Following research article describes the conditions for the formation of interactive knowledge bases, that are based on the formation of growing pyramidal networks in the analysis of textual narratives. The stability conditions of knowledge systems on the basis of their representation in the format of logical-linguistic models are determined. The authors also determined the conditions of atypical representation of linguistic constructs knowledge in the process of their transformation into a system. The use of lambda-calculus notation for the formation of stable logical-linguistic models of narrative descriptions is proposed.
The use of modern information in the activities of various specialists today is quite deep interdisciplinary. Moreover, the use of various information resources in solving applied problems requires the availability of service-developed interactive knowledge bases. And the effectiveness of their use depends on the truth of the content, which is determined by the information component.
The practical main part of productive knowledge today is concentrated in the form of text descriptions. At best, these narratives have their digital image in the form of their presentation in the formats of various editors and means of displaying texts in computer systems. However, these digital images don’t have interactive services. Therefore, it’s quite important to create intelligent services that can turn these texts into structurally organized knowledge bases.
There is already the problem of using a large number of narratives, which should sufficiently expand intertextual connections. It allows to create a digital image of knowledge systems used in a single display format.
The first stage of the process of transforming narrative descriptions into the format of interactive knowledge bases that are able to interact with each other is the formation of logical-linguistic models of text descriptions.
The information base of any interactive
knowledge system consists of different data types
[
However, it should be noted that everything
related to the data will be presented through the
concept of the term [
Further we will consider the final sequences of
characters that are plural in nature, that is, they
can be combined into plurals on certain grounds.
Moreover, these sets can be represented as
hierarchically related classes. Each such class
includes sequences that have at least one common
property [
The condition that SSFLs are divided into
classes according to certain properties defines
them as intentional [
Then all classes formed by SSFL concepts are
extensional [
The hierarchical structures formed from SSFL
in the form of GPN are marked trees. Their labels
are SSFL concepts, that are class names, and
SSFL-concepts, which aren’t extensional, that is
have only one semantic meaning. SSFL-concepts
that have only one meaning can’t be reduced, that
is broken down into simpler concepts. Such SSFL
concepts will be defined in the future as terminal
[
All SSFL-concepts form a certain set of names
, that are labels of all GPN nodes. Under such
conditions, GPN is unique to the set of Bohm trees
[
X1, X 2 ,..., X n , a1, a2 ,..., am , (1) where X i – class of SSFL-concepts, a j – terminal node (the non-extensional SSFLconcept).
Having determined the property classes
R1, R2,..., Rm , that implement the division of all
GPN concepts into classes, and determine the
relationship between the concepts, we obtain the
corresponding GPN. According to [
Based on the condition formulated at the
beginning, namely that an arbitrary type of SSFL
is a term, it can be argued that all names of
SSFLconcepts can form the set of terms , that’s
represented in the notation of lambda calculus [
We’ll note also one more constructive property
of GPN. Nodes that are hierarchically
interconnected can form truth statements that can
be calculated. Thus, based on the construction of
the GPN from SSFL-concepts, a certain system of
knowledge in terms of -terms is formed. Its
information base consists of certain linguistic
structures formed from SSFL-concepts, that are
terms. The values of these terms required for
calculations are determined in the process of
assigning them the appropriate contexts. This
process is interactive. According to [
It’s clear that both functional data and
linguistic structures that make up an interactive
system of knowledge, that we present in the form
of a set of -terms, have certain relationships
with each other, that is in a certain way logically
and functionally characterize each other.
Therefore, it’s most effective for further
consideration of the information base of arbitrary
IKB to present in aggregate form, which is
implemented in the form of the logical-linguistic
models (LLM) class. This class of models is
implemented on the basis of predicative
representation of information structures of
arbitrary type [
The predicativeness of the linguistic constructs of IKB, as the composition of Bohm trees, determines the nature of the formation of statements from the nodes of these trees. Moreover, the formation of GPN as the composition of Bohm trees is also predictive.
However, the process of LLM formation is realized on the basis of determining the order relation over certain sets of -terms, that leads to the loss of the nominal value of their terms. It gives the calculation of the contextual meanings of the terms semantic nature and thus implements an interactive act of interaction with the information base.
X1, X 2 ,..., X n , a1, a2 ,..., am
(2) X 1, X 2 ,..., X n , a1, a2 ,..., am ;
X 1 , X 2 ,..., X n X 1B, X 2 D,..., X n V , P ; U x1,x2 ,...,xn ,a1,a2 ,...,am , (3) (4) where - the smallest element of all SSFLcontext values; B, D,V , P - context values.
Expressions (2) - (4) reflect the generalized metaprocedure of IKB formation on the basis of definition of context values of SSFL-concepts and their transformation.
The introduction of the smallest value of the context and the definition of the contexts themselves passively determines the order relation over the set of -terms, and thus creates the conditions for the formation of the GPN . That is, expressions (2) - (4) are recursive.
It can then be argued that an arbitrary LLM has
a nonempty structure of relationships between
SSFL-concepts, which has a hierarchical form and
can be represented as a tree. LLM is also an open
structure. This means that the information base,
the logical and linguistic characteristics of which
it represents, can be supplemented at any time
with the latest concepts and their relationships.
The open nature of LLM determines that this class
of models has the property of inductance. That is,
their graph model in the form of a tree can grow
due to the latest concepts and their relationships.
One of the effective types of graph models of
LLM is a growing pyramidal network (GPN) [
The attributes of the concepts that make up the
GPN nodes can be contexts that describe their
semantics; belonging to a certain thematic class,
that is determined by their semantics; relations
between concepts, etc. That is, the inductive
process of forming the new nodes of the GPN can
be represented as a sequence of statements that are
formed on the basis of the contexts of each
inductively active concept. Thus, in the process of
forming GPN, as a structural reflection of LLM,
the formation of logical expressions of a certain
set of statements is realized. Using the attributes
of each concept of these statements, it’s possible
to form a formal expression in the form of a record
of the algebra of statements calculus [
All constructs of LLM, namely: statements, chains of knots of GPN, logical formulas are certain terms. Linguistic constructs from terms have an atypical representation and can also have a propositional character, that determines the nominal value of SSFL-concepts, which are interpreted by formulas in the notation of statements algebra. Moreover, contexts that semantically define concepts that are propositional variables also characterize these concepts as dichotomous. This means that each statement that is formed on the basis of the concepts of the GPN is characterized by one of two meanings, that is to answer arbitrary questions in the format of “YES” or “NO”.
For expressions (1) - (4), this means that they are significant in the case of “YES”, and may not be taken into account in the case of “NO”. That is, provided that the contexts of the GPN form a true expression formula (2) - (4), an interactive knowledge base is formed. If there is a case of “NO”, which means that the true statements haven’t been formed, IKB or a fragment of these GPN isn’t implemented.
This greatly simplifies the formation of a training sample for an interactive knowledge system. It can be based on concepts whose significance in relation to the question of belonging to certain classes is true. That’s, to the question of the existence of the certain certainty that the concept of GPN belongs to certain class or group of classes, we will always get the answer “YES”. But it is clear that when the latest concepts are included in the GPN, we will receive answers not only “YES” but also “NO”. And this determines the conditions for expanding the training sample of the intelligent system.
According to the homotopy type theory [
The atypical nature of expressions (1) - (4),
including the case of defining the contexts of
SSFL using propositional variables, means that
the type of meaning of these contexts isn’t
important for calculations. They can be both
numerical and non-numerical. Moreover, the
logical expressions from propositional variables
are quite stable to the order of their positioning in
the formal expression, so they can occupy an
arbitrary position in the record. Also, the values
that they receive in the calculation don’t require
determining the relationship of strict or non-strict
order. That’s, transformations (2) - (4) are always
able to determine the truth and objectivity of LLM
values [
Thus, the GPN is the primary LLM taxonomy of the narrative of the document being processed. The training sample, which is the primary basis of the process of machine learning of the interactive knowledge base, is formed from the concepts of this narrative. Then formed on this basis, the GPN provides a systematic reflection of all the narratives that make up the primary information base of the interactive knowledge system. The systemology of the interactive knowledge base follows from the systemology of LLM and GPN. This provides a complete and correct interpretation of the properties of all the concepts that make it up. And as a consequence, it implements the solution of problems of classification of concepts that determine the latest nodes of GPN, diagnosing the states of all concepts on the basis of the formation of logical formulas in the notation of the statements algebra. Also, the systemology and dichotomy of propositional expressions from the concepts of GPN create conditions for predicting the presence of certain properties in the newly formed nodes of GPN.
Prediction in our view of LLM can have a truncated form of expression (2), which is supplemented by a representation of the form (6), namely: X1, X 2 ,..., X n , a1, a2 ,..., am
(5)
X 1, X 2 ,..., X n , a1, a2 ,..., am ,
,
(6)
where the contexts for all SSFL-concepts are
defined. In this case, the set of -terms includes
certain functional expressions that implement
predictive calculations [
The decision tree, that is based on the relationship between the concepts of the GPN, is a composition of Bohm trees, and can be converted into a propositional expression. Its elementary expressions, within the conditions of the specific problem, take the meaning of “true” or “denial”. The calculation of these values is realized on the basis of determining the degree of belonging of the attributes of the new concepts to the characteristic descriptions that make up the contexts of the educational sample.
Expressions (5) - (6) define not only different functionalities, but also the systemic stability of the latest concepts of GPN. To do this, the procedure of discretization of -terms set is determined, which implements the definition of the corresponding numerical scales, that consist of intervals characteristic of the contexts values of SSFL-concepts in a particular state. These procedures also take into account the frequency distribution of concepts in different classes, thereby increasing their classification features in the GPN, and as a consequence, systemic accuracy. Another consequence is the formation of more effective propositional expressions with the use of the latest concepts of the GPN, which are unique to the decision tree, and as a result define more stable systemic rules.
BT M U x1,x2 ,...,xn , (7)
a1, a2 ,..., am
where BT (M ) according to [
Thus, the interactive system of knowledge, that is implemented on the basis of the formation of GPN in the process of processing documents and narratives, is determined by the high stability of the systemic features of the GPN concepts and their relations. This is ensured by the following procedural interpretation of the properties of the GPNs themselves, as certain objects of a complex hierarchical structure.
1) Formation of propositional expressions in the notation of the algebra expressions that determine the classes of GPN concepts based on the optimal definition and selection of attributes combinations that are significant in the interval of a certain scale. At the same time, due to the application of the operation “negation”, the procedure of minimizing the descriptions length of each class defined in the GPN is also implemented.
2) Reliable classification of all concepts included in the training sample for GPN, and as a consequence of the formation of propositional expressions that dynamically reveal the patterns of both relevant classes of concepts and the relationship between them, while regulating the compactness of the training sample, excluding quality assessment of patterns, that were discovered.
3) Defining the membership function, which implements the mechanisms of fuzzy logic in calculating the characteristic characteristics of GPN concepts and their classes, and obtaining clear and fuzzy levels of reliability and their ranks, the validity of attribute features of concepts and their properties and relationships, including zero value type “I don’t know”.
All these procedural actions ensure the formation of GPN and on its basis LLM, that determines the functional structure of the interactive knowledge system. Based on them, the linguistic-semantic and conceptual analysis and processing of multilingual natural-language narrative descriptions are realized in the environment of the specified system. The selection of linguistic constructs of different length and complexity, identification and selection of intercontextual relations for all concepts that determine the semantic features of GPN and LLM, including the educational sample, is provided.
GPN and as a consequence of LLM, that are built on the basis of the above-described machine learning procedures, are characterized by the property of inductance. The further development of GPN, based on the encapsulation of new concepts, also expands the set of propositional expressions, that are in fact certain linguistic constructs, built on the application of logical operations to disordered elementary records statements that don’t have logical operators inside.
This is functionally represented by expressions (2) - (7). When forming Bohm trees of the form (4) under conditions that the contexts of their nodes determine only the true values, we implement recursion from expressions (2) - (4).
The identification of intercontextual relations in the process of the latest concepts encapsulation and further inductive growth of the pyramidal network, realizes the discovery of new statements as systems of knowledge. The intercontexts of the relationship are revealed through the logical operation “conjunction”, and the direct growth of GPN is realized by the use of logical operations “disjunction”, “negation” and “following” both direct and reverse.
If we apply the rule of Godel's theorem on
incompleteness [
All undefined nodes are concepts of complex structure. Their concepts, like linguistic constructs, have logical operations inside them and can therefore take the form of complex statements. Then such concepts can also be presented in the form of propositional expressions, that are able to define and classify the latest concepts with a complex structure.
Also, uncertainty concepts based on the use of inductance properties implement the clustering procedure, that provides identification of semantically equivalent concepts and their classes. The degree of this equivalence is determined based on the application of the membership function. Depending on the significance of the degree of equivalence, the concepts of uncertainty either form the newest class or are included in an existing thematic class.
After all, the measure of equivalence allows us to apply the rule of logical inference “following” by analogy. With a predetermined degree of equivalence, it’s possible to draw conclusions about the belonging of new concepts and their classes to those already defined, and also to determine the degree of certain statements validity that are formed on the basis of concepts whose contexts are relevant.
The methodology and formation of growing pyramidal networks constructively ensures the transformation of narrative texts into the format of interactive knowledge bases. GPNs are able to determine the conditions for the stability of information databases of interactive knowledge systems, to implement the transformation into their formats of unstructured narrative descriptions of various types, from scientific articles to catalogs of scientific and technical products, monographs and more.
The conceptual basis of such transformations in the form of atypical expressions provides the implementation of intellectual services for processing narratives by means of linguisticsemantic and conceptual analysis with their subsequent transformation into the format of logical-linguistic models and interactive knowledge bases.