2013 Sixth International Conference on Advanced Computational Intelligence October 19-21, 2013 , Hangzhou, China

Default Inheritance Mechanism Enhanced Semantic Web

Incomplete Ontology Reasoning

Guanyu Li, Yafei Ding, Yuangang Wang

Abstract-It is known that ontology reasoning mechanism can not be directly applied to default reasoning. To solve this problem, all the characteristics of default reasoning, incomplete ontology and semantic web ontology inheritance mechanism should be dealt with simultaneously, so the method about default inheritance mechanism enhanced semantic web incomplete ontology reasoning is proposed. Firstly, default reasoning and inheritance mechanism are introduced into semantic web ontology to construct the weaken inheritance relation suitable for ontology reasoning. Secondly, to verify the effectiveness of weakened inheritance relation and to make the ontology reasoning non-monotonic and closer to the human brain reasoning, based on the characteristics of default, the concept of incomplete ontology and its expression are proposed. Finally, to provide an intelligent method for dealing with the missing information in ontology, the reasoning mechanism of incomplete ontology and its reasoning system that supports default reasoning are designed and implemented. The experimental result reveals that the default inheritance mechanism also called as weakened (or incomplete) ontology inheritance mechanism is feasible for semantic web ontology reasoning.

I. INTRODUCTION

As the world today is in the era of information explosion, WWW information amount rapidly expands at index level, and it exposes many kinds of problems of its own.

In 2000, T. Berners-Lee proposed the imagination of the next generation network-Semantic Web [1] [2], and constructed Semantic Web architecture model. In this model, ontology is the core of supporting Semantic Web [2].

Currently, there exist various kinds of reasoners realizing ontology reasoning [3], such as RacerPro [4], Pellet, KONG2, FaCTIFaCT++, etc., but they only can support monotonic reasoning.

Ontology reasoning is to deduce implication relations from existing defmed inter-concept relations in ontology, which mainly include four types: kind-of, part-of, instance-of, and attribute-of In ontology reasoning, a parent-child relation between classes is the most important relation in inter-concept relations in ontology, in which there are abundant semantic relations except for inheritance. On the

Guanyu Li is with the Faculty of Information Science and Technology. Dalian Maritime University, Dalian, 116026, China. He is now with the Intelligent Information Processing (Phone: 86-0411-8472-4515, Fax: 86-0411 -84 72-4515, E-mail: rabitlee@163.com).

Yafei Ding is with the Faculty of Information Science and Technology, Dalian Maritime University, Dalian,116026, China (Phone:86-0411- 8472-4515, Fax: 86- 0411-8472-4515, E-mail:yafei_dingI989@ 163.com).

Yuangang Wang is with the Faculty of Information Science and Technology, Dalian Maritime University, Dalian, 116026, China, (Phone: 86-0411-8472- 4515, Fax:86-0411-8472-45 I 5, E-mail: kbawygI9890601@163. com).

978-1-4673-6343-3 /13/$3l .00 ©2013 IEEE 45

basis of weakened (or incomplete) ontology inheritance mechanism that is a kind of default inheritance mechanism, a new method about semantic web incomplete ontology reasoning is proposed.

II. DEFAULT REASONING AND ITS EXTENSION

It is known that a generic inference is usually monotonic, but not all inferences can obey this monotonic strictly. In this case, adding a new axiom into a theory T will cause its previously deduced conclusions invalid, the reasoning of this kind is called as non-monotonic reasoning. Default reasoning is a typical non-monotonic reasoning.

In early 1980, Reiter proposed Default theory [5] to solve the problem of default reasoning, in which some information or knowledge is defaulted.

Definition 1: Let L is the set of flfSt order formulas. If there is no free variable in a formula of L, then the formula is called closed. To any closed formulary S and formula w, SH W means that it can deduce W from S in flfst-order logic. The theory generated from S is denoted as ThL(S), which can be defined as ThL(S)={W I, wEL, W is closed and SH W }.

Definition 2: Default rule is defined via formula (1): a(x): M p, (x), ... ,M !3,n(x)

OJ(x) (1)

Herein, a(x), P,(x), ... , Pm(x), a(x) are formulas, a(x) is rule premise, a(x) is rule result, and P,(x) is default condition (i=I, ... , m). M means that the default condition is supposed tenable and there is no proof to prove it true or false at present.

Definition 3: Let b.=(D, W) is a default theory, to any formulary SQ., f(S) is the minimum set which meets the following requirements: 1) W<;;;;f(S) 2) ThIJf(S))= f(S) 3) If(a: Mp" ... , Mpm/OJ)ED, aEf(S), and -,p" ... , -,pm

\l S, then r.o:= f(S). Definition 4: Formulary E can be taken as an extension of

default theory b.=(D, W), if and only if f(E) =E, that is, E is the fixed point of operator r

If proposition A is included in a certain extension of default reasoning b.=(D, W), then it is considered that proposition A can be deduced non-monotonously from b.=(D, W).

From the above-mentioned, how to construct an extension with operator r is the key to deal with non-monotonic. In other words, intuitively, the non-monotonic conclusion which is considered tenable currently evolves gradually under effect of default rules and conventional deduction reasoning, until it is extended to its own maximum extent and its conclusion set

(fixed points) tended to be stable is formed, so that the default theory is non-monotonic.

III. INHERITANCE THEORY

A. ISA Inheritance Theory

ISA namely "is a" is the most typical one in inheritance relations. For example, "penguin is a bird".

If symbols "+", "-", "#" are added to a class as its prefix, which are respectively on behalf of "positive", "negative" and "unknown", then the class possessed with such symbols is called "Token"[6].

For example, to class "Elephant", token "+ Elephant" means "is an elephant", "- Elephant" represents "is not an elephant", "# Elephant" represents "whether it is an elephant or not is unknown".

If let II is the set of all real classes existing in inheritance system and let B is a token set with above symbols, which can be described as B={+, -, #}xII, then the elements in BxB are called assertions about inheritance relations, which are serial combinatorials between tokens that are called ordered pairs. There are three forms of ordered pairs.

Let a and b are two real classes, then the three ordered pairs are intuitively interpreted as Table I.

TABLE I ORDERED PAIRS AND ITS INTERPRET A TlONS IN ISA INHERITANCE RELATION

Sequence

<+a, +b>

<+a, -b>

<+a, #b>

Interpretation

The set of all elements in a belong to the set of all elements in b

The set of all elements in a do not belong to the set of all elements in b

Whether the set of all elements in a belong to the set of all elements in b or not is unknown

B. Relation Inheritance Theory

The so-called relation inheritance is the one between an object and its relation. For instance, panda likes eating bamboo, Huanhuan is a panda, and then Huanhuan likes eating bamboo is inherited. Actually, there are three kinds of relation inheritances such as individual-individual, individual-group and group-group.

For instance, oviparous animals can produce eggs, Mingming is an oviparous animal, and the egg produced by Mingming is a kind of eggs, so Mingming can produce Mingming's eggs. As another example, Mingming is an oviparous animal, so Mingming can produce eggs. Again for example, birds are oviparous animals, so birds can produce eggs.

Cursor set B is defined as the Cartesian product between {+, -, #} and the predicates or individuals of II in ISA inheritance theory. Since relation predicates have been concluded in II, also relation cursors should be included in B.

For example, +LOVE[+Suny] is on behalf of something which loves Suny, -LOVE[+Suny] represents something which does not love Suny, and <+Jack, +LOVE[+Suny]> represents "Jack loves Suny".

Inheritance language is defined with twelve relation cursors, which are the Cartesian product between {+, -, #} and the four relation predicates {\i, 3,�, -,}.

46

The six relation cursors as shown in Table II can be formalized by the Self-Cognitive Non-Monotonic Logic proposed by Moore. The other six kinds of relation cursors are the inverse forms of their own.

In Table II, R is a relation, q is a predicate, and b is an individual.

TABLE II RELATION CURSORS

Relation Cursor Representation

+R(+b) -R(+b)

#R(+b)

+R(+q) -R(+q)

#R(+q)

Ax. R(x, b) Ax. -.R(x, b)

Ax. M[R(x, b))]/\M[-.R(x, b)]

Ax.(Vy)q(y)AM[R(x,y)] --> R(x,y) Ax. (Vy)q(y)AM[-.R(x, y)] -->-.R(x, y)

Ax.(Vy)q(y)AM[M[R(x,y)]/\M[-.R(x,y)ll-->

M[R(x,y)]AM[-.R(x,y)]

Since the relation cursors are appended, cursor set B is extended, and many new ordered pairs called relation pairs also can be produced from BxB. Afterwards, new elements are also added to the inheritance assertion (the subclass of BxB) so as to be extended.

Herein, 24 kinds of strictly-defined ordered pairs (relation pairs) are obtained. The first element in each relation pair is mainly composed of two normal cursors (individual cursor or predicate cursor mentioned above). Another element is a relation cursor which is one of the 12 kinds of relation cursors included in Table II together with their inverse forms.

By arranging and combining these relation cursors, 24 kinds of ordered pairs are produced, which are called relation pairs.

Let R is a binary relation R(x, y), a and b are individuals, p and q are predicates. Table III only list 12 kinds of ordered pairs and their intuitive interpretations, the other 12 kinds of relation pairs are their inverse forms, which are omitted in Table III for simplicity.

Sequence <+a, +R(+b»

<+a, -R(+b»

<+a, #R(+b»

<+a, +R(+q»

<+a, -R(+q»

<+a, #R(+q»

<+p, +R(+b»

<+p, -R(+b»

<+p, #R(+b»

<+p, +R(+q»

<+p, -R(+q»

<+p, #R(+q»

TABLE III RELATION PAIRS AND ITS INTERPRETATIONS

Interpretation a and b has relation R

a and b do not have relation R

Whether a and b has relation R or not is unknown a and elements of q have relation R

a and elements of q do not have relation R Whether a and elements of q have relation R or not is unknown Elements of p and b have relation R

Elements of p and b do not have relation R

Whether elements of p and b have relation R is unknown Elements of p and elements of q have relation R

Elements of p and elements of q do not have relation R Whether elements of p and elements of q have relation R is unknown

IV. DEFAULT REASONING AIDED SEMANTIC WEB ONTOLOGY INHERITANCE MECHANISM

A. The Significance of Ontology Inheritance

Ontology is the expression of knowledge in semantic web [7], which is mainly made of concepts and the relations between them. Therefore, there are extensive inheritance relations in concept-concept in ontology, concept-ontology, ontology- ontology, and relation-concepts. Since ontology reasoning is usually done through matching reasoning and inheritance reasoning, inheritance is widely used in ontology reasoning. In the ontology-oriented engineering field, inheritance is a key concept [8]. Also, ontology can be formed as a formal inherited system according to the inheritance relationship in ontology.

However, information uncertainties in ontology reasoning may cause reasoning obstructive and reasoning stagnation. Non-monotonic reasoning as represented by default reasoning is a good solution to solve this problem. If importing default into ontology inheritance relationship, then the problem can be subtly solved. It can not only enrich the inheritance relation, but also make the ontology reasoning execute more smoothly.

B. Default Inheritance Mechanism

Actually, default inheritance mechanism is an inheritance mechanism which is supported by default reasoning.

In this paper, ontology inheritance is mainly dealt with. Since ontology is mainly composed of concepts and relations between them, the theories of ISA inheritance and relation inheritance are mainly concerned with. As default reasoning theory [9] needs to be applied into inheritance theory, the restrictions on inheritance defmition should be liberalized to get the concept of default approximation inheritance.

Definition 5: Given two real classes a and b, in case some elements in a are uncertainly belong to b or few elements in a are not belonged to b, from common sense, the existing information can be described as a is default approximation inheritance of b, as shown in Fig.I.

: 1"_,,, Fig. 1. The default approximate inheritance relation

Herein, M is the condition of ignoring uncertainty elements or few exception elements, and XI ... Xi are elements of a.

For example, it is generally believed that people like living in cheap hotels with good environment when traveling. When such similar requests are not mentioned in their demand class, their actual demand class will approximately inherit the demand class of cheap hotels with good environment in default manner.

In terms of relation inheritance, the traditional relation inheritance is only related to the precise relation. That is, there certainly exists a relation R between a and b without any exception, that is, R(a)={xE a, YE bl(x, Y)E R}. In the condition that some interferential factors are ignored, a satisfactory

47

answer should be deduced yet. So, the concept of approximation relation inheritance needs to be defmed.

Extend relation R as RI"!., then will have formulas (2) and (3).

RI"!.(X) ={yE blVXE a, XEX=>xRy}= {yE b I X� Kl(y)} (2) Kll"!.(Y)={XE alVYE b, YE Y=>xRy}={ XE a I Y� R(x)} (3) Definition 6: RI"!. can be extended as�· k(X) ={yE b13K�

a, IKI=k, X\K�KI(y)}, �. k(X) is called as approximate

relation, in which the relation inheritance of individual pairs is called as approximation relation inheritance.

C. Inter-concept Inheritance

Inter-concept inheritance means the inheritance between concepts, which is similar to the inheritance between classes, and it is composed of inter-concept ISA inheritance and inter-concept relation inheritance. Inter-concept inheritance has much to do with ontology inheritance reasoning. Traditional inter-concept inheritance complies with classical inheritance theory (lSA inheritance theory).

Based on section ill, if symbols "+", "-", "#" are added to a concept name as its prefix, then "+c," means "It is c/" "-c," represents "It is not c/" and "#c/' represents "whether it is c,

or not is unknown". Let C is a set of all the concepts, B is the set of all tokens which could be deduced from C and described as B={+, -,#}xC, then the elements in BxB are inheritance assertions about ontology concepts.

To consider the exception into traditional inheritance theory, its original symbol "+" is extended and substituted with two new symbols "EE>" and "*" to be suitable for ontology inheritance mechanism. Herein, "EE>" means generally positive, "*" represents exception, and "*c," represents the set of exceptions in concept c" so B can be extended as B={+, -, #, *}xc. For instance, "*Bird={penguin, ostrich}" represents that {penguin, ostrich} is the exception of which bird usually can fly.

Given two concepts Cl and C2 of ontology, then the inheritance relations of their ISA inheritance are formalized and intuitively interpreted as Table IV.

TABLE IV EXTENDED INTER-CONCEPT ISA INHERITANCE RELATIONS AND ITS

Sequence

<$CI, *C2, -C2> <(Bc), 0, -c,> <(Bc), 0, #c,>

INTERPRETATIONS

Interpretation Whether CI is an exception of c, or not is unknown, then CI is usually the element of c, CI is an exception of c" so CI is not c, CI is not c, Whether CI is c, or not is unknown

For example, <EE>American spy, #*American, EE>American > means that there is an American spy, if there is no certain proof to indicate he is not American, then he is American generally.

In the relation inheritance, since relation predicates are added to an original object, the relation cursors should be included in original cursor set.

For instance, EE>EAT[EE> bamboo] means something that generally eats bamboo, -EAT [EE>bamboo] represents something that generally not eats bamboo, hence, <EE>panda,

#*EAT[bamboo], EE>EAT[EE> bamboo]> means that panda

usually eats bamboo except those exceptions of not eating bamboo.

Given a relation R and a concept c" there will be six kinds of relation cursors. Three of them are depicted in Table V, and the other three kinds of inter-concept relation cursors are the inverse forms of their own omitted in Table V for simplicity.

TABLE V INTER-CONCEPT RELATION CURSORS

Relation Cursor Representation (j)R[(j)c;] -R[(j)c;] #R[(j)c;]

3x.R(x, c;) Ax. -,R(x, c;) Ax.M[R(x, c;)]J\M[-,R(x, c;)]

Since the relation cursors are appended, and many relation pairs also can be produced, which include a kind of concept cursor and six kinds of inter-concept relation cursors, then there are six kinds of relation pairs totally, as shown in Table VI.

Let R is a binary relation R(x, y), Cm and Cn are concepts, the three ordered pairs and their interpretations are given in Table VI, the rest three are the inverse forms of their own omitted in Table VI for simplicity.

TABLE VI INTER-CONCEPT RELATION PAIRS AND ITS INTERPRETATIONS

Sequence

<(j)Cm, -R[(j)cn]>

<(j)Cm, #R[(j)cn]>

Interpretation Concepts Cm and Cn has relation R, except some exceptions (without this relation) Concepts Cm and Cn has no relation R, except some exceptions (with this relation) Whether Cm and Cn has relation R or not is unknown

D. Concept - Gntology Inheritance

Since ontology is composed of concepts and the relations between them, also ontology contains a number of sub­ontologies.

For example, Ontology animal is a large-sized ontology, in which human sub-ontology and inhuman sub-ontology are included, so there are some inheritance relations between concepts and ontologies called concept-ontology inheritance relation, which is more complex than inter-concept inheritance relation.

Concept inheritance not only inherits all concepts from ontology but also inherits complex relations from them.

The inheritance relationship between concept and ontology can be demonstrated as Fig. 2.

Fig. 2. Inheritance relationship between concept and ontology

Since the inheritance relationship between concept and ontology inner concept equals the inter-concept inheritance relationship, which is considered as a weakened inheritance relationship between concept and ontology, that is, although some exceptions exist in instances of concepts, it is still

48

considered that these concepts are approximately inherited from ontology.

The relations in ontology inherited by concepts are mainly dealt with in this paper. Usually, relations in ontology are very complex.

Ontology hierarchy structure is mainly composed of inheritance relation and other ones such as instance relation instance-of and attribute relation attribute-of etc. as described in section I.

Let 0. is ontology, 0. C is the set of concepts in 0., o.R is the set of relations in 0., c is a concept, R; and C; are elements of G.R and o.C respectively. Then, the concept-ontology relation cursors can be described in Table VII.

TABLE VII CONCEPT -ONTOLOG Y RELATION CURSORS

Relation Cursor Representation (j)O.R[(j)O.C] -O.R[(j)O.C] #O.R[(j)O.C]

3x.R;(x, c;) Ax. -.R;(x, c;) Ax.M[R;(x,c;)]J\M[-,R;(x, c;)]

As usual, there are three inverse situations about them omitted in Table VII for simplicity.

Thus, the pairs combined with one concept cursor and each of six concept-ontology relation cursors in Table VII are given in Table VIII.

TABLE VIII CONCEPT- ONTOLOGY RELATION PAIRS AND ITS INTERPRET A TlONS

Sequence <(j)C, (j)O.R[(j)O.C]>

<(j)C, -O.R[(j)o.C]>

<(j)C, #O.R[(j)o.C]>

Interpretation Concept C and each concept of ontology have corresponding relations except some exceptions (without this relation) Concept C and each concept of ontology have no corresponding relations except some exceptions (with this relation) Whether concept C has corresponding relations with each concept of ontology or not is unknown

E. Inter-ontology Inheritance

Since the two diverse inherited objects from ontology contain abundant concepts and intricate relations, and the inter-ontology inheritance called as inheritance relation between ontology and ontology is more complex.

Even so, they still have a certain weakened inheritance relationship, as shown in Fig. 3 .

Fig. 3 . Inheritance relation between ontology and ontology

Ontology 0.1 is inherited from ontology 0.2, and all the concepts of ontology 0.1 and its corresponding relations with 0.2 have an inheritance relation which is also an approximate inheritance relation.

In other words, each concept and the corresponding relation of ontology 0, inherit the ones from O2 respectively.

Let O,.C and 02'C are two concept sets of 0, and O2 respectively, O,.R and 02.R are their corresponding two relation sets of 0, and O2 respectively, Cm is any concept in O,.C, Cn is any concept in 02'C, Rill is any relation in O,.R, Rn is any relation in 02. R.

The extended inter-ontology ISA inheritance relations and its interpretations are shown as Table IX.

TABLE IX EXTENDED INTER-ONTOLOGY ISA INHERITANCE RELATIONS AND ITS

INTERPRET A TlONS

Relation Cursor Representation Elements of Cm are generally elements of Cn, but some elements are probably not included Elements of Cm are normally not elements of Cn, but some elements are probably included Whether elements of Cm are elements of Cn or not is unknown

The inter-ontology relation cursors are listed in Table X.

TABLE X INTER-ONTOLOGY RELATION CURSORS

Relation Cursor

®O,.R[®O,.C]

-O,.R [®O,.C]

#O,.R [®O,.C]

Representation

3x.Rm(x, cm)

Ax. -,Rm(x, Gm)

Ax.M[Rm(x,c,)]AM[-.Rm(x,Cm)]

According to the construction rules of relation pairs, the inter-ontology relation pairs made from Table X are shown as Table XI.

TABLE XI INTER-ONTOLOGY RELATION PAIRS AND ITS INTERPRETATIONS

Sequence <®Cn, ®O,.R[®O,.C]> <®cn, -O,.R[®O,. C]>

Interpretation Concept Cn and Cm generally has relation Rm except certain exceptions Concept Cn and Cm generally has no relation Rm except certain exceptions Whether concept Cn and Cm has relation Rm or not is unknown

V. DEFAULT INHERITANCE MECHANISM ENHANCED

INCOMPLETE ONTOLOGY REASONING

A. Default in Ontology

Since knowledge that people cognize may be incomplete, which will result in some information missing, ontology based on this information may also be incomplete. How to define the incomplete ontology as is a kind of uncertain ontology is a critical problem, on which the scientific community has not given any specific and consistent defmition.

However, the most related works about uncertain ontology are of emphasizing its other properties such as fuzziness and roughness.

Fuzzy ontology model [lO] is proposed to achieve the concept of fuzziness which is distinct from general precise ontology. Rough ontology model [11] is put forward to obtain the concept of roughness. But, incomplete ontology model has not been defmed so far.

49

It is known that some information is missed in incomplete ontology. If the missed information can be appended by some means, then the revised incomplete ontology can be used for reasoning.

In this paper, the missing information is taken as default. Default concept is similar to default rules in default reasoning. In other words, default rules in default reasoning are used to defme the defaults in incomplete ontology.

Definition 7: A default can be expressed as formula (4).

A:M B

C (4)

Herein, A is a premise, B is a conjecture under default condition, C is a conclusion, and M means that conjecture B is consistent with the existing information. A, B and C are all OWL expressions.

In ontology reasoner, default as definition 6 can be defined as Table XII.

TABLE XII DEFAULT INTERPRETATIONS IN INCOMPLETE ONTOLOGY REASONER

N2 Interpretations 1) Confirm concept classes in ontology concerned with premise A 2) If there is no conflict with the information in ontology, then conjecture

B based on experience which are actually existing reasoning rules, and then skip to step 3), otherwise, skip to step 4)

3) Add conclusion C obtained from default into ontology class description in OWL

4) End

B. Incomplete Ontology

Definition 8: Incomplete ontology is a kind of ontology with default, it can be formalized as DO=( 0, D), 0 is six-tuple ontology [12], and D is the default of 0.

Since OWL ontology representation is based on the 4 factors of individuals, classes, attributes and attribute limits, so concepts in ontology can be summed up as classes.

The expression DO=( 0, D) can be further expressed as the default class DC ={(C" {D,,, ... , D'n} ), ... , (Cn.{Dn" ... , Dnn})}.

The expression of incomplete ontology does not weaken the ability to express original ontology but strengthen its ability, which can be verified as follows.

The set of ontology Q, is described by use of 'P={ C, P, A, V, N}, the set of ontologyQ2 is described by use of DO=(E, F, 1, D), Q,�Q2'

Proof If ontology is without default which means D is null, to \i'f't={C" PI, A" V" NdEQ" ::IDO,=(F" E" it, D,)EQ2. Herein, F,=E,=0, 1,= 'f't, '1/, and DO, represent the same

ontology, so Q,�Q2' To \iD02 = (F2, E2, 12, 0)E � , 3 'P:z={C2, P2, A2, V2, N2}

= ( U X, -- Ez} U 12, 'P:z and D02 means the same ontology, X;EF2

so Q2=Q,. Thus, when ontology without default, Q2�Q,. When ontology with default, Q,�Q2' To sum up, QI�Q2' that is proved.

C. Incomplete Ontology Reasoning Mechanism

The reasoning based on ontology is to deduce implication relations from existing defmed ontology structure relations.

Since ontology inheritance is included in ontology reasoning, a method of applying default reasoning into semantic web ontology inheritance mechanism is proposed to solve the problem of incomplete ontology reasoning.

The incomplete ontology reasoning framework is given in Fig. 4.

incomplctcontologyrc3soningframcwork

In Fig. 4, as the scheduling algorithm has been proposed in current standard reasoner, so its detailed description is omitted.

The one key of default reasoner is that how to interpret default in reasoner, which is given in definition 7.

The consistency analysis about default reasoner is the other key to ensure M in the default of formula (4) which is same as the consistency analysis mechanism in standard reasoner.

The only thing to do is to add defined conjectures in the default into class description.

The consistency of new information is detected through the standard reasoning consistency analysis mechanism.

If it is consistent with the original information, and the newly added information will be permitted, otherwise reasoner will reject the new information.

Incomplete ontology reasoning steps can be described as Table XIII.

TABLEXITT INCOMPLETE ONTOLOGY REASONING STEPS

N2 Step Description I) Input OWL incomplete ontology 2) Confirm the default premise of incomplete ontology in inputted source

ontology; if successful, skip to step 3); otherwise, skip to Step 7) 3) Add conjectures in incomplete ontology of default into standard

ontology reasoner 4) Analyze consistency of these conjectures with inputted source ontology

using the standard ontology reasoner 5) If there is no conflict, skip to step 6); otherwise, skip to step 7) 6) Add the conclusion obtained under default into the class description,

and execute the standard reasoner to deduce conclusions from new class descriptions according to user's needs

7) End

The default inheritance mechanism enhanced incomplete ontology reasoning process is shown in Fig. 5.

50

Fig. 5. The process of incomplete ontology reasoning mechanism

Assuming someone wants to travel outside, to choose a good sightseeing place, he searches for ideal travel advices with an ontology-based Semantic Web search service about tourism.

The Semantic Web service needs to provide the best travel advices which can meet user needs.

In this case, for simplicity, Protege-OWL is used to express ontology instead of OWL-DL.

The Protege-OWL tourism ontology can be shown as Table XIV.

TABLE XIV PROTEGE-OWL TOURISM ONTOLOGY

Content Owl: Thing

Destination Shanghai Beijing Shenzhen Hangzhou Guangzhou Chengdu Dalian

Hotel_ Class Five stars Four stars

Continued

Three_ stars Hotel_ Price

Cheap Expensive Very_ Expensive

Travel MLTravel_' My_Travel_2 Travel_ Dalian_ Travel Dalian 2 Travel Dalian 3

The attributes and their domains and ranges should be included in the tourism ontology:

has _ class: domain: Travel, range: Hotel_ Class; has _ destination: domain: Travel, range: Destination; has _ price: domain: Travel, range: Hotel_ price. Assuming that two users put forward different demands

about the travel, one proposes to travel to Dalian, and the other proposes to travel to Dalian and wants to live in a four-star hotel. Obviously, the information they provide is incomplete. According to their demands, a limited description of My_Travel_l and My_Travel_2 is described as Table XV.

TABLE XV ALlMITED DESCRIPTIONOFMY TRAVEL I AND My TRAVEL 2

Content My_Travel_I Necessary:3has _destination Dalian

Continued My_Travel_2 Necessary:3has_destination Dalian

3has class Four stars

There are three sets of travel solutions provided by network searching which reflect in the limitation to the attributes of Travel_ Dalian _1, Travel_ Dalian _ 2 and Travel_ Dalian _3 that are given as Table XVI.

TABLEXVT TRA VEL SOLUTIONS PROVIDED By NETWORK SEARCHING

Content Continued Travel Dalian I Travel Dalian 3

Necessary and Sufficient: 3has destination Dalian 3has class Five stars

Necessary and Sufficient: 3has destination Dalian 3has class Four stars - - - -

3has _ price Cheap 3has_ price Cheap Travel Dalian 2

Necessary and Sufficient: 3has destination Dalian 3has class Four stars - -3has price Expensive

Which travel solution is more suitable for user's demands? The problem can be transformed into a problem of two classes with incomplete information to deduce their super-class.

Based on the experience (default), if the users do not submit their particular requests to live in what level of hotel, they generally like to live in a five-star hotel which is most comfortable.

The users will also select the cheaper one if they do not mention how much it costs. So the two defaults can be described as follows.

:M3has class Five stars D, = --

----='------=---

3has class Five stars

D _ :M3has price Cheap

2 -3has _ price Cheap

The two defaults are both lack of the premises, so that conjectures are equal to conclusions.

Meanwhile, lacking of premises means that the premises can always be verified in the ontology, conclusions are added to class descriptions based on the incomplete ontology reasoning mechanism mentioned above. Then, the solutions can be extended as Table XVII.

TABLEXVll TRAVEL SOLUTIONS DEDUCED FROM INCOMPLETE ONTOLOGY REASONING

MECHANISM

Content Continued My_Travel_1 My_Travel_2 Necessary:3has_ destination Dalian

3has_ class Five_ stars 3has price Cheap

Necessary:3has_ destination Dalian 3has_ class Four_ stars 3has price Cheap

Using the standard reasoner, My_Travel_l is the subclass of Travel_ Dalian _1 and My _ Travel_ 2 is the subclass of Travel_ Dalian _3 can be easily deduced, and the two travel solutions are fed back to the two users respectively through the application system as shown in Fig. 6.

y ing DestinatiOrn Hotell_Price Hotell_ Clus TravQ'1

• eTravel)allm_1 IM¥_ Tnl . .,.eU

eTraVel_DaJlm_2 y TraveLDalim..,:3

• IM¥_ Tn,Ylel-.:2 Fig.6. Class hierarchy diagram after reasoning

51

In case the new requirements are proposed, such as living what level of hotels or how much it costs, which is against default conjectures, then previous conclusions should be modified.

VI. CONCLUSIONS

With the development of further research on the semantic web, scientific and effective management of the inaccurate information even incomplete information plays an important role in the reasoning mechanism.

As the existing ontology reasoners which are usually based on the description logics can not support non-monotonic reasoning, a method of default inheritance mechanism enhanced semantic web incomplete ontology reasoning is proposed.

On the basis of the default reasoning and structural features of default rules, default reasoning is added to the ontology reasoning, concepts about ontology inner default and incomplete ontology are defined. Then, the incomplete ontology reasoning mechanism is put forward to realize ontology based non-monotonic reasoning, which is closer to the reasoning characteristics in human brain. The given examples verify that the reasoning mechanism is effective and able to meet actual demands.

ACKNOWLEDGMENT

This work is supported by National Natural Science Foundation of China (Grant No. 60972090, 61272171) and the Fundamental Research Funds for the Central Universities (No. 31320133305).

REFERENCES

[I] T. 8erners-Lee, J. Hendler, and O. Lassila, "The semantic web, " Scientism American, vol. 5, ED-284, pp. 34-43, 2001.

[2] 1. 1. Lu, Y. F. Zhang and Z. Miao, Semantic Web Theory and Technology, Beijing: Science Press, 2007.

[3] Y. F. W. Tao, 'The research of reasoner based on ontology, " Computer Engineering and Applications, vol. 9, pp. 48-49, 2006.

[4] V. Haarslev, K. Hidde, and R. Moller, "The RacerPro knowledge representation and reasoning system, " Semantic Web, vol. 3, pp. I-II, 2011.

[5] R. Reiter, "A logic for default reasoning, " Artificial intelligence, vol. ED-13, pp. 81-132, 1980.

[6] D. S. Touretzky, The Mathematics Of inheritance Systems. Pitman, London: Morgan Kaufinan Publishers, 1986, pp. 123-135.

[7] Z. H. Deng, S. W. Tang and M. Zhang, "Ontology research: a survey, " Journal of Peking University, vol.5, ED-38, pp.730-738, 2002.

[8] R. Studer, V. R. Benjamins and D. Fensel, "Knowledge engineering: principles and methods, " Data and Knowledge Engineering, vol. ED-25, pp.161-197, 1998.

[9] S. F. Chen, 1. G. Pan and D. X. Xu, "A method of default reasoning and its application, " Journal of Software, vol.4, ED-3, pp.32-36, 1992.

[10] Y. Zhao, G. Y. Li and Z. M. Rao, "A modular multi-strategy fuzzy ontology mapping method, " Application Research of Computers, vol. II, pp. 4166-4170, 2011.

[Il] D. Y. Wang, Y. H. Huang and G. Y. Li, "Lattice-tree transforming method of generating rough ontology, " Computer Engineering and Application, vol. 5, pp. 44-46, 2012.

[12] 1. Y. Li, T. L. Zong and Z. Fang, 'The storage mode and query strategy for event ontology, " in Proc. 2011 international Conference on Computer Science and Network Technology, pp. 2219-2223, 2011 .