Computation of an extensional of the conceptual construction may be done on the base of these couple of functions and by the function

F : CBag → CValBag, defined as follows

Fv ({}) = {}

Fv ((t, v) + b) = if f_s (t) = true, then f_v (v) + Fv (b), else Fv (b).

It may be possible to get different kind of specialized conceptual construction by defining differently type checking functions. Basic practically useful kinds of conceptual operations are “selection”, “projection”, and specialized “aggregate function”.

CONCEPTUAL CONSTRUCTIONS

The introducing semantic of operations over conceptual constructions may be built systematically by using a set of specialized polymorphic combinators, which could be considered as terms of a calculus of constructions. Thus calculus of constructions according to (Ismailova and Kosikov, 2010) is defined as the applicative computing system providing polymorphism both on types, and on terms.

We define general conditional operator (combinator): If : bool → a → a → a. Then we introduce a specialized polymorphic operator for a condition checking, including the condition exploited on a structure of an argument of the combinator:

If : a → (U → b) → (a → B) → (a → b) → b

is defined as

If_Str x a p q = If (px) a (K(qx)),

where x : a – an element of data which is under processing; a : U → b – a result of a processing in the case of checking of element is true;            p: a → B – a function of checking of the element; q: a → b – a processing function, called in the case of getting false  as a result  of a checking of an element; and combinator K is defined usually as follows:

K x y = x.

We consider further operators for baskets of objects. The completing step in a building of a set of specialized combinators is the support of the recursive processing.

The proposed approach for systematically constructing of a set of an operations over conceptual constructions:

• provides the systematic accounting of types of constructions coordinated with methods of creation of the appropriate conceptual domains;
• allows to make the analysis of the introduced operations for different sets of conceptual data (for example, in a case when values of some conceptual constructions can be passed);
• opens a way to systematic implementation of the offered operations by means of application-oriented ACSs.

CONCLUSION

An approach to creation of the conceptualized means of graphical representation of objects of data domain and their processing on the basis of a computational model of applicative type is offered. The applicative computational model on a  lambda calculus basis is constructed and means of its support in a form of a set of the specialized combinators providing representation and processing of graphically oriented conceptual data are offered.

The constructed model provides extensibility of the modelling tools which is reached due to support of computing character of the model. An extensibility provides possibility of introduction of schemes of typing of objects. They are adequate to the formalism of the description of data domain. Standard tasks of processing and the appropriate conceptual constructions are considered.

Applicative character of the offered computational model allows to offer a method of its further implementation with use of tools of applicative type. The considered combinators can be nested in an untyped lambda calculus and then computed by any of well-known methods of implementation of applicative systems (Ismailova, 2014) that gives the way to creation a practical systems processing of graphically oriented conceptual information.

ACKNOWLEDGEMENTS

This work is a generalization of the results, which are associated with the construction of conceptual and computational model obtained at different times during the projects, partially supported by RFBR grants 14-07- 00119-a, 14-07-00072-a, 13-07-00716-a, 14-07-00054-a.

References

1. Alkoffash M.S., Bawaneh M.J., Muaidi H., Alqrainy S., Muath A. 2014. A Survey of Digital Image Processing Techniques in Character Recognition. IJCSNS International Journal of Computer Science and Network Security , Vol. 14 No.3, March 2014
2. Barendregt H., Lambda Calculi with Types, Handbook of Logic in Computer Science, Volume II, Oxford University Press, 2012.
3. Beel J., Langer S. (2013). An Exploratory Analysis of Mind Maps. Proceedings of the 11th ACM Symposium on Document Engineering (DocEng'11).
4. Bhattacharyya S., 2011. A Brief Survey of Color Image Preprocessing and Segmentation Techniques real time applications. JPRR Vol 6, No 1 2011; doi:10.13176/11.19
5. Bounford, Trevor (2000). Digital diagrams. New York: Watson-Guptill Publications.
6. Cañas, A. J., Hill, G., & Lott, J. (2003). Support for constructing knowledge models in CmapTools in Technical Report No. IHMC CmapTools 2003-02. Pensacola, FL: Institute for Human and Machine Cognition.
7. Coquand, Thierry; Huet, Gérard. 1988. The Calculus of Constructions. Information and Computation 76 (2–3).
8. Ismailova, L.Y., 2014, Criteria for computational thinking in information and computational technologies. Life Science Journal, 2014, 11 (9 SPEC. ISSUE), art. no. 86, pp. 415-420.
9. Ismailova L.Y., Kosikov S. V., 2010. Applicative models, semantic scalability and specialized calculations for business games in jurisprudence. in Proceedings. International workshop «Innovation technologies – Theory and Practice», Dresden, September 06-10, 2010, Germany, Dresden-Rossendorf, FDZ, 2010. – pp. 33-35.
10. Kirkpatrick K., 2015 Putting the Data Science into Journalism – Communications of the ACM, Vol. 58 No. 5, Pages 15-17.
11. Horrocks I., Peter F. Patel-Schneider, Bechhofer S., and  Tsarkov D., 2005. OWL Rules: A Proposal and Prototype Implementation. of Web Semantics, 3(1):23-40, 2005.
12. Novak, J. D., Canas A. J., 2008. The Theory Underlying Concept Maps and How to Construct Them, Technical Report IHMC CmapTools 2006-01 Rev 01-2008.
13. Unified Modeling Language, http://www.omg.org/spec/UML/
14. Wolfengagen V.E., 2014. Computational Invariants in Applicative Model of Object Interaction. Life Science Journal 2014;11(09s):453-457
15. Wolfengagen V.E., 2010. Semantic modeling: Computational models of the concepts in 2010 International Conference on Computational Intelligence and Security, CIS 2010 pp. 42 - 46 doi: 10.1109/CIS.2010.16