Abstract Knowledge representation and reasoning aims at designing computer systems that reason about a machine­interpretable representation of the world, similar to human reasoning. Reasoning is a mechanism which helps in retracting the previously inferred facts or changing the confidence factors when conditions change while more complete information is received. This paper presents the design and implementation of Gurukulam – non­monotonic reasoning based learning system which involves extended description logics for knowledge representation. The knowledgebase is constructed by adapting the fundamental classification of world knowledge concepts as per Nyaya Sastra, the famous Indian Philosophy. The system simulates 5 student entities which inputs queries from the user interface and identifies the knowledge units which are grouped into a suitable structure to be fed to the reasoning services engine. Inferences are made from the submitted input and are later updated to their respective knowledge base. Any knowledge base conflicts arising at this juncture is raised as doubts to the teaching entity for further clarification. Upon user response, the system alters false beliefs which created conflicts during previous inferences, thus demonstrating learning by non­monotonic reasoning.

1 Introduction Learning through reasoning and inference, is a method of knowledge sharing. In most dialectic schools of philosophy, which encourages knowledge sharing and learning through discussion, knowledge sharing scenario deals with how much of knowledge is being revealed to the learner. The ancient school of Hinduism, Gurukula, adapted a strategy for learning where the learner actively participates in the discussion by submitting questions (propositions) and the teacher is prone to generate answers (propositions) in the way acceptable to the learner, by limiting the learner’s flow of arguments with less deviation from the subject of discussion. Any knowledge units (concepts / relations) unknown may be submitted as questions to the teacher to continue further learning. For every such query­response, the teacher evaluates the responses of the learners and thereby, corrects the mistakes or false beliefs of the learner. Hence, subsequent acquisition of new knowledge might lead one to discover that the situation is not typical as was believed, but exceptional; in this case, what had been assumed by default is revoked [26]. Researchers are still far from being able to formalise all kinds of human knowledge. Especially intuitive, temporal and spatial knowledge defy themselves from control and cannot be totally formalised today. Knowledge representation is a key to processing unsystematic information of the external world in order to get intelligible knowledge. Artificial intelligence research tries to develop systems that are able to act and react properly in the real world, a task that can only succeed if the problem of representing knowledge about the real world is solved.

A knowledge­based system maintains a knowledge base, which stores the symbols of the computational model in form of statements about the domain, and it performs reasoning by manipulating these symbols [32]. The way in which we, as humans, process knowledge is by reasoning, i.e. the process of reaching conclusions. Analogously, a computer processes the knowledge stored in a knowledge base by drawing conclusions from it, i.e by deriving new statements that follow from the given ones. Reasoning non­monotonically from a superficial knowledge base will prove time­consuming or inadequate while reasoning is performed. The problem of maintaining a knowledge base is substantially concerned with keeping track of rules that share common wisdom [17]. The structure of knowledge base in the form of a representative ontology also is the major criterion with which effective and efficient inferences are obtained by inference engines. With the growth of the field of knowledge bases, many different standards have been developed [32]. They all have different syntactic restrictions. To allow intertranslation, different "interchange" formalisms have been created. The specification of concept terms and their relations contained in a terminological ontology does not surely satisfy the requirements of a non­monotonic reasoner. Instead, there should be some descriptions about the concept within itself as in description logics [12], the knowledge representation structure for any reasoning system. Though description logic systems were effective in reasoning intelligently, they did not provide facilities for defining more enriched knowledge units [1], which would assist in better reasoning and inferencing. The concepts, relations and constructors were only primitive in nature [2].

Gurukulam: Reasoning based Learning System using Extended Description Logics

Mahalakshmi G.S. and Geetha T.V. Department of Computer Science and Engineering, Anna University, Chennai, Tamilnadu, INDIA.

mahalakshmi@cs.annauniv.edu, tvgeedir@cs.annauniv.edu

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Indian logic systems [2] define a concept in terms of member qualities and defines more meaningful relations between qualities so that, effective inference is possible [1]. For example, the concept flower is defined as flower:QC(inherent)smell,QM(has)color thus indicating the attribute smell to be ‘inherence’ related and the attribute color to be ‘has­a’ related [3]. The variables QM and QC define the quality mandatory and quality under constrained circumstances, whereas, DL systems [12] would define smell and color as two different concepts with relations flowing between all three concepts. Thus, the Indian logic based extension to description logics as proposed by KRIL, the Knowledge Representation System Using Indian Logic, provided ample opportunities for more elaborate reasoning [3]. It is this feature of KRIL combined with the systematic art of traditional education, which is the motivation to Gurukulam, the teaching­learning system based on extended description logics. An interesting feature of our system is that `rules' in our knowledge representation formalism are `default rules' and that the knowledge base of the participants in our system are updated over the course of a dialogue.

2 Knowledge Sharing – An Indian Logic Perspective 2.1 Knowledge Sharing Assumptions From the perspective of knowledge sharing, reasoning can be defined as a process of knowledge assimilation and interpretation from different perspectives. Due to the abstract nativity of theory of reasoning and inference, assuming an uncertain knowledge­sharing environment implies assumptions regarding common sense knowledge and the art of knowledge sharing. Knowledge Sharing through discussion involves imbalance between the knowledge expressed and the knowledge interpreted. The primary reason may be due to the uncertainty of the knowledge being expressed, multiple perspectives of interpretation, inconsistency in the state of existence of the listener etc. In this paper, knowledge sharing is based on two assumptions: first, both the active participants possess identical fundamental world knowledge as common sense; second, both the participants are totally involved in the discussion without any deviation. With these assumptions, knowledge sharing has the only objective of identification and elimination of doubts around the discussion ideas, thereby paving way for enhanced learning through discussion [29].

2.2 Ontology in Knowledge Sharing One essential component of knowledge sharing is the need to have a common vocabulary at a lower instance level and terminological ontology at a higher level, to support the sharing and reuse of formally represented knowledge utilized for reasoning [18]. A common ontology defines such a vocabulary using which queries and assertions are exchanged among the entities involved in knowledge sharing. In the context of knowledge sharing, ontology means a specification of a conceptualization. Ontology facilitates the sharing of world knowledge and therefore, dynamic matching of distributed ontologies facilitates co­operative learning in a virtual knowledge sharing environment. One of the major claims for ontologies is that they will facilitate the interchange of knowledge between (for example) agents, or the reuse in different systems. However, if each agent or system has an imperfect model of its universe, knowledge interchange or sharing may increase or compound errors, which were not visible in the initial use of an ontology [11].

In this paper, the knowledge sharing entities use default rules and default reasoning which enables them to reason using default and concise knowledge received from other participating entities. In the process of knowledge sharing, ontology is the base of common shared world knowledge concepts. Removal of old concepts, revision / expansion of existing ones and addition of new concepts within the general framework of the shared knowledgebase are important aspects of the knowledge sharing process. Thus, in essence, the knowledge used for reasoning is dynamic in nature. A number of challenges exist when representing and reasoning with such dynamic knowledge. In this scenario there is a need to have suitable modeling techniques to deal with the dynamic nature of knowledge and specialized techniques to reason and take actions based on this constantly changing knowledge base. Ontologies are the appropriate modelling structures for representing world knowledge. In general, ontology

specifically represents common, shared conceptual structures which form the semantic context for high level automatic reasoning mechanisms. The vocabulary of concepts arranged as per the classification hierarchy of ontology is utilized by the reasoning services for various inference purposes [16]. Ontological commitments are agreements to use the shared vocabulary of ontology in a coherent and consistent manner. While ontology is concerned with what exists in the world, ontological commitments define the clear boundary of how to view the world, purposely sidestepping the issues surrounding claims of what exists in the ontology [25]. Indian schools of philosophy have laid an awesome foundation on the categorization of world knowledge into a classification framework, which are associated with certain ontological commitments [2]. The classification of world knowledge assumed in this paper, is based on Nyaya Sastra, the famous India Logic.

2.3 The classification system of Nyaya Sastra Navya­Nyaya, the famous Indian system of Logic, poses a two­fold approach in its course of discussion. The first is classification, where things are grouped based on the similarity of their characteristics, next is inferencing, various ways by which the above characteristics can be used to arrive at a logical conclusion [10,15]. This classification framework attempts to classify all entities in the world from atom to universe into

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seven basic categories namely substance, quality, action, particularity, generality, inherence and absence. Of the seven categories, the substances are only nine namely, earth, water, light, air, ether, time, space, soul and mind. The qualities are twenty­four in number: color, taste, odour, touch, number, magnitude, separateness, conjunction, disjunction, remoteness, proximity, weight, fluidity, viscidity, sound, intellect, pleasure, pain, desire, aversion, volition, merit, demerit and tendency. Action is of five kinds: upward motion, downward motion, contraction, expansion and motion from one place to another. The more comprehensive and less comprehensive are the two kinds of generality.

In addition relations between the entities associated with the categories are also abstracted and represented. Most knowledge representation schemes have relations such as “is­a” which is a generalization relation and “has” which is part­whole relation. Nyaya [33] defines many more fundamental relations at the highest level of abstraction. We state here, fourteen relations as per the Nyaya definition: part­whole, generality, contact­action, contact­contact, absence, pervade, use, inherence, absence­temporal, presence­ temporal, cause­effect, limit, determinant, qualify, absence­environment; Relations can exist both between concepts and between any concept and its member qualities. Certain relations are said to exist only between concepts; or only between concept and its qualities; some at both the perspectives. The “Inherence” relation exists only between concept and its associated qualities. Relations such as, “part­whole”, “generality”, ”contact­action”, ”contact­contact”, ”pervade” and “use”, exist only between concepts, while there are other relations such as ‘absence­temporal’, ‘presence­temporal’, ‘cause­effect’, ‘limit’, ‘determinant’, ‘qualify’, ‘absence­environment’ which exists mostly between concepts and their member qualities, at the lower levels of the domain hierarchy. It is at these lower levels in the hierarchy that domain dependent entities and relationships are defined. The relation between two entities is divided into two main classes, namely, occurrence­exacting and non­occurrence exacting. Nyaya defines eight types of abstract associations between entities like: cause and effect, part­whole, determining aspect and what is determined, limiting aspect and what is limited, pervading aspect and what is pervaded, the chief qualifier and what is being qualified, the underlying promoter and what is produced by it. Two concepts can also be related by more number of relations [20]. The associated qualities, which characterize the concept, may be mandatory or optional.

Nyaya also analyses the terminology of absence or negation in different ways. Antecedent negation, destructive negation, absolute negation and mutual negation are the four types of negation discussed in Nyaya Sastra [20,33]. One of the possible negations ‘Prior non­existence’ or antecedent negation describes that it is prior to the production of an effect and is characterized as beginningless but having an end. The other negation ‘Posterior non­existence’ or destructive negation, describes that this type of non­existence occurs after an effect is destroyed and is characterized as having a beginning and no end. Thus, interpretations of negation associated with concepts and qualities, account for the temporal perspective of defining and reasoning about state changes. Reasoning and knowledge sharing over such an elaborate knowledge structure is still more complex during inference but more complete inference is promised while reasoning over such detailed knowledge units.

3 Knowledge Representation formalisms The type of knowledge representation formalism determines how information is stored. Each knowledge representation formalisms needs a strict syntax, semantics and inference procedure in order to be clear and computable. Most formalisms have attributes to be able to express information more clearly. There are attributes that provide the possibility to add new information to the system without creating any inconsistencies, and the possibility to create a "closed­world" assumption. A problem for knowledge representation formalisms is that expressive power and deductive reasoning are mutually exclusive. In order to get a greater deductive power, expressiveness is sacrificed and vice versa. The efficient storage and retrieval of classified world knowledge [20] with reference to the ontology is highly dependent on the representation formalism, which is the major issue in building the ontology. Therefore, logic similar to description logics has to be used for effective knowledge representation from a detailed knowledge base.

Logic provides an effective and direct technique for representing knowledge and reasoning [22]. Without logic, a knowledge representation is vague, with no criteria for determining whether statements are redundant or contradictory [18]. Logic can be considered as the universal medium that allows for the semantic analysis of knowledge and the validation of reasoning. To build a machine that is resourceful enough to have humanlike common sense, it is essential to identify techniques to combine the advantages of multiple methods to represent knowledge, multiple ways to make inferences, and multiple ways to learn [21]. Reasoning allows modification and updation of an intelligent entity’s store of beliefs as the result of new information or new insight about the relations among existing beliefs while inferencing [23]. Therefore, the representation language chosen should be compatible and resourceful enough to cater to all challenges of knowledge representation and reasoning.

3.1. Description Logics as knowledge representation formalisms Description logics (DL) form a family of both class­based and logic­based knowledge representation languages, which allow for modeling an application domain in terms of objects, classes and relationships between classes, and for reasoning about them. Differently from object­oriented languages used in databases and programming languages, DLs permit the specification of a domain by providing the definition of classes, and by describing classes using a rich set of logical operators [30]. By using DLs, one can specify not only the

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necessary conditions that objects of a given class must obey, but also the sufficient conditions for an object to belong to a certain class. A knowledge base built using Description Logics is formed by two components: the intensional one, called Tbox, and the extensional one, called ABox. The basic building blocks are concepts, roles and individuals. Concepts describe the common properties of a collection of individuals and can be considered as unary predicates, which are interpreted as sets of objects. Roles are interpreted as binary relations between objects. Each description logic defines also a number of language constructs (such as intersection, union, role quantification, etc.) that can be used to define new concepts and roles. DL support inference patterns which occur in many applications of intelligent information processing systems.

The techniques for reasoning in Description Logics, refers to four different settings: 1) reasoning with plain concept expressions 2) reasoning with instances of concepts 3) reasoning with axioms expressing properties of concepts 4) reasoning with both instances of concepts and axioms. The reasoning services of DL are: Subsumption, Classification, Satisfiability, Consistency, Entailment and Instantiation [5]. The classification hierarchy of ontology expressed as per description logics provides useful information on the connection between different concepts, and it can be used to speed­up other inference services. The following section gives an insight into quite a few practically implemented DL systems.

3.2. Related work ­ Knowledge Representation Systems on Description Logics

Any DL based KR system is more than an inference engine by itself. KL­ONE, CLASSIC, BACK, LOOM, KRIS, CRACK are quite a few knowledge representation systems built on description logics. KL­ONE [7] is one of the typical systems of earlier generation DL systems. KL­ONE inherently included the notion of inferring implicit knowledge from given declarations. It also supported generic concepts, which denote classes of individuals, and individual concepts to denote individuals. More important and unique to KL­ONE is the core idea of providing ways to specify concept definitions allowing a knowledge engineer to declare the relations between high­level concepts and lower­level primitives. CLASSIC is a knowledge representation system [8] based on DL designed for applications where only limited expressive power is necessary, but rapid responses to questions are essential. LOOM introduced the notion of Tbox and Abox for dealing with concept definitions and assertion regarding the concepts respectively [19]. The LOOM was developed for applications like natural language and image interpretation. A problem with the LOOM approach is that it is hard to characterize the source of incompleteness of reasoning algorithms, which might lead to unexpected behavior.

BACK is based on DL, implemented in PROLOG. The BACK architecture was designed to support incremental additions to the Abox and retraction of old information. Abox assertions can be retrieved from a database by automatically computing SQL queries. The BACK system was considered highly suitable for the applications where reasoning about time was important. The BACK description logic is an extension of AL where exist a number of useful operations for concrete applications, and especially knowledge and data management. FLEX [24], a successor of BACK included the facility for reasoning about equations and inequalities concerning integers. The CRACK system [9] supported the DL language with all basic extensions in the constructor zone and the inference algorithms. KRIL is based on extended description logics [3]. KRIL basically provided all fundamental definitions and reasoning services of every other DL systems but the definition of knowledge base in KRIL followed the systems of Indian Logic.

Many description logics can be defined as extensions of ALC by concept and/or role constructs [11]. Systems which reason about concepts by combining Formal concept analysis with ALC, are also developed [6,28,31]. The system CEL1 is a first step towards realizing the dream of a description logic system that offers both sound and complete polynomial­time algorithms and expressive means that allow its use in real­world applications [14]. WSML2 reasoner D1.10 provides a reasoner prototype for WSML­DL, the variant that captures the expressive Description Logic SHIQ(D). Using this prototype we can, among others, perform the reasoning tasks of checking ontology consistency, entailment and instance retrieval. It also validates WSML­ DL ontologies and allows to serialize the latter to OWL DL ontologies [35]. FaCT++ is a new DL reasoner [13] designed as a platform for experimenting with new tableaux algorithms and optimisation techniques. It provides reasoning services for ontology engineering tools supporting the OWL DL ontology language.

3.3 Motivation for Extended Description Logics Description Logics represent the knowledge of an application domain by first defining the relevant concepts of the domain, and then using these concepts to specify properties of objects and individuals occurring in the domain. The classification hierarchy of ontology expressed as per description logics provides useful information on the connection between different concepts, and it can be used to speed­up other inference services. Classification of individuals (or objects) determines whether a given individual is always an instance of a certain concept [27]. It also defines a number of language constructs (such as intersection, union, role quantification, etc.) that can be used to define new concepts and roles [4]. However, DL systems failed to construct the atomic concept in terms of its member qualities. Also the relations defined possessed heavy limitations with respect to their scope and were only superficial, i.e. between atomic concepts.

The DL systems discussed above (in section 3.2, except KRIL [3]) were only aiming at representing and reasoning from the stored knowledge, which would be of use to the external user who queries the KR systems. But, simulation of human querying and thereby initiating the reasoning and inferencing was not addressed by any of the above systems. The reason is that description logics, the knowledge representation mechanism

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followed by those systems were not enriched enough to incorporate human­like reasoning. Hence, there arose the need to extend the DL representation to suit the requirements of Indian Logic. The following section describes the significance of Extended Description Logics.

3.4. Extended Description Logics – An Overview According to Extended Description Logics [3], the ontology essentially consists of three levels of knowledge namely world knowledge, domain knowledge and instantiated knowledge. World knowledge is the basic and generic knowledge about the events and processes in the real world. Domain knowledge is the specialized real world knowledge within a particular field. Though domain knowledge is considered to be the specialized knowledge, it can be divided into domain independent abstracted knowledge and domain dependent specialized knowledge. The instantiated knowledge describes the specific instances about the individual entities or events that model the domain under consideration. Every concept is defined in terms of other primitive concepts. A primitive concept is described as a collection of its member qualities and the relation between them. The relations fall into two categories: relations between concepts (as in DL) and the relations between concept and member qualities. These structures contribute more meaning to any concept unlike DL systems. For example, the concept Mercury can be stated to possess the mandatory qualities, color and fluidity where as, in DL, it would take 4 concepts to define Mercury (refer Fig 1.). Therefore, the inadequate definition of DL not only has more number of concepts and relation entities but also the necessary information about qualities is missing. The details about certain qualities defined as mandatory and certain other qualities defined as optional and the relations defined between them also are found to be missing in the DL ontology.

Figure 1. Comparison of Extended DL ontology with simple DL ontology

The ‘quality’ in extended DL shall be mapped to ‘property’ in ALC [11], and the type of qualities, mandatory and optional may be compared with that of the constrained implementation of qualities of ALC. But relations that exist in extended DL are not only at the conceptual level but also between concept and its member qualities. Thus, by enhancing the number and type of relations that can be defined at the highest level of abstraction, inference becomes multi­relational rather than been restricted to the normal hierarchical, part­ of and instantiation relations [33]. Due to the added requirements of ontology representation based on Nyaya, the DL is extended both at the concept­constructor level and the relation level, so as to improve its expressiveness and inference capability in KRIL [3]. The following section discusses the structure and functions of KRIL, a knowledge representation system which utilizes the speciality of extended description logics as suitable knowledge representation mechanism.

3.4.1 Inference language of KRIL The facilities to define, manipulate and reason with Nyaya ontology are provided through the use of extended description logics, which allows interaction with the inference engine module of the system. The inference engine does three functions: building of the definitional part of the Nyaya ontology, the manipulation of knowledge and the reasoning required by the query processing. KRIL’s knowledge representation language consisting of concept/relationship definition language (CRDL), concept/relation manipulation language (CRML) and a set of editing commands and a query language. This knowledge representation language can be further used to define, manipulate and query the various levels of knowledge. The following figures 2a, 2b and 2c details the commands of CRDL, CRML and query language used by SISHYA. CN refers to Concept name, QN refers to Quality Name, V – Quality value (Ex: concept: Mercury; quality: color; value: Silver) RN refers to Role name, I refer to Instance and Rdesc refers to Role descriptions.

The CRDL constitutes the commands for defining the concepts, instances and relationships. Top and Bottom concepts are assumed by the system as default. The concept definitions have been recognized and the knowledge hierarchy is built. All the defined concepts associated with its mandatory and optional qualities have been fixed in some level. Qualities though mandatory or optional, may have value or a set of values associated with them. The qualities and their respective value set defined through the CRDL have been pre­ checked for their validity of existence in the quality and value master repository. Using CRDL the user can build the ontology from scratch [4]. Here, the user can define concepts, qualities associated with concepts and values of concepts. Concepts can be linked to one another through relations where relations can be is­a, owns, part­of and uses. Relations can also be defined between concept and quality. Instances of concepts can also be defined using CRDL. The CRML provides necessary commands [4] for deleting and updating of concepts and associated qualities in the knowledge hierarchy. The query language of KRIL supports querying the classification hierarchy and summarizing the results of queries. The TAML commands have been utilized for

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the management of Tbox and Abox [4]. The system shell is managed by ‘create taxonomy’ and ‘use taxonomy’ which are used primarily for mounting and dismounting the Tbox and Aboxes. Upon commit, the information contained in the classification hierarchy is stored in a separate file, which also records every inference performed by the system. In addition the system provides concept and instance dictionary files, which summarises the total number of instances present in the classification hierarchy. Using CRML, the ontology shall be updated or modified. The concepts created, associated qualities and their values, the relation between concepts and its member qualities can be manipulated using the commands of CRML.

Figure 2. (a) CRDL of SISHYA

Figure 2 (b) CRML of SISHYA Figure 2 (c) Query Language of SISHYA

3.4.2 Reasoning services of KRIL The reasoning services of KRIL are primarily divided into two categories: Reasoning tasks for Abox and Reasoning tasks for Tbox. The Abox reasoning services discussed are instance checking and consistency checking [4]. Consistency checking contained relation existence checking, inherence checking and temporally constrained existence checking. The reasoning tasks for Tbox contained satisfiability checking and subsumption checking. Every similar functionality of KRIL is incorporated in GURUKULAM, the proposed teaching­learning system using extended description logics. The following section describes the architecture of GURUKULAM knowledge sharing system.

4. Architecture of GURUKULAM

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Figure 3. Knowledge sharing Model of GURUKULAM

GURUKULAM, the reasoning and knowledge sharing (through teaching –learning) system discussed in this paper (fig 4.), is fundamentally based on KRIL, a knowledge representation system based on extended description logics [3]. Extended description logics is the Nyaya­satisfying extension made to the well­known description logics, thus allowing more detailed and elaborate reasoning and inferencing. GURUKULAM has fundamentally two action zones: knowledge representation zone and the reasoning service zone. The knowledge representation zone follows from KRIL. The knowledge sharing and learning algorithm is implemented as part of the reasoning service zone.

The community of GURUKULAM is composed of a single teaching entity with multiple student entities (fig. 3). The knowledgebase of teacher or GURU entity is assumed to have every concept details about the world knowledge; the students or SISHYA entities are assumed to have various levels of knowledge among the group. Every individual participant of GURUKULAM consists of a common sense knowledge base, KRIL reasoning engine and the Non­monotonic reasoning engine, which behaves like the knowledge­sharing engine. The system removes the invalid knowledge by recording the new, valid information and thus gets exposed to new experiences about the world knowledge, which can be considered as a ‘new light’ to the system.

Figure 4. (a) Design of a SISHYA node of GURUKULAM (b) Design of GURU node of GURUKULAM

The Discussion Engine consists of a responder, a communication interface and a message board. All the learning entities listen and respond to the questions from the teaching entity. Through discussion, the teaching entity attempts to kindle the quality of knowledge lying in every learner entity. Based on the response of learning entities, the quality of knowledge is assessed by the Tracker and Evaluator, present in the discussion engine of teaching entity and later, the evaluations are disclosed. Poorly evaluated learner entity attempts to correct the mistakes and reflects the updation of its knowledge while responding to following queries. The

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entire community is modeled after Gurukula, the traditional system of education in ancient India and hence, the system is named GURUKULAM.

4.1 Knowledge Representation zone The knowledge base is similar to KRIL. It consists of a Tbox – Terminological box and Abox – Assertion box. Tbox consists of concepts, their explanations in terms of member qualities, and the relations that exist between them. Abox unifies the instantiations to the Tbox. The KRIL engine also is a part of knowledge representation zone. Details about the discussion of KRIL are already presented in section 3. Reasoning services zone acts upon the knowledge base by means of KRIL specification languages. There is also a separate connectivity between reasoning services zone and the knowledge base, which will be used to track the versioning of knowledge base.

4.2 Reasoning services zone The reasoning services of Gurukulam basically constitute a non­monotonic reasoning engine, which also tracks the changes and versioning of the knowledge base. The engine has two active components: responder and consistency checker. The responder interacts with the user via user interface. The knowledge entered by the user is parsed and converted to KRIL syntax by the responder. The consistency checker gets the user information in terms of KRIL syntax via the responder, and checks for information and knowledge consistency. On account of non­monotonic nature of information, consistency checking may further generate more queries regarding the status and validity of the existing information with respect to the knowledge base. Therefore, all communications of consistency checking of the knowledge base necessarily pass through the KRIL engine.

The conflicting information from the knowledge base is obtained by the KRIL engine, and is displayed to the user by the responder. Any addition of non­monotonic nature of information involves deleting the invalid information from the knowledge base and adding the new, valid information as recommended by the user. The invalidity of the information may be found with the entire concept or with the member qualities of a given concept, or, with the optional quality migrating to the mandatory quality zone or vice versa. Similarly, relations between concepts or between concept and its member qualities may also undergo inconsistency during conflict analysis. In addition to this, disjoint concepts, which cascade the negation operator throughout the definition of respective concept hierarchies, may also undergo some definitional change that may require cascading the concept and relation definitions throughout the knowledge base. The conflicts (and cascading conflicts) in the knowledge base are carefully analysed by the consistency checker while carrying out the required additions, which is also automatically tracked by the change tracker of the reasoning engine. The overall non­monotonic reasoning algorithm is explained in figure 5:

Step 1: Input user command Step 2: Parse the user command //Perform KRIL parsing Step 3: Identify the information units Step 4: Identify the KRIL command category Step 5: If QL then step 6 else

If CRML then step 7 else If CRDL then step 8 end

Step 6: Perform KRIL querying, end Step 7: Perform CRML with KRIL, end Step 8: //Perform consistency checking If knowledge base consistent then

allow CRDL definitions through responder, end Step 9: Check Tbox consistency If not consistent then

Check concept consistency Check concept­quality consistency

Check relation consistency End if Step 10: check Abox consistency. If not consistent, step 11.

Step 11: Display inconsistent nodes, step 1 End

Figure 5. Algorithm for Non­monotonic Reasoning in GURUKULAM

After identifying the inconsistent nodes that contribute to knowledge conflict, by CRDL commands, the user is expected to alter the information that is causing the conflict with the knowledge base. Once the conflict is cleared, new information may be added to the knowledge base through CRDL commands of the KRIL

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engine. Before every new additional fact is deposited to the knowledge base, the change tracker creates an old version of the knowledge base so that, upon non­monotonic nature of the newly added information, the knowledge can be revoked from the older version.

5. Results For experimental purposes, we have considered the knowledgebase of GURU to have concepts and

relations from the ‘Birds’ domain. The snapshot of description of knowledgebase of GURU is given below in Figure 6. The ‘Top’ is the supermost concept which includes every other concepts defined in the universe [2,20]. The shaded nodes are the fundamental abstract categorization of world knowledge as per Nyaya Sastra [2,20]. The subsequent layers are domain­specific in nature. SISHYA1 is assumed to have the same knowledge as GURU. SISHYA2 is said to know all the details about bird domain except about ‘ostrich’. The snapshot of conceptual ontology of SISHYA 2 is shown in Figure 7. The various knowledge assumptions of discussion agents are summarized in table 1. By partial knowledge, we mean, the entities does not know about the exceptional property of that particular

concept. For ‘Ostrich’ and ‘Penguin’, we mean, the exceptional feature is that ‘they are birds; but they do not fly’. The following figure 8. illustrates the conversation between GURU and other SISHYA. Every compartment in the output screen of SISHYAs relates to every individual response to the GURU. Figure 8 presents two rows of conversation windows, three in every row. The first row consists of (from left) GURU, SISHYA1 and SISHYA2. The second row has SISHYA3, SISHYA4 and SISHYA5. The conversation illustrates both question­answering and evaluating the answers. When the answers are found to be varying, the GURU transmits the message about the evaluation of respective answers to SISHYAs. Evaluation also happens by self­observations. Upon evaluation, SISHYA attempts to correct the mistaken information and updates its knowledgebase.

Figure 6. Conceptual ontology of GURU in ‘Bird’ Domain

Figure 7. A snapshot of conceptual ontology of SISHYA2

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Table 1. Summary of Beliefs of Knowledge Sharing Entities of Gurukulam

Agent Believes in Partial Knowledge

Lack of Knowledge

GURU All concepts ­ ­ SISHYA 1 Crow, Ostrich, Penguin ­ ­ SISHYA 2 Crow, Penguin ­ Ostrich SISHYA 3 Crow Ostrich Penguin SISHYA 4 Crow Penguin Ostrich

SISHYA 5 Crow ­ Penguin, Ostrich

Figure 8. Knowledge Sharing between GURU and SISHYAs – part 1

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Figure 9. Knowledge Sharing between GURU and SISHYAs – part 2

This can be seen from figure 8. (i.e.) when the GURU makes a statement like ‘penguin is a bird’, SISHYA3 and SISHYA5 responds as ‘Don’t Know’. This is because both have no concept called ‘Penguin’ in their knowledgebase (refer Table 1). After this happens, by observing their individual knowledgebase and identifying the lack of knowledge of the concept ‘Penguin’, both SISHYA try to update the new concept ‘Penguin’ which is immediately summarized at the output (for our convenience). This is reflected at the conversation only with the next answer. When the GURU asks ‘Will Penguin fly?’, SISHYA3 and SISHYA5 answers ‘Yes’, because they just knew from the previous statement of GURU that, ‘Penguins are birds’ and they have absolutely no idea about the exceptional nature of ‘Penguin’. We refer this as self­evaluation and the knowledge sharing entities learn concepts automatically. SISHYA 4 already is assumed to have partial knowledge about ‘Penguin’; so the response of SISHYA 4 is also ‘Yes’ in this situation. SISHYA 1 and SISHYA 2 have thorough knowledge about ‘Penguin’ and they pass the given situation.

Therefore, for the response of previous question ‘Will Penguin fly?’, there are two set of responses ‘No’ and ‘Yes’. GURU evaluates the responses and transmits either who is wrong or who is right. We refer this as

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cross­evaluation. On interpreting this message, SISHYAs try to update the knowledgebase after identifying the root cause of the false belief. Here, when the GURU says ‘SISHYA 3, SISHYA 4, SISHYA 5 are wrong’ (this can be considered as a control statement in the knowledge sharing setting) all the above three SISHYA reverse their false beliefs. This behavior demonstrates the non­monotonic nature of world knowledge concepts within the knowledge sharing entities, which is a realistic phenomenon. This is immediately summarized at the output as ‘Penguin !fly’ (refer figure 8). The same shall be applied for the following set of questions about the concept ‘Ostrich’; the self­evaluation and cross­evaluation shall be seen from the responses shown in figure 9.

The entire conversation and reasoning is listed in table 2. For experimental convenience, we have just assumed only few concepts about the Birds domain in the knowledgebase and practically, this can be extended to any number and levels of concepts including dynamic expansion of knowledge base during discussion which is the common goal of knowledge sharing. It can be observed from figure 8 and 9 that, after every occurrence of the reply ‘Ok’, the SISHYA learns the new concept, which is reflected at the listing of concept summaries of the respective knowledge bases. Thus, reasoning based learning system gains new insights and experiences for the participating entities which is very appealing in a teaching­learning setting.

Table 2. Summary of Conversation between the teaching­learning entities in GURUKULAM

A quantitative evaluation of the architecture of GURUKULAM would result in more interesting results with respect to the amount of knowledge shared and the increment of knowledge obtained after knowledge sharing. Therefore, we have also implemented a quantitative model for GURUKULAM. The

Conversation #

GURU

SISH

YA1

SISH

YA2

SISH

YA3

SISH

YA4

SISH

YA5

1 Bird fly? Yes Yes Yes Yes Yes

2 Penguin is a bird

Yes Yes Don’t Know Yes Don’t Know

3 System learns about ‘Penguin is a bird’

System learns about ‘Penguin is a bird’

4 Penguin fly? No No Yes Yes Yes 5 SISHYA3,

SISHYA4, SISHYA5 are wrong

Ok Ok Ok

6 System revokes the false belief

System revokes the false belief

System revokes the false belief

7 Ostrich fly? No Don’t Know Yes Don’t Know Don’t Know 8 SISHYA3

wrong Ok

9 System revokes the false belief

10 Ostrich is a bird

Yes Ok Yes Ok Ok

11 System learns about ‘Ostrich is a bird’

System learns about ‘Ostrich is a bird’

System learns about ‘Ostrich is a bird’

12 Ostrich don’t fly?

Yes No Yes No No

13 SISHYA2, SISHYA4, SISHYA5 are wrong

Ok Ok Ok

14 System revokes the false belief

System revokes the false belief

System revokes the false belief

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G.S.Mahalakshmi et al. 25

evaluation model consists of reward values for exchange of concepts and relations. For every relation that exists, the reward value increases by 0.5 and then it will also increment according to the nature of the relation as depicted in table 3.

Table 3. Rewards for Relation factor

Relation type Reward Relation category Reward Invariable concomitance 2 Reflexive 3 Exclusive 1.5 Symmetric 2 Exceptional 1 Anti symmetric 2 Direct 0.5 Asymmetric 2 ­ ­ Transitive 1

For every quality that exists for a concept, the reward value increases by 0.5 and then it will also increment according to the constraint of the quality as depicted in table 4.

Table 4. Rewards for Concept­quality factor

Quality type Reward Mandatory 1 Optional .5 Exclusive 2 Exceptional 2

Question 1: question in sishya w’s domain : “chk­relation swims­in penguin water exceptional,null”

sishya w replies “relation exists”; others answer “don’t know” self evaluation takes place at : sishya x, sishya y,sishya z.

Question 2: question posed by guru in sishya x’s domain “ chk­relation neighbor­of India SriLanka direct,symmetric”

sishya x , sishya y – replies “relation exist” sishya z, sishya w replies “relation doesn’t exist” cross evaluation takes place at : sishya z, sishya w

Question 3: question posed by guru from domain of sishya y “chk­relation on­churning thayir vennai direct,null”

sishya y replies “relation exists” sishya w , sishya x replies “relation doesn’t exist” sishya z replies “don’t know”

self evaluation takes place at sishya z cross evaluation takes place at sishya w and sishya x

Figure 10. Discussion Summary

In the evaluation model, the members of GURUKULAM are assumed to possess multi­disciplinary knowledge over various domains: dairy domain – entity Y, geographical domain – entity X, birds domain – entity W, metals domain – entity Z (fig. 15). Dotted lines depict special domain relations and normal lines denote the general ‘is­a’, ‘has­a’, ‘part­of’ relations. The questions are exchanged and the answers are obtained across the discussion which is shown in table 5. The discussion results are summarised in Figure 10 and the evaluation of knowledge sharing for all the entities is presented in Figure 11 to 14.

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Knowledge Sharing of X

39

40

41

42

43

Before Evaluation During Cross­ Evaluation

After Evaluation

know

ledg

e

Q1 Q2 Q3

Figure 11. Evaluation of Knowledge of X

Knowledge Sharing of Y

60

61

62

63

64

Before Evaluation During Cross­ Evaluation

After Evaluation

know

ledg

e

Q1 Q2 Q3

Figure 12. Evaluation of Knowledge of Y

Knowledge Sharing of Z

33

34

35

36

37

38

Before Evaluation During Cross­ Evaluation

After Evaluation

know

ledg

e

Q1 Q2 Q3

Figure 13. Evaluation of Knowledge of Z

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Knowledge Sharing of W

31

32

33

34

35

36

Before Evaluation During Cross­ Evaluation

After Evaluation

know

ledg

e

Q1 Q2 Q3

Figure 14. Evaluation of Knowledge of W

The entity X has attained new knowledge over Q1 which is shown by a rise in the curve in Fig. 11. With Q2, the entity X has no gain. The query Q3 makes the entity X to discard some of the invalid knowledge from its knowledge base which can be observed from the downstream curve in Fig 11. The evaluation of knowledge attained for other members can thus be observed through figures 12 to 14. Here, it is to be noted that the entities participate in giving responses with continuity from Q1 to Q3. In other words, the knowledge resulted from Q1 at the ‘after evaluation’ stage is utilized to provide the response to Q2. The knowledge resulted after participation with Q2 is then utilized to answer the query Q3. By the above phenomenon, the natural dynamism in acquiring and eliminating world knowledge is simulated in GURUKULAM.

6. Future Directions The proposed design of GURUKULAM system for demonstrating learning through non­monotonic reasoning, is built on the ontological commitments based on Navya­Nyaya system of Indian philosophy. The current model of the system is more like an expert system communicating with the user alone, with additional expertise in reasoning non­monotonically with justifications. Memorizing and understanding the KRIL syntax for interpreting and expressing the user­related information is currently a barrier to naïve users. Therefore, users if allowed to enter the communications in natural language will be highly benefited. To enable this happen, we need to construct a NFA along with the responder so that, the input sentence is parsed and the knowledge units are extracted before being fed to consistency checker. The same holds good for generating responses to the user. In such cases, KRIL engine will also have a role to play with the responder.

Only basic relations between concepts and between concepts and its member qualities are currently incorporated into the KRIL engine of GURUKULAM. More extensions to enrich and strengthen the structure of ontology in the perspective of Navya­Nyaya (for example: invariable concomitance relation) [34] will extend the reasoning horizon to a greater extent. Also, presently, the KRIL engine has no unique interpretation of mentioning selective knowledge units as default units (or monotonic). The system treats the entire content of the knowledge base as default and starts to reason with it. As in case of default reasoning, a mechanism to highlight certain aspects of knowledge base as default during the stage of definition will help us in reasoning non­monotonically as and when the knowledge base is updated.

The unit values for qualities and relations are assumed for implementation purposes and does not derive their values from anywhere in any sense. More interesting method of deriving the reward values need to be incorporated in future. Also, the entire knowledge­sharing entities totally rely and depend upon the central entity GURU to update or revoke their false beliefs. This is because the GURU is modeled as a teacher and therefore, it is assumed to know everything right about the domain; no purpose of conflicts or inconsistency with the knowledgebase arises upon interpreting the statement of GURU. This may rather be a great excuse because we have devised a teaching­learning setting and not a true knowledge sharing setting. i.e. all the entities here totally trust the GURU. But when this situation is applied to a general knowledge sharing scenario where there is no regulatory authority like GURU, we need to have some dependency or confidence factor upon every entity believes other knowledge sharing entity in the community, thus the entire model transforms to a new horizon of autonomous knowledge sharing based only on trust and reputation, which is considered to be our interesting future work. Obviously, increasing the domain details of ontology will expand the knowledge base and provide room for further inferencing.

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Table 5. Describing Multi­disciplinary Sample Scenarios Between Guru and Sishyas

7. Conclusion This paper has explicitly proposed the architecture and implementation details for modeling

learning through reasoning in a traditional teaching­learning setting with a fundamental commonsense knowledge and a little added domain knowledge. The system is constructed on the ontological structure represented by extended description an logic which provides enriched concepts and relations to be useful in teaching­learning. By performing interactions with the student entities and by thus allowing non­ monotonic reasoning, old and invalid assumptions are over ruled by recent, more valid information from the teacher entity, without altering the consistency of the existing knowledge base. Thus, knowledge gets expanded at every step of inference, which is analogous to traditional classroom learning experiences.

Question GURU W(1) X(2) Y(3) Z(4)

1. chk­relation

swims­in

penguin water

exceptional,null

Send the

question .1 (from

W dom

ain)

Send Reply:

Relation exists

Send Reply:

Don’t know

Send Reply:

Don’t know

Send Reply:

Don’t know

Self evaluation

takes place ,by

inferring sishya W

answer

Self evaluation

takes place ,by

inferring sishya W

answer

Self evaluation

takes place ,by

inferring sishya W

answer

2. chk­relation

neighbor­of

India SriLanka

direct,

symmetric

Send the

question 2

(from X

domain)

Send Reply:

Relation

doesn’t exist

Send Reply:

Relation exists

Send Reply:

Relation exists

Send Reply:

Relation

doesn’t exist

Sends “update

know

ledge “

message to

sishya W

, Sishya Z

(cross

evaluation)

Updates

know

ledge

Updates

know

ledge

3. chk­

relation on­

churning

curd

cheese

direct,null

Send question

3 (from Y

domain)

Send Reply:

Relation

doesn’t exist

Send Reply:

Relation

doesn’t exist

Send Reply:

Relation exist

Send Reply:

Don’t know

Sends

“update

know

ledge

“ message

to sishya X

, Sishya W

(cross

evaluation)

Update

know

ledge

Update

know

ledge

Self

evaluation

takes place

,by

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Figure 15. Multi­disciplinary domain knowledge of the entities in the discussion forum

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