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2 Hendrix's Partitioned Semantic Networks

2 Hendrix's Partitioned Semantic Networks

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M. Kr´

otkiewicz et al.

Main Features of the Extended Semantic Nets Module



Basic Assumptions and Primitive Notions of ESNM

The basic primitive notions of ESNM include: an operator, an operand and a

role. An operator links operands using roles. Operators can be of widely varied

characters. They can be, for example, actions being performed. In the sentence

“John goes to New York City by car.” the action represented by the verb (to)

“go” is the operator. It links operands designated by “John”, “New York City”

and “car ” through appropriate roles termed “actor ”, “destination” and “tool ”.

This is demonstrated in a graph in Fig. 1.

Fig. 1. Graph representing the sentence “John goes to New York City by car.”

Operators may be of various types depending on their behavioral character.

A list of operator types is shown in Table 1:

Table 1. List of operator types.

Operator type Symbol Question



What is it doing?



What state is it in?



What property does it have?

An activity type denotes an action/operation which is being performed by

the actor or actors. State is the state of the described object or objects. Property

means defining a property of the object or objects and is used to e.g. define the

values of attributes. A list of predefined operand roles is shown in Table 2.

A relationship can also be an operand. For example, the term “marriage”

could be represented in semantic networks as an operator linking two operands

via roles termed “husband ” and “wife”. Figure 2 shows a graph corresponding

to this relationship.

An SKB has a far more complex way of building semantic networks than what

is shown above. It was termed Extended Semantic Network Module because of

its various features significantly expanding them in terms of both grammar and


SKB: Quantifiers and Multiplicity in Extended Semantic Networks Module


Table 2. List of predefined operand roles.

Operand role





With whose participation?





Modality internal

Is he able to? Does he want to? Does he need to?

Modality external

Is he allowed to? Should he? Does he have to?


In what relation/In what kind of relationship?

Adverbial of manner How?


Where from?


Where to?


Using what?

Fig. 2. Graph representing a relationship termed marriage.


Extensions of the Classic Semantic Networks in ESNM

Among the most important extensions of classic semantic networks are such

concepts as: modifiers, quantifiers, cardinality and certainty factor.

Modifiers. Modifiers enable additional properties and values for operators,

operands as well as for modifiers themselves.

Fig. 3. Graph representing the sentence “John goes very fast to New York City by big



M. Kr´

otkiewicz et al.

For example, the sentence shown in the previous section could be expanded

to “John goes very fast to New York City by big car.” The graph representing it

is shown in Fig. 3.

The operand “car ” was supplemented by the modifier “big”, while the operator (to) “go” was extended by the modifier “fast”, and the modifier itself was

extended by the modifier “very”.

Quantifiers. Quantifiers significantly complement the information concerning

operators and operands. The following types of information which can quantify these elements were selected: certainty factor (cf ), time quantifier (tq),

space quantifier (sq), intensity quantifier (iq). Certainty factor (cf ) takes values between [0, 1] and shows the degree of certainty about a described element

of information. For example, the sentence from the previous section could be

expanded to: “Probably (cf =0.5) John goes very fast to New York City by big

probably (cf =0.9) car.” (Fig. 4).

Fig. 4. Graph representing the sentence “Probably (cf =0.5) John goes very fast to New

York City by big probably (cf =0.9) car.”

Fig. 5. Graph representing the sentence “Probably (cf =0.5) John goes very fast

rarely (tq=0.1) to New York City by big probably (cf =0.9) , everywhere (sq=1) car.”

SKB: Quantifiers and Multiplicity in Extended Semantic Networks Module


It should be noted that the certainty factor (cf ) does not pertain to an

entire fact, but only to its selected element. Every quantifier can be completely

independently defined for the operator and each operand.

The time quantifier (tq) and the space quantifier (sq) take values between

[0, 1], where 0 means never or nowhere respectively, while a value of 1 should

be interpreted as always or everywhere. The graph presented in Fig. 5 contains

both a time quantifier (tq) and a space quantifier (sq).

These quantifiers are linked to the operator or an operand; however, it is easier

to interpret them in the context of the role they fulfill. An intensity quantifier (iq)

defines the level of intensity with which a given element fulfills its role. If the role is

e.g. an “actor ”, the intensity quantifier defines how deeply is he engaged in fulfilling the role of a given operator. An example of a graph representing information

which takes the intensity quantifier (iq) into account is shown in Fig. 6.

Fig. 6. Graph representing the sentence “Probably (cf =0.5) John (iq=0.7) goes very fast

rarely (tq=0.1) to New York City by big probably (cf =0.9) , everywhere (sq=1) car.”

Fig. 7. Graph representing the sentence “Probably (cf =0.5) John (iq=0.7) goes with 3 to

4 passengers very fast rarely (tq=0.1) to New York City by big probably (cf =0.9) , everywhere (sq=1) car.”


M. Kr´

otkiewicz et al.

Multiplicity. The multiplicity of a relationship is defined by minimum

(cardinalitymin) and maximum (cardinalitymax) number of elements constituting operands which participate in a given role. The default values are:

cardinalitymin = 1, cardinalitymax = 1. Considering the sentence: “Probably (cf =0.5) John goes with 3 to 4 passengers very fast rarely (tq=0.1) to New York

City by big probably (cf =0.9) , everywhere (sq=1) car.” a graph shown in Fig. 7 can

be created.


Association-Oriented Database Metamodel (AODB)

AODB [9,12] is complete and consistent database metamodel. All of its components have been elaborated exclusively for this metamodel and are dedicated

to it, i.e. it does not use any language, data storage model or other element of

known database systems.

Association-oriented metamodel is based on the following primitives:

– intensional (structures): database (Db), association (Assoc), role (Role), collection (Coll ), attribute (Attr ),

– extensional (data): association object (AssocObj ), object (Obj ), role object

(RoleObj ).

In the extensional matter the most important categories are the following:

association (Assoc) and collection (Coll ). Association (♦) is primitive realizing

conception of relationships between data and the function of collection ( ) is to

store data.

Association is the owner of roles. Roles are lists of references to linked

elements, that can be either objects (instances of collection) or association

objects(instances of association). Roles in given association can have any cardinality, which means unrestricted arity of relationships. Each role is defined with

number of properties, such as: identifier (name) of role unique within association, multiplicity on the side of association, multiplicity on the side of linked

element, lifetime dependency between linking and linked elements (both directions), furthermore navigability and restriction on number of reduplication of

bound elements.

Apart from standard roles, in AODB one can specify description role. In

certain sense, one can approximately treat them like specific and redefined kind

of role, which features with having no identifier, can bind only association and

collection, is unidirectional, i.e. objects bound with description do not store

information about it, multiplicity constraint on the side of collection is 0..1 and

there is no mutual constraint of lifetime of bound elements.

Collection corresponds to the concept of data storage. In the intensional

sense, collection is well defined by set of attributes, which define types of values

stored in objects.

Association does not have ability to store data, and collection does not have

possibility to create relationships, because internal structure of those primitives

of association-oriented metamodel forces completely distinct way of their usage.

SKB: Quantifiers and Multiplicity in Extended Semantic Networks Module


Both categories independently are subject to the mechanisms such as inheritance. Associations can inherit from other associations and similarly trees of

generalizations can be created for collections. Separation of data and relationships is complete, since in AODB each primitive performs only one, separate

function. This means that if there are collections on database schema, one can

conclude from the definition of association metamodel that they perform only

one function strictly defined in terms of grammar. The situation known from

relational or object metamodel does not occur, where relation or respectively

class can perform function involving data storage (tuples of objects) and at the

same time build n-ary relationship. AODB is completely unambiguous in terms

of semantics of particular grammatical elements of metamodel. It is very significant not just whilst modeling, but also while attempting to analyze existing

model or altering complex database schema.

Apart from definition of association metamodel (M), the descriptive part (D)

and behavioral part (B) of AODB have been developed. The descriptive part

comprise Formal Notation (AFN), which is strict, concise, formal and symbolical

language of description of intensional and extensional part of metamodel. Modeling Language (AML) is graphical language of structures and data in AODB.

It is fully consistent with AFN and metamodel definition. Both of the description languages namely (AFN and AML) are designed only for AODB and they

are not any modification or subset of existing languages. The behavioral part

of AODB contains Query Language (AQL) and Data Language (ADL). Both

the languages fully correspond to metamodel and are completely original solutions for data selection or alteration problem, because they work directly on

hypergraph structures, which represent the basis of AODB data model.


Modeling Language – AML

This section addresses the most important aspects of grammar and semantics of

AML – Association-Oriented Modeling Language. It is a graphical language used

to design database schemata in the Association-Oriented Database Metamodel.

Intensional Diagram. The graphical representation has been provided in

Fig. 8. In AML, colors do not matter in syntactic terms, although using them

may increase the diagram transparency.

Association corresponds to a semantic category (Assoc).

Abstract Association means that association cannot create its instances.

Collection corresponds to a semantic category (Coll ).

Abstract Collection means that one collection cannot create its instances.

Role corresponds to a semantic category (Coll ). The graphical form in

AML depends on navigability, directionality and composability.

(6) Role Ownership,

(7) Navigability,

(8) Composition,







M. Kr´

otkiewicz et al.

Fig. 8. Sample database schema diagram in AODB

(9) Multiplicity is a part of the graphical form of a role (Role).

(10) Attribute is a part of the graphical form o a collection (Coll ). Attribute

(Attr ) has a name, scope of visibility, quantity, type and default value.

(11) Attribute Type is a part of the graphical form of an attribute (Attr ).

(12) Collection Generalization is a relationship which may link two collections.

(13) Association Generalization is a relationship which may link two associations. This relationship is described by an inheritance mode for roles.

(14) Association Description is a relationship which may link an association

(Assoc) and a collection (Coll ).

(15) Role Description is a relationship which may link a role and a collection.

(16) Derived Role is a relationship which may be represented in the diagram in

a form similar to a role (Role).

(17) Derived right to fulfill the Role is a relationship which may be represented

in the diagram analogically to the Derived Role case.

(18) Derived Role Description is a relationship which may be represented in the

diagram, having an identical form as in the Role Description.

SKB: Quantifiers and Multiplicity in Extended Semantic Networks Module


Fig. 9. An exemplary extensional AML diagram

Extensional Diagram. The Fig. 9 shows an exemplary extensional diagram

for association-oriented metamodel. AML Extensional diagram may contain the

items listed below.

– Association objects – diamonds containing names of association objects, colon

and name of association, which they belong to. The name of association object

may be omitted, if it is insignificant. The text containing name of association

object and name of association is underlined.

– Objects – rectangles with names of the objects, colond and name of collection,

which they belong to. The name of object may be omitted, if it is insignificant.

The text containing name of object and name of collection is underlined.

– Role objects – small circles filled with grey or other collor that differs from

white and black, with underlined role name.

Moreover, it contains the following lines linking:

– association objects with role objects – solid lines with a small circle on the

side of the association objects, indicating the role owner,

– role objects with association objects or objects – solid lines,

– role objects with objects describing them – dashed lines,

– association objects with objects describing them – dashed lines.


Extended Semantic Nets Module Implementation

A structure of SKB was modeled and realized in an Association-Oriented Database Metamodel. The AODB operates mainly on such primitive notions as: collection, attribute, association, role. Figure 10 shows a structure of ESNMSKB

in the AODB that has been slightly simplified for the purposes of this article.

As ESNM is part of the SKB it fullfills all of its benefits and constrains, i.e.

it is defined within AODB, stored with the use of AODB data storage model

and can be queried by the use of AQL. SKB development involves the research


M. Kr´

otkiewicz et al.

over a specialised knowledge query language, that will also have dedicated solutions towards semantic networks. There is also a inference module being prepared. However, those topics are not a subjects of this paper and won’t be

evaluated here.

Fig. 10. Extended Semantic Nets Module (ESNM) diagram in SKB

The operator has a list of operands which has to contain at least a single

operand. The operator is any CONCEPT. The association of the operands is

abstract since it can take the form of either a particular CONCEPT or another

operator. The latter option realizes the concepts of partitioned networks. Regardless, each operand fulfills a single Role defined by any CONCEPT and has a list of

Modifiers. Modifiers can have their own modifiers, so a Modifier association has

a role which links to itself. Furthermore, it refers to a CONCEPT and a QUANTIFIER which, however, is optional. The operator also has a list of Modifiers and

an optional QUANTIFIER. Moreover, it is linked to the OPERATOR collection

which constitutes its description, i.e. it stores the attribute defining the type of

the operator. Similarly, the OPERAND collection describes the OperandInstance



An Example Data Structure for ESNM in SKB

Figure 11 is a AODB data representation for the fact “Probably (cf =0.5) John goes

very fast rarely (tq=0.1) to New York City by big probably (cf =0.9) , everywhere (sq=1)

car.”. The semantics of the sentence and thus the illustration has been presented

earlier, so it shall not be deeply elaborated here. However, it is important to

observe that each and every element of the sentance that carries any direct

and explicit meaning has its own representation as an object of the CONCEPT

collection, i.e. John, go, fast, very, car, big, New York City. All of other words

are represented by appropriate structures of ESNM, e.g. probably (cf =0.5) as the

SKB: Quantifiers and Multiplicity in Extended Semantic Networks Module


Fig. 11. A data diagram of the associative metamodel (AODB) for the conceptual

graph in Fig. 10 expressed in the ESNM structure of an SKB system

object of QUANTIFIER collection with the cf attribute value set to 0.5, etc.

Moreover, the are several objects of CONCEPT collection that represent the roles

assigned to each of operands of the created semantic network, e.g. tool, actor,

co-operator, etc. The diamond-shaped elements represent association objects of

corresponding associations defined as elements of ESNM and identify, by the use

of roles, the function of particular elements in the presented semantic network,

e.g. the concept John fulfills the role of Operand being an actor.



1. An Extended Semantic Nets Module dedicated to storing complex facts and

rules for the purposes of an SKB system was demonstrated.

2. The functional scope and a realization of an extension of the idea of semantic

networks in the scope of implementing quantifiers and multiplicity of elements

were presented.

3. The presented assumptions of extending the semantic networks have been verified by an implementation in a database structure developed in an advanced

association-oriented database metamodel.

The authors see great strength in the Extended Semantic Nets Module,

mainly stemming from the possibility of a flexible approach to the knowledge

stored therein. It should be noted, however, that the strength of this module

comes directly from the fact that every element used, whether as an operator,

operand or even a modifier, has to be defined in advance in the SKB as a concept

existing in the structural module. Such a solution is meant to efficiently manage

polymorphism in the scope of stored and processed knowledge.


M. Kr´

otkiewicz et al.


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