JP2004326812A - Device and method for designing information - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To secure the interoperability of information systems. <P>SOLUTION: An assembly level process block 200 extracts a plurality of object assemblies from an object assembly storage part 900. A phase space level process block 300 designs an object assembly as phase space. An adhesion space level process block 400 specifies an equivalent relationship over the plurality of object assembles and designs an adhesion space to which partial spaces associated with one another by the equivalent relationship adhere. A cell space level process block 500 expresses the objects' attributes in the form of cells and designs the dimensions of the cells. An expression level process block 600 designs the expressions of the cells. A view level process block 700 designs view to users. A homotopy level process block 100 designs changes in the object assemblies as homotopy, which changes are caused by operations performed by each process block. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to an information design technique, and more particularly to an information design apparatus and an information design method for designing specifications to be satisfied by an object set step by step.

  The construction of information systems, for example, is typically seen in integrated systems associated with the integration of major banks, and is moving at an accelerating pace from a single large-scale site to a multi-distributed large-scale site. However, the current software engineering and re-engineering technology, which is the basic technology, lacks an engineering model as a basic framework to cope with this. The reason for this is that since the integration method is lacking at the model level, the engineers in charge of each site construction individually devise and design the module group. For this reason, module group specifications naturally differ for each site. If the specifications of the module group are mutually disclosed, restructuring is possible, but the combination of the number of modules exponentially increases the number of restructuring systems, causing a so-called “development man-hour explosion”. In addition, actually, in many cases, the specification of the module group is not disclosed for corporate confidentiality. In this case, although the interface creation information between the modules is disclosed, the number of interfaces increases exponentially depending on the combination, so that the "explosion of development man-hours" becomes more remarkable.

  In Japan and abroad, relational database (RDB) models, ER models, XML based on tags, UML based on graphs, etc. have been studied and applied, but the theoretical basis for constructing large-scale distributed information systems is model-based. For example, the interface specifications between modules are not a theoretical system that can be handled uniformly between different sites. Therefore, the aforementioned "explosion of development man-hours" cannot be solved.

  In addition, due to the severe economic situation in each country in recent years, company integration is increasing steadily, but information processing can be freely performed with consistency between different information systems, that is, interoperability of information systems is ensured As a result, the costs of operating and maintaining information systems are increasing.

  The present invention has been made in view of such a background, and an object of the present invention is to provide an information design technique that can guarantee interoperability of an information system as a linear model.

  One embodiment of the present invention relates to an incrementally modular information design apparatus. The apparatus has a modularized abstract hierarchical block configured to be able to operate on an object set in each hierarchy, and inherits an equivalence relation of the object set between the abstract hierarchical blocks as an invariant, The specification to be satisfied by the set is incrementally detailed for each of the abstract hierarchical blocks.

  An “object set” is a set of data handled by the information system, and the “information system” is an arbitrary system for managing, processing, and processing information in some form. Thus, examples of information systems include sites, software, databases, and any digitally managed information, such as management, finance, and personnel.

  The modularized abstract hierarchical block performs a set operation on the object set, and specifies a set to a set design unit that designs a plurality of desired object sets and a set having a subset of the object set as an element. Thereby, a topological space design unit that designs the object set as a topological space, and a subspace that defines an equivalence relation on the plurality of object sets, each of which is designed as a topological space, and is associated with the equivalence relation A bonding space designing unit that designs a bonding space in which the cells are bonded, a cell space designing unit that expresses attributes of objects belonging to the plurality of object sets in the bonding space by cells, and designs a dimension of the cell, And an expression design unit that designs an expression form. The modularized abstract hierarchical block may further include a view design unit that designs a view for a user with respect to the plurality of object sets.

  The modularized abstract hierarchical block is designed so that a change in the object set caused by an operation on the object set by each design unit has a homotopy equivalent, so that the object set can be returned to the state before the change. The apparatus may further include a homotopy design unit that records operation procedures.

  According to this apparatus, a specification to be satisfied by an object set is gradually designed in each abstract hierarchy while defining an equivalence relation between a plurality of object sets and inheriting the equivalence relation as an invariant between abstract layers. be able to. Equivalency is guaranteed through the aggregation level, the topological space level, the glue space level, the cell space level, the representation level, and the view level, and finally the instances of the object are output in a mathematically consistent manner. Further, each abstract hierarchy is modularized, and even when an object is added, deleted, or modified, the design can be incrementally changed while moving up and down the abstract hierarchy. Furthermore, by treating an operation performed on an object set as a homotopy, the object set can always be returned to the state before the change.

  Another embodiment of the present invention relates to an incrementally modular information design method. The method includes a modularized abstract hierarchy step configured to enable operation on an object set in each hierarchy, and inheriting an equivalence relation of the object set as an invariant between the abstract hierarchy steps, The specification to be satisfied by the set is incrementally detailed for each of the abstract hierarchy steps.

  Still another embodiment of the present invention relates to a program. This program performs a set operation on an object set to design a desired plurality of object sets, and defines the topology in a set having a subset of the object set as an element, thereby defining the object set. A phase space designing step of designing as a topological space, and defining an equivalence relation on the plurality of object sets each designed as a topological space, and designing an adhesion space in which the subspaces associated with the equivalence relation are adhered. A bonding space designing step, a cell space designing step of expressing attributes of objects belonging to the plurality of object sets in the bonding space by cells, and designing a dimension of the cells, and an expression design of designing an expression form of the cells Steps and a view to the user with respect to the plurality of object sets To execute and view designing step of designing the computer.

  It is to be noted that any combination of the above-described components and any conversion of the expression of the present invention between a method, an apparatus, a system, a recording medium, a computer program, a data structure, and the like are also effective as embodiments of the present invention.

  ADVANTAGE OF THE INVENTION According to this invention, the interoperability of an information system can be ensured and the efficiency of information sharing and reuse can be improved.

  Hereinafter, the present invention will be described based on preferred embodiments. First, an incrementally modular abstraction hierarchy proposed by the present inventor will be described, and then an information processing device that implements the incrementally modular abstraction hierarchy will be described.

[1] Set-theoretic design First, the design of the cyber world is started by defining a group of objects to be constructed in the cyber space. In order for such collections to be able to perform automated operations using a computer as an intelligent machine, each collection must be a "set". Computers are built as set-theoretic machines. Intuitively, the set X is a set of all objects x having the same property P (x). To express this symbolically, X = {x | P (x)}. Any object included in a set is called an element or an element. A set having no elements is called an empty set φ. If all elements are interior, the set is said to be an open set. Given sets X and Y, the computer computes a union X∪Y, a product or intersection X∩Y, a difference XY (also written as x＼y), a negation (negation). ) Apply a set-theoretic operation such as X.

は、Ｕを含むＸのすべての閉部分集合の積である。言い換えれば、Ｕの閉包は、Ｕの外部（exterior）要素でないＸの要素である。Ｘの部分集合｛Ｕ｜Ｕ⊆Ｘ｝のすべてからなる集合をＸの巾（べき）集合といい、２^Ｘと表記する。これはまたＸの離散位相（discrete topology）とも呼ばれる。離散位相はサイバースペースを部分サイバースペースからなるものとして設計する上でたいへん有用である。なお、集合を要素とする集合（いわゆる「集合の集合」）を「集合族」（family of sets）ということがある。Ｘの巾集合は、集合Ｘのすべての部分集合を要素とする集合族である。 Let's start designing the cyberspace architecture from set X as the first cyberspace. Given all the elements u of the unknown cyberspace U, if it is confirmed that all the elements are elements of the cyberspace X, the unknown cyberspace is defined as a subset of X, that is, X Is referred to as a partial cyberspace, and expressed as U @ X. Whether it is a subset can be automatically checked by processing (∀u) (u∈U → u∈X). U closure

Is the product of all closed subsets of X including U. In other words, the closure of U is an element of X that is not an exterior element of U. A set consisting of all subsets of X {U | U {X} is called a width (power) set of ^X and is denoted by 2 ^X. This is also referred to as the discrete topology of X. Discrete phases are very useful in designing cyberspace as consisting of partial cyberspace. A set having a set as an element (a so-called “set of sets”) is sometimes referred to as a “family of sets”. The width set of X is a set family whose elements are all subsets of the set X.

[2] Topological Design From now on, we will start to design the cyberspace as the sum of the (multiple) partial cyberspaces of X and their overlap. The cyberspace designed in this way is generally called a topological (topological) space (X, T). Here is a T⊆2 ^X. The design of the phase space is automated according to the following specifications.
1) X∈T and φ∈T;
2) For any set of subscripts J,
∀j∈J (U _j ∈T) → ∪ _j∈J U _{j ∈T} ;
3) U, V∈T → U∩V∈T.

The design specification 1) is that the empty set and the whole set are the elements of T, 2) is that the elements are elements of T even if the sum of the elements of T is taken and 3) is the element of T This shows that the product (intersection) of two elements is also an element of T. The computer designs T from the width set 2 ^{X of X} to satisfy this design specification.

  T is called the phase (topology) of the phase space (X, T). Given two phases T1 and T2 where T1⊂T2, T1 is said to be weaker or smaller than T2. Conversely, T2 is said to be stronger or larger than T1. Also, T2 may be finer than T1, or T1 may be coarser than T2. As is evident, the strongest phase is the discrete phase or width set, and the weakest phase is the empty set φ. For simplicity, X is often used instead of (X, T) to represent the phase space, unless ambiguity occurs.

と書く。 Given two topological spaces (X, T) and (Y, T '), how can (X, T) and (Y, T') be equivalent? Using a computer, we provide here a criterion for automatically validating that these spaces are topologically equivalent. The two phase spaces (X, T) and (Y, T ′) are continuous with a continuous function f: (X, T) → (Y, T ′), and an inverse function thereof. If so, it is said to be topologically equivalent, ie, in-phase, in-phase, or homeomorphic. (X, T) is in-phase with (Y, T ')

Write

So how can we prove the continuity of the function f? First, it is checked that ∀B∈T ′, f ⁻¹ (B) ∈T. Here, f ⁻¹ (B) means an inverse image of B by f. Next, check that the following holds.
Δf ⁻¹ (B) where B is open is also open at X.

[3] Function When a function f: X → Y is given, there are a total function and a partial function. Function f: When → x∈X, ∃f (x) for X → Y, and only then, function f is said to be a global function. Function f: X ′ → Y | X′⊇X is called a partial function. At this time, f (x) does not always exist for every x∈X.

There are three basic types of relationships or mappings for global functions.
1. Single shot (injective or into)
∀x, y∈X, x ≠ y⇒f (x) ≠ f (y)
In other words,
∀x, y∈X, f (x) = f (y) ⇒x = y
2. Surjective or onto
(∀y∈Y) (∃x∈X) [f (x) = y]
3. Bijective
Injective and bijective

[4] Equivalence relation For any binary relation R⊆X × X on the set X, R is
1) If (∀x∈X) [xRx], it is reflective,
2) If (∀x, y∈X) [xRy⇒yRx], there is symmetry,
3) If (∀x, y, z∈X) [[xRy⇒yRx] ⇒xRz], it is said that there is transitivity. The conditions 1) to 3) are called a reflection rule, a symmetry rule, and a transition rule, respectively.

  When R has reflectivity, symmetry, and transitivity, R is called an equivalence relation and is denoted by.

これは集合Ｘが空でない互いに素の（すなわち共通要素をもたない）同値類に分割される（分解されるともいう）ことを意味する。 Given x∈X, a subset of X defined by x / 〜 = {y∈X: x〜y} is called an equivalent class of x. Here, a class actually means a set, but it is traditionally called a class, and it is difficult to change it now. The set X / ~ of all equivalence classes is called the quotient space or the equalization space of X.
X / 〜 = ｛x / ∈∈2 ^X | x∈X｝ ⊆2 ^X
According to the transition law, the following holds for each x∈X, x / ≠≠ φ.

This means that the set X is divided (also referred to as decomposed) into nonempty disjoint equivalence classes (ie, having no common elements).

  In general, when the equivalence relation is defined on a set X, a set in which all elements having the same value as a with respect to the element a of a certain X can be considered. This subset of X is an equivalence class having a as a representative element, and is expressed as [a]. Here, no matter which of the elements included in the equivalence class is taken, the equivalence classes whose representative elements are the same set. That is, the equivalence class does not depend on how to take the representative element. Since the equivalence classes satisfy the reflection rule, symmetry rule, and transitive rule, each equivalence class is not empty, a belongs to the equivalence class of a, and there is no common element in different equivalence classes. Thus, when all equivalence classes are collected, they do not intersect each other, and the total union is equal to X. That is, the set X is divided into a disjoint union of equivalence classes. This direct sum division is called a classification of the set X with respect to the equivalence relation R, and the set of all the equivalence classes is called a quotient set by the equivalence relation of the set X. A quotient set whose topology is defined is called a quotient space as described above.

  This will be described using a simple example. Given that X is a set of rational integers and the relation R between the elements x and y of X is "xy is an even number", this is an equivalence relation. If the set X is classified by the equivalence relation R, the set X is divided into a direct sum of an odd equivalence class and an even equivalence class.

  In Euclidean geometry, when a set of figures is given, the congruence relation is an equivalence relation, and the entire set of figures is divided into a quotient space into a direct sum of a subset of congruent figures. The similarity relationship is also an equivalence relationship, and the whole set of figures is divided into a quotient space by a direct sum of a subset of similar figures. Congruence and similarity are examples of affine transformations. The symmetry relation in the group theory divides the entire set of figures into a direct sum of subsets composed of symmetric figures as a quotient space.

Note that in electronic commerce, "being an electronic product" is an equivalence relationship, while "electronic commerce" is a partially ordered relationship. The binary relation S on the set X is a semi-order relation when the following three conditions are satisfied.
1) (∀x∈X) [xSx] (reflection law)
2) (∀x, y∈X) [xSy, ySx → x = y] (antisymmetric rule)
3) (∀x, y, z∈X) [[xSy⇒ySz] ⇒xSz] (transition rule)

  A set having a partially ordered relation is called a partially ordered set, and is often called a poset, taking the initials. When two elements x and y of a set are either xSy or ySx, they are said to be comparable. A partially ordered set in which any two elements can be compared is called a totally ordered set.

  The relationship between electronic transactions is a semi-order relationship because the relationship between the seller and the buyer is asymmetric and does not satisfy the symmetric rule but satisfies the antisymmetric rule. On the other hand, the relationship of being an electronic product is symmetric and equivalent since the electronic product for the seller is also the electronic product for the buyer.

  Strength can be defined for equivalence relations. Regarding two equivalence relations R and S in one set X, when xRy⇒xSy, it is said that R is stronger than S and S is weaker than R. Also, the classification by R is finer than the classification by S, and the classification by S is coarser than the classification by R. The strongest equivalence relation is an equivalence relation of “the same thing”, and the weakest equivalence relation is an equivalence relation that any two elements of X are equivalent.

[5] Quotient space (equalized space)
Let X be the phase space. a quotient map (often an equalization map (f), which is a surjective and continuous mapping of f and maps each point x∈X to an equivalence class x / ∈∈X / 〜 which is a subset containing x. identification map)).
f: X → X / ~
Here, as already described, “map f: X → Y is a surjection”
(∀y∈Y) (∃x∈X) [f (x) = y]
Means

For a subset X ⁰ ⊆X of X,
X ⁰ is open {f ^-1 (X ⁰ ) | y} A is open at X (this means that f is continuous)
Considering a bijection map f such that the following holds, X / 〜 is called a quotient space (or an equalization space) by a quotient mapping (or an equalization mapping) f. There is a reason that quotient space is also called equalization space. This is because, as described above, the quotient space can be obtained by equating the equivalence classes x / ∈X / 〜, which are the respective elements, with the points x に X included in x / 〜.

と表す。逆に集合Ｃは互いに素である２つの集合Ａと集合Ｂに直和分解されるということができる。 [6] Adhesive Space Generally, when there is no common element between the set A and the set B, that is, when A∩B = φ, it is said that A and B are mutually disjoint. The union C of the disjoint sets A and B is particularly called a disjoint union (also called “exclusive OR”).

It expresses. Conversely, it can be said that the set C is directly sum-decomposed into two disjoint sets A and B.

は、接着写像（attaching map）ｆによってＹをＸに接着（attach）することによって得られる接着空間（attaching space）である。この接着写像ｆは、各点ｙ∈Ｙ_０｜Ｙ_０⊂Ｙをその像ｆ（ｙ）∈Ｘと同一視することにより同値関係を規定するものである。 Now, starting from the phase space X, another phase space Y is adhered to this. FIG. 1 is a diagram illustrating a state in which a bonding space is generated from two disjoint phase spaces X and Y.

Is an attaching space obtained by attaching Y to X by an attaching map f. This bond map f defines the equivalence relation by equating each point y∈Y ₀ | Y ₀ ⊂Y with its image f (y) ∈X.

は商空間の一例であり、

である。この場合における等化写像（identification map）ｇは、

である。すなわち、等化写像ｇは、互いに素である２つの位相空間Ｘ、Ｙの直和

を、接着写像ｆによって規定される同値関係による同値類の直和

に写像する。 The bonding map f is a continuous mapping where f: Y ₀ → X. However, Y ₀ ⊂Y. Thus, the bonding space

Is an example of a quotient space,

It is. The equalization map (identification map) g in this case is

It is. That is, the equalization map g is a direct sum of two disjoint phase spaces X and Y.

Is the direct sum of the equivalence classes according to the equivalence relation defined by the bonding map f.

Map to

である。ここで
ｉ：Ｘ→Ｙは、包含（inclusion）である。すなわち
∀ｘ∈Ｘ，ｉ（ｘ）＝ｘ
である。 [7] Restriction and inclusion For any function g: Y → Z, the restriction of g to X (X⊆Y) is

It is. Here, i: X → Y is an inclusion. That is, {x} X, i (x) = x
It is.

[8] Extension and Retraction of Continuous Mapping For a phase space X, Y and a subspace A⊂X, a continuous mapping f: X → Y that satisfies f | A: A → Y is a mapping f from A to X f | Continuous extension of A (or simply extension). Extensions are partial functions.

Restriction r is a continuous extension of the identity map 1 _A : A → A that satisfies r: X → A. Therefore, r | A = _1A .

を満たすレトラクション（retraction）ｒ：Ｘ→Ａがあるならば、ＡをＸの変形レトラクト（deformation retract）と呼び、

で表す。
もし、Ａがただ一つの点Ａ＝｛ａ｝⊂Ｘであるならば、Ａはレトラクト可能(retractable)といい、

で表す。 For A⊂X,

If there is a retraction r: X → A that satisfies, A is called a deformation retract of X,

Expressed by
If A is the only point A = ｛a｝ ⊂X, then A is said to be retractable,

Expressed by

[9] Homotopy Homotopy is an example of an extension. X and Y are phase spaces, f and g: X → Y are continuous maps, and I = [0, 1]. The homotopy is designed as follows.
H: X × I → Y
However, for t∈I,
When t = 0, H = f
When t = 1, H = g
Holds. At this time, f is said to be a homotopic topic for g.

Homotopy is a continuous mapping extension,
H | X × {0} = fi ₀
H | X × {1} = gi ₁
Where i ₀ = X × {0} → X
i ₁ = X × {1} → X

である、すなわち同じホモトピー型をもつように設計する。それは、次の条件が満たされるように設計することでなされる。 Now, the design of the phase space at the homotopy level will be described. Two phase spaces X and Y are homomotopically equivalent

That is, they are designed to have the same homotopy type. It does so by designing to meet the following conditions:

である。ここで１_Ｘおよび１_Ｙは恒等写像、すなわち１_Ｘ：Ｘ→Ｘ、１_Ｙ：Ｙ→Ｙである。 For two continuous maps f: X → Y and h: Y → X,

It is. Here, 1 _X and 1 _Y are identity maps, that is, 1 _X : X → X, 1 _Y : Y → Y.

  Homotopy equivalence is an example of an equivalence relationship, but homotopy equivalence is a broader concept than topology equivalence. Homotopy equivalence can identify changes in information that after a change are no longer topologically equivalent. Information changes by various operations and processes, and the operations and processes are specified by homotopy, and changes in information are verified by homotopy equivalents. In fact, homotopy equivalence is more abstract than set-theoretic equivalence in terms of the abstraction of invariance. This is because, when a given set is changed by adding or deleting elements, the set can be made homotopy equivalent by saving the operation procedure of addition or deletion and the added or deleted elements. In addition, by performing cell disassembly, which will be described later, so as to have the same homotopy, it is possible to reverse the cell disassembly to return to the state before the disassembly.

[10] Cell structure space (cell space) design A cell is a topology that is topologically equivalent (ie, in-phase) with a closed sphere (called a closed n-cell) of an arbitrary dimension (for example, n dimensions, where n is a natural number). Space X.

と表記する。 Closed n-cell

Notation.

と表記する（しばしばｅ^ｎとも書かれる）。 Open n-cell

It referred to as (often written as ^{e n).}

は、ｎ次元閉球体（closed n-dimensional ball）である。ここで

はｎ次元の実数である。 Closed n cells

Is a closed n-dimensional ball. here

Is an n-dimensional real number.

は、ｎ次元開球体（open n-dimensional ball）であり、ｎ次元閉球体

の内部である。

は、閉のｎセルの境界であり、これは（ｎ−１）次元球面（sphere）Ｓ^ｎ−１である。 Open n cells

Is an n-dimensional open sphere and an n-dimensional closed sphere

Inside.

Is the boundary of a closed n-cell, which is a (n-1) -dimensional sphere Sn ^-1 .

は、連続関数

であり、次を満たす。

Characteristic map for the phase space X

Is a continuous function

And satisfies the following.

は、開のｎセルであり、

は、閉のｎセルである。

Is an open n-cell,

Is a closed n cell.

From the phase space X, the index is given by the integer set Z, finite or infinite series of cells X ^p is a subspace of ^{X {X p | X p ⊆X} , p∈Z} can be configured. This is called filtration and satisfies the following conditions. X ^p is the coating of X (covering), i.e., _X = ∪ p∈Z X ^{p, and} the subspace of ^{X p-1} is ^{X p,} namely ^{X 0 ⊆X 1 ⊆X 2 ⊆ ...} ⊆X p- ¹ {X ^p } ... {X (this is called the skeleton). A skeleton with a maximum p dimension is called a p-skeleton.

^{C = {X p | X P} ⊂X, p∈Z} cell decomposition of the phase space X (cell decomposition), or phase space X, that division into subspace ^{X p} is a closed cell (partition). (X, C) is called a CW-complex.

  When performing cell decomposition while preserving the cell adhesion map, the cell space can be turned into a reusable resource. Such stored and shared information is referred to as a cellular database, and a system that manages the cell database is referred to as a cellular database management system (cellular database).

によって、Ｘ^ｐ−１にｐ次元閉球体の直和（disjoint union）

を接着することによって作られる。 More precisely, according to JHC Whitehead, "Algebraic Homotopy Theory", Proceedings of International Congress of Mathematics, II, Harvard University Press, pp. 354-357, 1950, when a phase space X is given, a skeleton X ⁰ ⊆X ¹ ⊆X ² ⊆ ... can recursively composing the ⊆X ^p-1 ⊆X ^p ⊆ ... filtration ^{X p} having ⊆X as the following conditions are met phase space.
(1) X ⁰ ⊂X is a subspace whose elements are 0-dimensional cells of X, and (2) X ^p is created from X ^{p−1 as} follows. That is, X ^p is a surjective and continuous mapping called an adhesive mapping.

By Xp ^-1 , the disjoint union of the p-dimensional closed sphere is obtained.

Made by gluing.

を求め、

における各点ｘ、すなわち

を、連続写像

（ただし、各インデックスｉに対してｘ〜ｆ_ｉ（ｘ）である）
によって、その像

と同一視（identify）することによって、Ｘ^ｐ−１から構成される。 In other words, X ^p is a direct sum

,

At each point x, ie

Is a continuous mapping

(However, x to f _i (x) for each index i)
By the statue

And Xp ^-1 by identifying.

と書くことができ、これは、接着空間の一例である。写像Ｆ_ｉはセル

の接着写像の一例である。 Thus, X ^p is a quotient space or an identification space,

Which is an example of an adhesive space. The mapping _Fi is a cell

3 is an example of an adhesive map of FIG.

Filtration space is a homomotopically equivalent space to filtration. The phase space X and the skeleton X ⁰ ⊆X ¹ ⊆X ² ⊆... ⊆X ^{p -1} ⊆X ^p ⊆... ⊆X are collectively called a CW space (CW-space). As described above, as a cell complex, this is called a CW-complex.

を等化写像（identification map）の一例として得る。

In this way, the mapping

Is obtained as an example of an equalization map.

に対する特性写像（characteristic map）

は、

と書ける。 Each n cells

Characteristic map for

Is

Can be written.

と書ける。 Embedding X ^p-1 as a closed subspace of X ^p is

Can be written.

  If the CW space is diffeomorphic, this is equivalent to a manifold space.

  A space in which the attributes of an object constructed in cyberspace are represented by such cells is called a cellular structured space or simply a cellular space. In cell modeling, cell construction (composition) and cell decomposition (decomposition) are possible while maintaining the cell dimensions.

  An example of a cell dimension will be described. For example, in the cyber world, the degree of freedom of an object having one attribute cannot be shifted from one attribute to another attribute, and thus the dimension of the cell is zero. This object is represented as a point at the representation level. Here, the attribute means an independent set for designating a characteristic or characteristic that the object originally has.

  In an object having two attributes, the transition from one attribute to the other is possible, so that the degree of freedom is one and the dimension of the cell is one. This object can be represented as a straight line at the representation level. Similarly, an object having three or four attributes has two or three degrees of freedom, respectively, and can be expressed as a curved surface or a sphere, respectively. In general, an object with n attributes has n-1 degrees of freedom and a dimension of n-1. This can be represented as a (n-1) -dimensional sphere. The relational model expresses an object having n attributes as a relational schema, and generates an n-column table as an instance thereof. The relational model is based on the direct product of sets, so it can be said to be an expression at the set theory level.

  The cell space is obtained by adding the concept of dimension to the adhesive space. In the cell space design, the dimension of the attribute of the object in the adhesive space is defined. When the dimension of the attribute of the object included in each equivalence class is inconsistent in the adhesion space that is a direct sum of the equivalence classes, a process of adjusting the dimension of the attribute of the object is performed.

[11] Expression Design After the dimensions of the cell are designed at the cell space level, the presentation of the cell is designed at the expression level. In the expression design, the expression format such as the data type and the number of digits of the attribute of the object is detailed. If there is an inconsistency in the expression form of the attribute of the object, processing is performed to match the expression form with the acceptable expression (Admissible Representation). The inconsistency in the expression form of the attribute of the object includes, for example, a difference in the data type or the number of digits, and the difference can be resolved by data type conversion or digit number conversion.

[12] View Design After the expression form of the attribute of the cell is detailed at the expression level, a view, that is, a range that can be seen by the user is determined. There is a demand that the user wants to view only the part of interest in the collection of objects in an appropriate format. In addition, it is necessary to limit the range that the user can refer to for security reasons. For this reason, in the view design, a subset of objects that can be referred to for a user and a view in which the attributes of objects that can be viewed are restricted are determined.

[13] Incremental modular abstraction hierarchy Each of the above described levels of homotopy, set, topological space, adhesion space, cell space, representation, and view forms an incrementally modular abstraction hierarchy. I do.
1. Homotopy level 2. 2. Set theory level Topological level 4. 4. Adhesive space level 5. Cell space level Expression level 7. View level

  These hierarchies are modularized, allowing information to be manipulated incrementally in each hierarchy, and are extremely useful in hierarchically inheriting equivalence relations that indicate the invariant of the cyber world. It is.

  First, an object to be made equivalent to a specific element of a plurality of object sets is selected. Next, the topology is defined in the object set, and the equivalence relation is defined in the topology space, so that the plurality of object sets are designed as a bonding space that is a direct sum of the equivalent classes. Furthermore, the cell is decomposed into equivalent cells and other cells in the cell space, so that the equivalence relation is inherited up to the cell space level.

  Further, the equivalence relation is inherited up to the expression level by defining the expression form of the cell based on the acceptance expression, and the equivalence relation is inherited up to the view level by defining the user's view last. If an acceptance expression level for defining an acceptance expression is provided as one instance of the expression level, the object can be made equivalent at the expression level.

  In this way, in the incrementally-modular abstract hierarchy model, while the equivalence relationship is inherited between the abstract hierarchies, the specifications to be satisfied by the objects are designed in each hierarchy, so that the abstraction is performed while incrementally adding, deleting and modifying information. You can go back and forth between hierarchies to refine object specifications. Further, the object designed in this way can be made into a part in a reusable form.

  In a set S composed of a subset of the set X, when the union of all the sets belonging to S is equal to X, S is called covering the set X. When integrating n information systems, a "business operation integration decision" is equivalent to a decision to make a cover of n sets on an incrementally modular abstract hierarchy. Here, the work may be from different organizations. The n sets generally have overlap. For example, the same employee may participate in a plurality of operations. The business integration is implemented by inheriting the covering of the n sets between the incrementally modular abstract hierarchies. In other words, the generation of business coverage at each of the homotopy level, the phase space level, the adhesion space level, the cell space level, the expression level, and the view level is business integration. Once the covering is created, the integration and manipulation between the n information systems is all done through the covering on an incrementally modular abstract hierarchy. As a result, the integration and operation between the n information systems are both linear. As described above, according to the incrementally-modular abstract hierarchy, it is possible to realize a linear interoperability by configuring a linear interface called covering between n information systems.

The phase space in incrementer Li modular abstraction hierarchy model is not limited to the Hausdorff space (Hausdorff space) i.e. T ₂ phase space. In the T ₂ phase space, _two different points can be separated by an open set due to the separation axiom. However, even in a T ₀ phase space or a T ₁ phase space where two different points cannot be separated by an open set, the same is applied. Note that the space can be designed. Therefore, the abstract hierarchical model is very versatile.

  Adhesive space is modeled by abstracting the characteristics common to influential commercial information systems used by major companies and public institutions so as to be equivalent between different information systems in the form of adhesive space. As described above, the bonding space is a novel data model capable of linearly integrating disparate information systems, and greatly contributes to avoiding a combined explosion of integrated work. For the automation of linear interface generation after linear integration at the glue space level, the above-described incrementally modular abstract hierarchy is used. According to this abstract hierarchy, since equivalence relations are inherited to lower hierarchies, it is possible to provide an interface to an existing information system and realize linear interoperability for executing integrated system-scale tasks. .

  For comparison, a relational database system will be described as an example. In a relational database system, a relation is a set of tuples. The relation changes over time by inserting a new tuple into the relation, deleting an existing tuple, or modifying the attribute value of the tuple. For example, consider "employee (employee number, name, affiliation, joining year)" as a relation. When a new employee joins the company, a tapple representing that employee must be inserted into the "Employee" relation. On the other hand, when an employee retires, the relationship "employee" must remove the tuple representing the employee. Further, when the assignment destination of a certain employee changes due to the rearrangement, the value of the attribute “affiliation” in the employee's tuple must be corrected.

  As described above, in the relational database, the relation changes with time due to insertion, deletion, and modification of the tuple. However, relations have the unique property of representing the employee's employee number, name, affiliation, and year of joining, which is invariant over time. Relations have such a structure that is invariant with respect to time, and this is called a relation schema.

  Since the relational database model is based on set theory, equivalence relations cannot be defined at the level of the topological space. Therefore, in order to integrate a plurality of different databases, it is necessary to redesign the database, for example, by re-assigning IDs, thereby causing a problem of man-hour explosion. On the other hand, in the incrementally modular abstract hierarchical model, the equivalence relation defined by the superordinate concept can be reduced to the expression level, so that a plurality of different information systems can be integrated by a linear operation. That is, the interface of each element of the information system can be obtained only by one conversion to the bonding space, the interoperability is guaranteed by n conversions with n elements, and the number of interfaces is linear.

  As described above, since the conventional relational model does not model the equivalence relation with respect to the abstract hierarchical model of the present invention, information cannot be treated in a unified manner. At best, another table showing the relationship between the tables is provided in the manner of applying a patch, and an attempt is made to take an interface, but this increases the number of interfaces exponentially. On the other hand, SAP and UML (Unified Modeling Language), which are based on the ER (Entity Relation) model, are all intuitive graph theory models, and the models themselves cannot handle equivalence relations. Problems arise. This is the current state of social infrastructure information systems, and the major problem is that the systems do not have clear interoperability.

[14] Application Examples [14.1] Web Information Modeling Usually, the job of a Web information management system is to perform very close interaction with human recognition through visualizing information using Web graphics. While managing information on the Web. The task of Web graphics is to project various images on a graphics screen for human understanding. Humans understand the displayed image by linking the image displayed in the display space to the recognition target in the human recognition space. Often, low-priority geometric shapes, even geometrically accurate representations that are not usually essential information in the cyber world, can mislead human perception. For web information management, web graphics must be able to convey important messages on the screen so that humans can immediately recognize them at the speed of the changes in the cyber world. Hereinafter, a simple example will be described.

と表記することができる。一般化のために、ＸとＹを位相空間とする。ファンドＹ_０は金融取引会社Ｙの属性の一部であるから、Ｙ_０⊂Ｙが成り立つ。図２は、Ｗｅｂ上のエレクトロニックファイナンスのプロセスをＷｅｂグラフィックスにおいて図示したものである。次に、ファンドが取引のために特定された後、顧客Ｘは取引会社Ｙとどのようにして関係づけられるかを述べる。ここで提案するＷｅｂ情報モデルは、顧客Ｘと取引会社Ｙの関係を接着写像ｆによって正確に表現し、また、「ファンドＹ_０が取引のために特定されている」という状況を２つの互いに素である位相空間Ｘ（顧客）と位相空間Ｙ（金融取引会社）の接着空間として表現する。この接着空間は、顧客Ｘから始めて、金融取引会社Ｙを顧客Ｘに接着することにより得られる。ここで、ＹのＸへの接着は、連続写像ｆを介して、各点ｙ∈Ｙ_０｜Ｙ_０⊆Ｙをその像ｆ（ｙ）∈Ｘと同一視することによって行われ、その結果、ｘ〜ｆ（ｙ）｜∀ｙ∈Ｙ_０である。このように、〜で表記される同値は、Ｗｅｂ情報の接着空間モデルとして接着空間を作成するために、Ｗｅｂ情報モデリングにおいて中心的な役割を果たす。 [14.2] in Web information modeling Electronic Finance of electronic finance, find customer X is, when you are surfing the Web, the fund Y ₀ can be expected of the revenue that has been posted on the home page of the Web page of the financial transaction company Y Suppose. At this point, since the customer X is in the stage of “window shopping” on the Web, the customer X and the trading company Y have not yet shared the fund. Therefore, X and Y are disjoint and have no common elements. That is,

Can be written as For generalization, let X and Y be topological spaces. Fund Y ₀ is because it is part of the attributes of a financial transaction company Y, Y ₀ ⊂Y holds. FIG. 2 illustrates the electronic financing process on the web in web graphics. Next, after the fund has been identified for trading, we will describe how customer X is associated with trading company Y. The Web information model proposed here accurately expresses the relationship between the customer X and the trading company Y by means of the bonding map f, and also describes the situation that “Fund Y ₀ is specified for trading” by two disjoint elements. Is expressed as an adhesion space between a topological space X (customer) and a topological space Y (financial trading company). This bonding space is obtained by bonding the financial trading company Y to the customer X, starting from the customer X. Here, the bonding of Y to X is performed by identifying each point y∈Y ₀ | Y ₀ ⊆Y with its image f (y) ∈X via a continuous map f, and as a result, x~f (y) | ∀y∈Y is _0. As described above, the equivalent value represented by plays a central role in Web information modeling in order to create an adhesion space as an adhesion space model of Web information.

  The bonding space model described above can be applied quite equally equally in electronic manufacturing. Exactly the same technology is required to manage and display the electronic manufacturing process. In order for electronic manufacturing to respond effectively to market demands, it must specify how components of various sizes are assembled in a unified design. By thinking that Electronic Finance presented above is to assemble customers and trading companies as components of Electronic Manufacturing, the Web Information Management System and Web Graphics for Electronic Finance has actually become a part of Electronic Manufacturing. It becomes applicable to. If different technologies are used for different applications, the rapidly growing cyber world cannot be managed in a timely manner by the Web information management system or displayed by Web graphics.

[14.3] Web Information Modeling of Electronic Manufacturing Web information modeling of electronic manufacturing using an adhesive space model is quite simple. Basically, manufacturing on the web called electronic manufacturing is modeled as web information including the following information on the electronic manufacturing process.
1) Product specifications 2) Assembly specifications 3) Purchase of parts on the Web 4) Purchase at the assembly site on the Web

Each step is broken down into smaller sub-steps as needed. For example, step 1 can be broken down into the following sub-steps:
1.1) Market research of products in the electronic market 1.2) Product requirements derived from market research 1.3) Product specifications to meet the requirements

  A core part of the whole Web technology for electronic manufacturing is the modeling of products and assemblies on the Web as Web information modeling. FIG. 3 clearly illustrates the modeling of the most rudimentary assembly, using a simple example of a chair having two components, a seat and a support. In electronic manufacturing as an advanced manufacturing, the components of the product are modularized and can be replaced to buy higher quality components, make the most effective upgrades or repair. Have been.

  It is clear that electronic financing and electronic manufacturing share the same information modeling on the basis of adhesion space and equivalence.

[15] Example FIG. 4 shows the configuration of the information design apparatus 10 according to the embodiment. The object set storage unit 900 holds a set of objects used in the information system. The information design device 10 refers to a collection of objects stored in the object set storage unit 900. The information design apparatus 10 may acquire an object set from an information system on the web without referring to the object set storage unit 900 and refer to the object set. In the following, in the embodiment, for convenience of explanation, a case will be described in which a predetermined correspondence or interface is defined between two object sets. This is just an example of defining an interface between them.

  The information design apparatus 10 includes a homotopy level processing block 100, an aggregation level processing block 200, a phase space level processing block 300, an adhesion space level processing block 400, a cell space level processing block 500, an expression level processing block 600, and a view level processing block. 700, and performs processing at each hierarchical level in the incrementally modular abstract hierarchical model described above.

が確定する。 The set level processing block 200 appropriately performs a set operation on a set of objects stored in the object set storage unit 900 to specify two object sets to be designed. The phase space level processing block 300 specifies the phases for the two object sets specified by the set level processing block 200, so that the two object sets are designed as phase spaces X and Y, respectively. At this point, the two phase spaces X and Y are disjoint, and are a direct sum or an exclusive OR of these phase spaces X and Y.

Is determined.

  The adhesion space level processing block 400 includes an equivalence relation setting unit 44, an equivalence relation holding unit 52, a corresponding element extraction unit 20, an adhesion mapping acquisition unit 22, and an equalization mapping acquisition unit 24, as shown in FIG. , A procedure acquisition unit 26, and a procedure recording unit 28.

  The equivalence relation setting unit 44 receives an input of an equivalence relation to be applied to two object sets from a user, and also automatically generates an equivalence relation based on the input of the user. The equivalence relation holding unit 52 stores in advance equivalence relation candidates so that the user can easily set the objective equivalence relation. Further, an interface may be provided so that a user can specify an element of an object set and describe an equivalence relation.

  The equivalence relation set by the equivalence relation setting unit 44 (hereinafter also referred to as a target equivalence relation) is transmitted to the corresponding element extraction unit 20. The corresponding element extracting unit 20 extracts a constituent element (hereinafter, also referred to as a “target element”) for which a corresponding relation is to be defined in two object sets based on the objective equivalence relation. At this time, the user may specify one of the target elements in one object set, and the corresponding element extraction unit 20 may extract the corresponding target element from the other object set based on the objective equivalence relationship.

  The target elements that are found to correspond to each other by the corresponding element extraction unit 20 form one partial phase space, that is, an equivalence class. According to the theoretical guarantee of the adhesion space model, the adhesion space is formed as an exclusive OR of the equivalence classes. It is formed. Since equivalence classes are classified based on invariants defined by equivalence relations, an object set can be objectively classified, and the classification result does not include individual differences between system designers. When one target element is determined, the other target element is determined. As described above, the correspondence or the number of interfaces becomes linear, and interoperability is guaranteed.

と定まる。接着空間は、もとは共通部分をもたない位相空間ＸとＹの間に、接着写像ｆを媒介として対応関係を持たせた位相空間である。 When the objective equivalence relationship is determined, the meaning of the correspondence between the target elements and the relationship are uniquely determined. Therefore, the bonding map acquisition unit 22 can specify the bonding map f indicating the correspondence between the target elements. When the bonding map f is determined, the bonding space also becomes

Is determined. The bonding space is a phase space in which a correspondence is provided between the phase spaces X and Y, which originally have no common part, via the bonding map f.

  The equalization mapping obtaining unit 24 obtains an equalization mapping g that is a mapping to a bonding space determined by a bonding map f from a space of a mere exclusive OR of the phase spaces X and Y. In practice, the equalization map g can be described by the phase spaces X and Y and the adhesion map f from its definition.

The procedure acquisition unit 26 receives the input of the objective equivalence relation from the equivalence relation setting unit 44, the input of the target element from the corresponding element extraction unit 20, the adhesion map f from the adhesion mapping acquisition unit 22, and the equalization mapping g from the equalization mapping acquisition unit 24. , The target element specified by the user and the objective equivalence relationship (hereinafter, also referred to as “attention procedure”) are specified as a homotopy, and are specified by a result of a series of processes.
・ Topological space X, Y
・ Objective equivalence relation ・ Glued map f
.Equalization mapping g
Is recorded in the procedure recording unit 28 in association with.

  The cell space level processing block 500 includes a cell joining section 62, a cell dimension adjusting section 64, and a correspondence table holding section 66, as shown in FIG. The cell space level processing block 500 inherits the specification of a plurality of object sets designed as a bonding space based on the objective equivalence relationship in the bonding space level processing block 400, and refines the specification of the object set at the cell space level. I do. The cell structure space model is a model in which dimensions are introduced into the adhesion space model, and the specification regarding the ID of the attribute of the object and the number of attributes is detailed at the cell space level.

  The cell joining unit 62 joins two target elements that have a correspondence relationship between two object sets according to a purpose equivalence relationship, and expresses attributes of objects belonging to each object set by cells. When there is an inconsistency regarding the dimension of the attribute between the two corresponding target elements, the cell dimension adjusting unit 64 performs a process for eliminating the inconsistency. The inconsistency regarding the dimensions of the cell includes a difference in the ID or number of attributes of the target element. The cell dimension adjusting unit 64 adjusts the irregularity of the attribute ID and the number of attributes between the two target elements, if necessary, and stores a table indicating the attribute correspondence between the two target elements in the correspondence table holding unit 66. To be stored.

  The expression level processing block 600 includes an expression generation unit 72, an expression format adjustment unit 74, and a conversion table holding unit 76, as shown in detail in FIG. The expression level processing block 600 inherits the specification of the object set refined at the cell space level in the cell space level processing block 500, and further refines the specification of the object set at the expression level. At the expression level, in order to determine the specific expression format of the cell, specifications regarding the data type and the number of digits of the attribute of the object will be detailed.

  The expression generation unit 72 generates an expression of an attribute of an object belonging to each of the two object sets. When there is an inconsistency in the expression level between two target elements that have a correspondence relationship due to the objective equivalence relationship, the expression format adjustment unit 74 performs a process for adjusting the inconsistency. The inconsistency of the expression level includes a difference in the data type and the number of digits of the attribute of the target element. The data types include Boolean values, signed integers, positive integers, real numbers, double-precision real numbers, character types, and the like. The expression format adjustment unit 74 converts these data types and aligns the data types of the target elements. Is also good. If the number of digits such as the number of digits of a character string or the number of significant digits of a numerical value is different even if the data type is the same, the expression format adjustment unit 74 adjusts and adjusts the number of digits of the attribute between the two target elements. Is also good. As another example of inconsistency, there is a difference in units such as measurement and money, and one unit system is converted to the other unit system using a conversion formula.

  When bonding the phase space Y to the phase space X, the expression format adjustment unit 74 determines, at the expression level, the data type and the number of digits of the attribute of the target element of the object set of the phase space X and the attribute of the target element of the object set of the phase space Y. Are compared, and the data type and the number of digits are converted in accordance with the attribute having higher accuracy. The same applies to the case where the inconsistency of the expression level of the attribute is adjusted among the target elements of three or more object sets. An attribute expression with high accuracy is selected, and the attribute expression of another low-precision target element is adjusted to match the attribute expression of the high-precision target element. As a result, it is possible to prevent the loss of the original data due to data type conversion, digit skip, or the like after bonding of target elements having different precisions.

  The expression format adjustment unit 74 acts as an expression filter having a receptive expression having the maximum number of characters and digits, and expressions passed through the expression filter have the same value at the expression level. The expression format adjustment unit 74 stores, in the conversion table holding unit 76, a table describing the conversion rule when the expression mismatch is adjusted.

  The view level processing block 700 sets a view according to the user, and displays a set of objects on a display or the like according to the view.

  The homotopy level processing block 100 guarantees that, when each processing block of the information design apparatus 10 performs an operation on an object set, a change in the object set caused by the operation becomes homotopy equivalent. The homotopy level processing block 100 includes a table of interest stored in the procedure recording unit 28, which is related to the generation of the adhesive space, a table stored in the correspondence table storage 66, which indicates the correspondence of the cell dimension mismatch, and a conversion table storage 76. By using the table indicating the conversion rule of the cell expression stored in the object set and reversely following the change brought to the object set by each operation, the object set can be returned to the state before the change.

  In this way, starting from the aggregate level processing block 200, the phase space level processing block 300, the adhesion space level processing block 400, the cell space level processing block 500, the expression level processing block 600, and the view level processing block 700 are equivalent. By successively refining the specifications of the two object sets while inheriting the relationship, the two object sets are output as equivalent to the expression level. As described above, the information design apparatus 10 based on the incrementally-modular abstract hierarchical model has a coherent guarantee that guarantees equivalence relations from the aggregation level to the top space level, the additional space level, the cell space level, the expression level, and the view level. The object set that functions as a filter and that has passed the filter is output as an instance whose equivalence relation is mathematically guaranteed.

  If there is more than one component to be associated, by setting the objective equivalence relationship for each component, the glue mapping is defined in the same way, and finally the result of gluing the corresponding elements between multiple object sets Is output. If one object set has n components of interest, the correspondence between any of the n components and any component of the other object set is specified, so the number of interfaces is linear. The problem of man-hour explosion is solved.

  According to the present embodiment, if an equivalence relation is set, it is possible to associate between the components of a plurality of object sets, and the components which have the equivalence relationship are always the same while the non-corresponding components are left as they are. Since information can be stored, and invariants can be classified and associated with each other, efficiency of information sharing and use can be further improved.

  The embodiment has been described above. The embodiments are exemplifications, and various modifications are possible, and it is understood by those skilled in the art that such modifications are also included in the present invention.

It is a figure explaining signs that an adhesion space is generated from two disjoint topological spaces. It is a figure explaining a mode that the topological space of a customer and a trading company is bonded. It is a figure explaining signs that a phase space of a seat and a support part is bonded. 1 is a configuration diagram of an information design device according to an embodiment. FIG. 3 is a configuration diagram of a bonding space level processing block of FIG. 2. FIG. 3 is a configuration diagram of a cell space level processing block of FIG. 2. FIG. 3 is a configuration diagram of an expression level processing block of FIG. 2.

Explanation of reference numerals

  DESCRIPTION OF SYMBOLS 10 Information design apparatus, 20 Corresponding element extraction part, 22 Adhesion mapping acquisition part, 24 Equalization mapping acquisition part, 26 Procedure acquisition part, 28 Procedure recording part, 44 Equivalence relation setting part, 52 Equivalence relation holding part, 62 Cell junction part , 64 cell dimension adjustment unit, 66 correspondence table storage unit, 72 expression generation unit, 74 expression format adjustment unit, 76 conversion table storage unit, 100 homotopy level processing block, 200 aggregate level processing block, 300 phase space level processing block, 400 Adhesion space level processing block, 500 cell space level processing block, 600 expression level processing block, 700 view level processing block, 900 object set storage unit.

Claims (13)

  Each of the layers has a modularized abstract hierarchical block configured to be able to operate on an object set, and the object set should satisfy while inheriting an equivalence relation of the object set between the abstract hierarchical blocks as an invariant. An incremental and modular information design apparatus, wherein specifications are incrementally detailed for each of the abstract hierarchical blocks. The modularized abstract hierarchical block comprises:
A set design unit that performs a set operation on the object set to design a desired plurality of object sets;
By defining the topology to a set having a subset of the object set as an element, a topological space design unit that designs the object set as a topological space,
An adhesion space design unit that defines an equivalence relationship on the plurality of object sets each designed as a topological space, and designs an adhesion space in which the subspaces associated with the equivalence relationship are adhered.
A cell space design unit that expresses attributes of objects belonging to the plurality of object sets in the adhesive space by cells, and designs dimensions of the cells;
The information design apparatus according to claim 1, further comprising: an expression design unit that designs an expression format of the cell.   The information design apparatus according to claim 2, wherein the modularized abstract hierarchical block further includes a view design unit that designs a view for a user with respect to the plurality of object sets.   The modularized abstract hierarchical block is designed so that a change in the object set caused by an operation on the object set by each design unit has a homotopy equivalent, so that the object set can be returned to the state before the change. The information design apparatus according to claim 2, further comprising a homotopy design unit that records an operation procedure. The bonding space design unit,
For a first phase space X and a second phase space Y which are relatively prime, a continuous mapping from a subspace Y ₀ of Y of the second phase space to the first phase space X is represented by the equivalent An adhesion map acquisition unit that acquires as an adhesion map f representing the relationship;
Each point y in said subspace Y ₀ of the second phase space Y, by identified with the image f (y) in the first phase space X by the adhesive mapping f, the second phase space The information design apparatus according to claim 2, further comprising: an equalization map acquisition unit that adheres Y to the first phase space and acquires the adhesion space as an exclusive OR of equivalent classes. The cell space design unit,
A cell joining unit that associates the object in the first phase space X and the object in the second phase space Y identified in the cell space with each other in the cell space,
The information design apparatus according to claim 5, further comprising a cell dimension adjusting unit that adjusts a mismatch in a cell dimension when associating in the cell space.   7. The information design according to claim 6, wherein the expression design unit includes an expression format adjustment unit that adjusts the expression format of the object associated in the cell space based on the receptive expression in the expression format of the object. apparatus.   Each of the layers has a modularized abstract hierarchy step configured to be able to operate on an object set, and the object set should satisfy while inheriting an equivalence relation of the object set as an invariant between the abstract hierarchy steps. An incrementally modular information design method, wherein specifications are incrementally detailed for each of the abstract layer steps. The modularized abstract hierarchy step comprises:
A set design step of performing a set operation on the object set to design a desired plurality of object sets;
A topology space design step of designing the object set as a topology space by defining a topology in a set having a subset of the object set as an element;
An adhesive space design step of defining an equivalence relationship on the plurality of object sets each designed as a topological space, and designing an adhesive space in which the subspaces associated with the equivalence relationship are adhered;
A cell space design step of expressing attributes of objects belonging to the plurality of object sets in the adhesive space by cells, and designing dimensions of the cells;
9. The information design method according to claim 8, further comprising an expression design step of designing an expression format of the cell.   10. The information design method according to claim 9, wherein the modularized abstract hierarchy step further includes a view design step of designing a view for a user with respect to the plurality of object sets.   The modularized abstract hierarchy step is designed so that a change in the object set caused by an operation on the object set in each design step becomes a homotopy equivalent, and the object set can be returned to a state before the change. The information design method according to claim 9, further comprising a homotopy design step of recording an operation procedure. A set design step of performing a set operation on the object set to design a desired plurality of object sets;
A topology space design step of designing the object set as a topology space by defining a topology in a set having a subset of the object set as an element;
An adhesive space design step of defining an equivalence relationship on the plurality of object sets each designed as a topological space, and designing an adhesive space in which the subspaces associated with the equivalence relationship are adhered;
A cell space design step of expressing attributes of objects belonging to the plurality of object sets in the adhesive space by cells, and designing dimensions of the cells;
An expression design step of designing an expression form of the cell,
And a view designing step of designing a view for a user with respect to the plurality of object sets. A homotopy design step of designing a change of the object set caused by an operation on the object set by each design step to have a homotopy equivalent, and recording an operation procedure thereof so that the object set can be returned to a state before the change. 13. The program according to claim 12, which is executed by a computer.

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