Correlating and Cross-linking Knowledge Threads in Informledge

System for Creating New Knowledge

T. R. Gopalakrishnan Nair

1,2

and Meenakshi Malhotra

3,4

Saudi Aramco Endowed Chair, Technology and Information Management, PMU, Al Khobar, K.S.A

Vice President Advanced AI and Bio Computing, RIIC, D. S. Institutions, Bangalore, India

Advanced AI and Bio Computing, RIIC, D. S. Institutions, Bangalore, India

Lecturer, Dept. of Computer Science Eng, The Oxford College of Engineering, Bangalore, India

Keywords: Informledge System (ILS), Knowledge Network Node (KNN), Multi-Lateral Links, Weighted Graphs,

Tensor Graph Product, Concept, Concept State Diagram (CSD).

Abstract: There has been a considerable advance in computing, to mimic the way in which the brain tries to

comprehend and structure the information to retrieve meaningful knowledge. It is identified that neuronal

entities hold whole of the knowledge that the species makes use of. We intended to develop a modified

knowledge based system, termed as Informledge System (ILS) with autonomous nodes and intelligent links

that integrate and structure the pieces of knowledge. We conceive that every piece of knowledge is a cluster

of cross-linked and correlated structure. In this paper, we put forward the theory of the nodes depicting

concepts, referred as Entity Concept State which in turn is dealt with Concept State Diagrams (CSD). This

theory is based on an abstract framework provided by the concepts. The framework represents the ILS as

the weighted graph where the weights attached with the linked nodes help in knowledge retrieval by

providing the direction of connectivity of autonomous nodes present in knowledge thread traversal. Here for

the first time in the process of developing Informledge, we apply tenor computation for creating intelligent

combinatorial knowledge with cross mutation to create fresh knowledge which looks to be the fundamentals

of a typical thought process.

1 INTRODUCTION

With the advancement in the field of artificial

intelligence and cognitive science, development of

knowledge based systems has taken a greater leap.

Artificial Intelligence as stated is the study of the

computations that make it possible to perceive

reasons and act (Winston and Patrick Henry, 1992).

Cognitive Science as referred by Thagard, Paul

(2005) is the field of study of mind and its

computational intelligence. Researchers from both

the fields have been striving to develop a knowledge

based system that could simulate the mode of

existence or either of human knowledge and human

information processing mechanism or both.

Knowledge management field developed so far

involve information storage, processing and retrieval

of information stored in databases in the form of

fixed sentences and words. At present there is no

meaningful system at hand that can store elements of

concepts from different domains coherently and can

retrieve correlated knowledge. To overcome this, we

had suggested Informledge System (ILS) in our

work published earlier (T. R. Gopalakrishnan Nair

and Meenakshi Malhotra, 2011 and 2010). In ILS,

knowledge units belonging to same or different

knowledge domains are linked together to form a

knowledge network using the autonomous nodes and

intelligent links. These links play an important role

in connecting correlated concepts stored at the

knowledge units. The knowledge unit in ILS is

termed as Knowledge Network Node (KNN) as

defined by T. R. Gopalakrishnan Nair, Meenakshi

Malhotra (2010).In this paper we put forward the

theory of concepts represented by KNNs and the

Concept State Diagram (CSD) depicted by the

knowledge thread. This knowledge thread, formed

during knowledge embedding and retrieval, is the

result of intelligent linking of KNNs, wherein every

link formed is composed of multiple strands each of

which hold a property (T. R. Gopalakrishnan Nair

and Meenakshi Malhotra, 2011).

251

R. Gopalakrishnan Nair T. and Malhotra M..

Correlating and Cross-linking Knowledge Threads in Informledge System for Creating New Knowledge.

DOI: 10.5220/0004143302510256

In Proceedings of the International Conference on Knowledge Engineering and Ontology Development (KEOD-2012), pages 251-256

ISBN: 978-989-8565-30-3

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

This paper is organized as follows. Section II

discusses Research Background. It is then followed

by a brief introduction to the understanding of the

theory of concept in section III. Section IV gives the

Structural Organization of Concepts and CSD and in

section V we discuss the formation of knowledge

threads in ILS and section VI focuses on details

about Tensor algebra applied to the CSD. Finally,

we conclude the work in section VII.

2 RESEARCH BACKGROUND

As believed, all the information processing for

human cognition is held at the neurons. A neuron

receive information, process it and forward the

control to another neuron for the further information

processing, in the interconnected mesh of neurons

(David Sánchez, 2010). In almost similar process

ILS, the KNN receive the inputs and have the inbuilt

ability to infer and reason the linkages to the other

nodes (T.R. Gopalakrishnan Nair and Meenakshi

Malhotra, 2011).

In addition to this, knowledge-based

neurocomputing has gained importance in last two

decades. It is stated that Knowledge-based

neurocomputing (KBN) concerns with methods to

address the explicit representation and processing of

knowledge where a neurocomputing system is

involved (Ian Cloete and Jacek M. Zurada, 2000).

The key element involved in knowledge

processing and retrieval is the knowledge and its

representation. Knowledge representation has been

recognized as an imperative field of artificial

intelligence which involves information embedding

and processing for computation in cognitive models.

Knowledge has been represented using network,

graphs, and finite automata and using concept maps.

According to Christopher Brewster (2004) many

knowledge based representations involve use of

Ontology. Ontology finds its origin from the field of

philosophy whereas its implication in the field of

computer science is stated as “ontology is formal,

explicit specification of a shared conceptualization”

(Thomas R. Gruber, 1993). Also, there have been

efforts to define the set of attributes for the concepts

involved during ontology development (Priss, U.,

2006.).

Different strategies have been adopted to

represent concepts. Concept maps are used to

represent and convey knowledge. It is a diagram that

connects pieces with of information entities that are

linked by labelled straight lines without any

processing power. ‘‘Mind Maps’’ are such a type of

meaning diagram as shown by Beth Crandall et al.

(2006) and Farrand, P et al. (2002).The connecting

lines in Mind Map are not labelled and they

represent just the connection between ideas (Open

Directory - Reference: Knowledge Management,

2009). Also, the diagrams that are referred to as

‘‘Cognitive Maps’’ are large web like diagrams

which involve representation of sentences and short

paragraphs as ideas resulting in hundreds of joins

and the same has been shown with example by

(Robert M. Kitchin, 1994). However these maps are

just the fixed representation of joints representing

words whereas the knowledge representation does

not involve the language alone. Similarly, the

knowledge formation in human brain includes

concept formation and its representation in different

regions as stated in the field of neuroscience (Eric R.

Kandel et al., 2000).While the mind maps connect

the ideas they are not capable of processing the

knowledge nodes, but in the case of ILS, the system

is intelligent by virtue of its capability to formulate

and process the concepts which is kept apart from

how the knowledge is represented (Nair, T.R.G.,

Malhotra, Meenakshi, 2011).

Conceptual graph is a graphical representation of

knowledge depiction and reasoning. The translation

to and from the spoken language, used for

understanding, into some computer understandable

representation can be done by means of these

graphs (Sowa, John F., 1984). As stated by Michel

Chein , Marie-Laure Mugnier (2008), conceptual

graph involve mainly relations between concepts as

“is a” and “has property”. This restricts the way in

which knowledge can be linked, whereas ILS

provides the flexibility in linking properties of the

KNNs through the use of its multi-stranded links.

3 CONCEPT THEORY

Knowledge is nothing but a collection of linked

concepts. However many attempted to create

knowledge bases, connect words and sentences

rather than concepts (Rajendra Akerkar, Priti Sajja,

2010). In his book, Gregory L. Murphy (2002)

referred that many properties of concepts are found

in word-meaning and use, suggesting that meanings

are psychologically represented through the

conceptual system. Most of this type of approach

ended connecting words through lines where as the

meaning of the knowledge structure is created in the

human mind. But actual breakthrough is required in

incorporating a meaning creation processing

capability in the nodes and in the links by adding

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intelligence in both. In ILS, the information is stored

at the intelligent knowledge network nodes (KNN)

which is an integral part of this knowledge network.

A concept is represented partially or completely by a

KNN. The link between these autonomous nodes

represents the affinity between the concepts. For the

loosely related concepts the thickness of the link is

less whereas for tightly coupled concepts the

thickness is more. As more and more information is

added into the network, there is cross-linking of

concepts and new knowledge threads can be

retrieved through the interlinked concepts

correlation and cross-linking. In the first case of

existing knowledge bases, they were static

representation of the thinking process and where as

ILS is capable of furnishing active computation

process.

4 CONCEPT FRAMEWORK

Concept State Diagram (CSD) is the diagram that

depicts the states of the concepts that are connected

by strengthening of the links. CSD is basically a

knowledge thread where state is associated with the

concepts as shown in Figure 1.

The knowledge that can be retrieved after

incorporating knowledge representation in to the

retrieved knowledge threads is anomalous to the

sentence in language. The knowledge thread formed

by connecting concepts have two basic knowledge

units namely Apex Knowledge Unit (AKU) and

Subsidiary Knowledge Unit (SKU).

CSD, which is a form of a knowledge thread

comprise of these knowledge units defined as

follows:

4.1 Apex Knowledge Unit (AKU)

This knowledge unit in the CSD is the key concept

which implies that the knowledge thread formed by

CSD has this knowledge unit (KNN) representing

the concept about which something is stated in the

knowledge thread. E.g. considering the knowledge

thread “Continent is the largest and continuous

landmass on earth” can be represented in CSD as

shown in Figure 1.

Figure 1: Concept State Diagram for a Knowledge Thread.

Where the KNN’s shown in figure, 1 holds the

concepts shown in table 1 below

Table 1: Concepts and KNNs shown in figure 1.

KNN KNN1 KNN2 KNN3 KNN4 KNN5

Concept Continent Largest Continuous Landmass Earth

The AKUs here can be continent (KNN1), landmass

(KNN4) or earth (KNN5). The centre concept for

this CSD can be taken as any of the three. The

weight attached with any of the AKU would be more

than the weight attached with the nodes that are far

from the AKU. The weight attached with interlinked

concepts decreases as we traverse from AKU to

SKU.

4.2 Subsidiary Knowledge Unit (SKU)

This knowledge unit in the CSD is an auxiliary

concept which implies that the knowledge thread

formed by CSD has these knowledge units (KNNs)

in the form of supplementary concept. E.g.

considering the CSD as shown in Figure 1, largest

(KNN2) and continuous (KNN3) are the SKUs.

These SKUs supplement the AKUs, in common

language representation SKUs represent the

predicates whereas AKU’s represent subjects.

Hence the AKU and SKU provides a much wider

representation for knowledge in ILS analogous to

subject and predicates used in human language

representation.

5 CONCEPT FORMATION

ILS is an organized knowledge network, in which

connectivity and search is done through an ordered

set of links. Methods of understanding is in links

which includes classifying, correlating and

extrapolating the information. Properties of links

leads to processing where by several logically

interlinked concepts can be retrieved through it. The

interlinked links form CSDs, which facilitate to form

the cluster to knowledge threads during retrieval.

Before we put forward how this knowledge cluster is

formed, we brief about the CSDs.

The necessary and sufficient conditions for CSD

formation are stated as follows:

5.1 Every CSD that is Formed should

Consist of at Least One AKU and

Several SKUs

This can be proved by contradiction, by including

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253

the following two cases:



Let us presume CSD doesn’t have an AKU

Assume that there is a CSD that doesn’t have

an AKU. Let’s consider such a CSD shown in

figure 2, for this CSD there is no AKU

specified during embedding of this

knowledge. So this implies that all KNNs

linked would be SKUs only.

As stated earlier AKU and SKU are like

subject and predicates, so AKU could be

similar to what the knowledge thread is about.

Absence of AKU would imply that some

concepts represented by SKUs are linked but

doesn’t provide any information about

anything. Such a CSD is termed as irrelevant

and meaningless.

Figure 2: Incorrect CSD without AKU.

As shown in figure 2 the concepts grow, thin,

breathe, eat and strong, are just linked together

but no information can be retrieved from their

linking. Also, in ILS links properties provide

weightage which tend to present weak threads

linking these concepts.

 Let us presume CSD have multiple AKU’s

and no SKU

On the other hand if no SKUs are there then

it’s similar to a sentence not having any

predicates. This would mean some subjects

are linked, leading to no bigger concept. Main

objective behind linking concepts is to form a

bigger concept, whereas linking only AKU

would not provide any meaningful knowledge.

Same is depicted in the figure 3 where animal,

plant, stick, door and hands are linked but this

CSD does not provide any meaningful

knowledge.

Figure 3: Incorrect CSD with multiple AKU and no SKU.

These AKUs when put together doesn’t lead to

formation of any bigger concept or a valid

knowledge thread. These two points can be

considered similar to some invalid human

knowledge formation wherein one speaks about the

properties of an entity and not the entity itself or

someone connects some entities with weak links.

Thus, every CSD should consist of least one AKU

and one or more SKUs.

5.2 CSDs interact to form a Cluster of

Correct and Incorrect CSDs

During knowledge retrieval, the link processor at

KNN helps in retrieving the knowledge threads. The

intelligence of the system lies in interaction of these

retrieved knowledge threads. CSDs interaction is

basically interaction between two knowledge threads

that can connect and form multiple CSDs in the form

of knowledge cluster depending on the state of

individual knowledge units. The CSDs that are

formed by CSD interaction may be correct and

incorrect.

5.3 The CSD formed after Learning

has Got only One Form

During knowledge retrieval, CSDs interact to form a

cluster of valid and invalid CSDs. In addition to

having invalid CSDs, the cluster comprises of

repeated connected concepts based on the weights of

the concepts involved. The learning process involves

removal of invalid and the redundant CSDs. So after

the learning process, which is an integral part of

retrieval, is complete only one form of the CSD

would be there in the knowledge network.

5.4 The Final CSD must be

Conceptually Correct

It is stated for the proof of Statement 3 that the

invalid CSDs are removed during learning process.

Hence the final CSD in the ILS are conceptually

correct.

To retrieve knowledge intelligently from this

network, concepts need to be combined during

retrieval. These concepts interact to form

combination of ideas, which is possible due to

interaction between KNNs. During this interaction

various links are formed which comprise to

formation of both correct and incorrect CSDs. The

incorrect CSDs are discarded based on the

rationality involved in learning. CSDs are formed

during knowledge embedding and retrieval.

The splinters retrieved during the interaction of

CSDs have to pass through learning process. The

process includes sieving out of the CSDs that are

secondary and redundant invalid CSDs. Removal of

the same from the system, lead to consistent

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knowledge in ILS knowledge network.

6 CSD AND TENSOR ALGEBRA

CSD’s once formed interact during retrieval to form

the cluster. This involves tensor algebra from the

graph theory. In view of tensor algebra, as defined

by Sandi Klavžar and Simone Severini (2010)

The tensor product, K = G H, of graphs G =

(V(G), E(G)) and H = (V(H), E(H)) is the graph

with vertex set V(K) = V(G) × V(H) and {(g,

h), (g ', h ')} E(K) if and only if {g, g '}

E(G) and {h, h '} E(H).(

p. 3)

Now as a CSD is just a graph of nodes connected

together we can apply tensor product to the same.

This implies that if two CSDs interact they can

actually form a tensor product and the resultant

graph is a cluster of CSDs composed of relevant and

irrelevant CSDs. This cluster has a group of

concepts which are collection of AKUs and SKUs.

Let’s consider two knowledge threads kt1 and

kt2 as shown in the figure 4 and figure5.

Figure 4: Knowledge Thread kt1.

For the knowledge thread, kt1 shown in figure 4

represent the following knowledge and the concepts.

Knowledge thread, kt1 is “World has living and

non-living things.”

Table 2: Concepts represented by KNNs shown in figure

KNN Knn1 Knn2 Knn3 Knn4

Concept World Thing Living Non-living

Figure 1: Knowledge Thread, kt2

The knowledge thread, Kt2 is “Living things

grow and breathe like animals”.

For the knowledge thread, kt2 shown in figure 5

represent the following knowledge and the concepts.

Table 3: Concepts represented by KNNs shown in figure

KNN KNN2 KNN3 KNN5 KNN6 KNN7

Concept Thing Living Grow Breathe Animals

Here kt1 is similar to G and kt2 is similar to H

and the vertices set for both are as follows:

V (kt1) = {KNN1, KNN2, KNN3, KNN4}

V (kt2) = {KNN2, KNN3, KNN5, KNN6,

KNN7}

V (kt1)

⊗

V (kt2) = 4*5=20 vertices, which

comprise of the node space after the 2 knowledge

threads interact.

The cluster of CSDs formed after applying

tensor algebra for product of connected graphs is

applied to kt1

and kt2 shown in figure 4 and figure 5

respectively, is given in figure 6.

The edges connecting nodes of clusters combine

to form the link space as shown in figure 6.

Figure 6: CSD Cluster formed after interaction of two

knowledge threads, kt1 and kt2.

From the definition of tensor product of graphs,

the edge with vertices (KNN1, KNN2 (kt2)) and

(KNN2 (knn1), KNN3) in the cluster exist if and

only if (KNN1, KNN2 (kt1) is an edge (link) in kt1

and (KNN2 (kt2), KNN3) is an edge (link) in kt2. In

this cluster many CSD’s are correct or valid and

many are incorrect or invalid. E.g.: KNN2—KNN3--

-KNN6 are connected which means concepts living,

thing, breathe are linked to make a bigger concept

which is valid. Whereas KNN4 --- KNN6 are

connected which mean concept non-living and

breathe are linked which is invalid.

As we cannot multiply word here and there and

absurd things cannot connect. Whereas in

comparison to this we can multiply two concepts or

linked concepts are multiplied using tensor algebra

to form a bigger concept. So it’s only the concepts

that are involved in the interaction which result into

formation of a bigger valid concepts represented by

CSDs.

7 CONCLUSIONS

In this paper, we presented the theory of KNNs

which are capable of actively representing concepts

and the knowledge thread as Concept State Diagram

(CSD). The intelligence of ILS is depicted in

formulating correlated and cross-linked cluster of

CSDs through tensorial interaction of the CSDs.

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255

This correlation and cross-linking is established by

the tensor algebraically manipulations. Thus ILS is

capable to classifying and extrapolating the two

knowledge threads retrieved and can derive all the

cross-linked knowledge threads out of the

interaction. On forced interaction between two

tensorial knowledge threads, it can form new

clusters that consist of relevant and irrelevant CSDs,

from which the irrelevant CSDs can be sieved out

during learning process or so to say a thinking

process. The tensor algebra has been applied for

CSDs manipulations on the CSDs retrieved from a

single domain and this arrangement of manipulation

of CSDs for multiple domain need to be evaluated in

the next phase.

ACKNOWLEDGEMENTS

Authors express their sincere thanks to the IP

managers, for the patenting process on the sequence

of theories related to this.

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