Embedding Matrices Ontology into Math Software Engines to Support Reasoning and Mission Oriented Calculation in Developing Semantic Agents A. Elçi, B. Rahnama, and K. Bahreini Dept. of Computer Engineering, and Internet Technologies Research Center, Eastern Mediterranean University, Famagusta, Turkey {atilla.elci, behnam.rahnama, kiavash.bahreini}@emu.edu.tr Abstract–The Semantic Web Technologies (SWTs) are utilized in different areas of research as a tool to represent meaningful and inferable data. Yet researchers try to come up with standardization for usage of SWTs to be able to apply it in various fields. However, the current implementations are very specialized to task and are not flexible for different instances. In this paper, we focus on design and implementation of an interface between matrix data structures utilized in various mathematical software and OWL ontology files. Therefore, ontology files can be embedded into math software for reasoning and calculation purposes. Moreover, the result of math software can be represented in form of ontology files. This issue resolves the lack of math engines to work with semantic web services. In this case a new framework for real-time human interactive communication and semantic software agents are proposed. The representation of traffic network as labyrinth into ontology files helps other information systems to interact much easier. This representation is in terms of an optimized adjacency matrix. As result, the realtime system can detect an ambulance and flow the traffic in such a way that it reaches the nearest hospital much faster. Hence, the labyrinth data should be transformed to an optimized matrix for labyrinth discovery software agents to respond user interactive queries such as finding the best path to an accident for traffic police officers. In this framework, collecting the Drivers’ identities and also passengers with use of RFID tags as a part of their ID cards is possible. These data could be used for statistics purposes. The results of the developed system have been tested on cooperative labyrinth discovery agents with great achievements. I. INTRODUCTION Aiming to build a framework for design and implementation of real-time semantic agents [1], [6] needs specific base modules to work and result individually. These multi module structures should work as independent as possible to be run in parallel and result a better outcome for developing semantic multi agents[3], [4]. Unfortunately, such a framework does not exist yet to remedy such difficulties. One of these bases which play an important role is math software engines that can handle a lot of calculations much faster and much easier. Nevertheless, there is no standard bridge between semantic web technology data representations and math engines [9]. This gap can be covered by embedding matrices ontology into math software engines to support reasoning and mission oriented calculations. On the other hand, software and human interactive communication requires ease of use and semantic data understanding for machines and software robots which basically utilize mathematic formulas and data structures to solve human queries [5], [7]. This research focus on design and implementation of embedding semantic data representatives into math software engines as one of the bases of futuristic design of such mentioned framework. The following section demonstrates instances of semantic data representations in matrix form. Consequent sections provide a scheme for such presentation. Then a test case is mentioned to measure the implemented scheme. Finally we conclude the paper by showing the obtained results. II. INSTANCES OF REPRESENTATION AND OPTIMIZATION OF MATRICES IN COOPERATIVE SEMANTIC AGENTS SYSTEMS The Traffic Management and Information System (TMIS) is a platform where semantic mobile agents collaborating with each other to balance the traffic and also help an ambulance to find the shortest possible path to hospital or providing the fastest path to firefighters to reach their destination without letting people understand these issues [2]. Such cars can be easily recognized by traffic junctions using RFID tags embedded in body of the car [8]. We can easily imagine that the traffic system is like a directed graph which can be represented using adjacency matrices. Therefore by having such representation, queries can be solved much faster while a lot of formulas for graphs using matrices exist. However adjacency matrices are suffered from data redundancy, lack of loop representation, and defining the edge names. It is required to be improved and optimized to work more efficiently with reasoning engines. Finding the shortest possible path for an ambulance in traffic network is almost like cooperative labyrinth discovery robots finding a way out of very large maze. Conversely the mobile robots are fixed at junctions and cars are passing through the junctions. Such data can be represented as maze matrices. But these matrices require optimization whereas redundant elements such as walls at intersection of two block of maze are kept extra. More detail on this optimization is given as follows: The Cooperative Labyrinth Discovery Robots (CLDs) [9] trace the maze partially and share the results of the traversed sub-sets as shortest path and path to exit with other CLD robots. However CLD suffer from controlling data redundancy in maze set data structure whereas each wall is shared between two neighboring blocks. Correspondingly memory usage which has important bearing in microcontroller programming In Proc. The 2008 International Conference on Semantic Web and Web Services (SWWS'08), of the 2008 World Congress in Computer Science, Computer Engineering, and Applied Computing (WORLDCOMP'08), July 14-17, 2008, Las Vegas, USA. would not be efficient. In order to avoid storing redundant data, we have come up with a set of mapping functions to store/retrieve preferred walled/non-walled edges. In this case the maze is stored as a set of a matrix of non-redundant edges and a matrix of blocks’ properties. The maze set consists of a table of blocks bounded by 4 edges. Therefore, it can be represented as a structure including the block properties such as number of visits and 4 different Boolean variables for edges, say “true” or “1” if walled. Hence each wall except maze boundaries is shared between two blocks, updating its value in run-time requires a transaction containing two updates. Consequently, the data structure contains repeated elements. The space needed for such a representation is (4 + 1)n 2 for a n × n maze set, where each edge and property element consumes 1 unit of memory. Instead, we define a 2n × (n + 1) matrix for walls of a n × n size. Correspondingly, matrix with for ∀i, j | 1 ≤ i, j ≤ n , four different walls of a cell are retrieved as follows: (left ) ⇒ (i, j ) (right ) ⇒ (i, j + 1) (up ) ⇒ ( j + n, i ) (down) ⇒ ( j + n, i + 1) (1) And we need a n × n size matrix for blocks properties. Figure below demonstrates an example on 3× 3 maze set as 6× 4 size matrix. 4, 1 5, 1 6, 1 1, 1 1, 2 4, 2 1, 3 5, 2 1, 4 6, 2 2, 1 2, 2 4, 3 2, 3 5, 3 2, 4 6, 3 3, 1 3, 2 4, 4 3, 3 5, 4 3, 4 6, 4 Fig.1. Representation of n×n maze as 2n × (n + 1) ( ) 2n 2 + 2n − n 2 + 2n + 1 n + n + 2n − n − 2n − 1 2 2 2 ⇒ ∀(n > 1), n 2 − 1 > 0 (4) III. ONTOLOGY REPRESENTATION OF MATRICES Such matrices presented above can be shown as OWL ontology files based on following constraints. • A Matrix may consist of more than two dimensions. Therefore, the engine should dynamically allocate proper space for such matrix. Additionally, nested loops for filling the values to proper places of matrix should be developed in run-time. Therefore, we designed an algorithm to provide nested loops for any n dimensional matrix in O(n log n) instead of O(2n). • Row and column operation should be easily applied. And each two individual elements of a matrix are independent to each other. Due to the structure of the implemented output files. There is no dependent tag. Hence the above requirements are satisfied. The program was implemented in J Builder 2006 with JDK 1.6.0 environment. The reason of selecting Java as implementation language was its compatibility with other semantic web software and also issues such as platform independence. The sample program asks user the name of the matrix, its type, number of dimensions, and also the value for each dimension. Then, it generates a dynamic data structure for input values of matrix cells. Then it converts the user input data in terms of OWL ontology file. The order of cell representation is based on the indices. First index; then second index and so on, such as first row then column and then depth. The following screenshots represents the program run-time. Note that usually matrices exist or it is imported from math software. Therefore this step is not always utilized. matrix A more optimized solution is to keep corners (nodes) as block representatives. Therefore each edge is noted in an 2 adjacency matrix of (n + 1) size. Moreover there is no limit in dimension and shape of maze set due to the applied mesh data structure. As a result, the space used for representation of maze set in terms of blocks, edges, and corners are as follows: { } ∀ (n > 1 ), 4 n 2 > 2 n 2 + 2 n > n 2 + 2 n + 1 (2) Fig.2. Entering values for creating a 2 by 3 by 4 matrix Then the result of the program is an OWL file as follows. Proof: ( 4n 2 − 2n 2 + 2 n ) 2n + 2 n − 2n − 2n 2 2 2 ⇒ ∀(n > 1),2n − 2n > 0 2 (3) <?xml version="1.0" encoding="UTF-8"?> <!DOCTYPE rdf:RDF[<!ENTITY xsd "http://www.w3.org/2001/XMLSchema#">]> <rdf:RDF xmlns:xsd="http://www.w3.org/2001/XMLSchema#" xmlns:rdf="http://www.w3.org/1999/02/22-rdfsyntax-ns#" xmlns:rdfs="http://www.w3.org/2000/01/rdfschema#" xmlns="http://www.matrixConversion.com/arrayont#" xml:base="http://www.matrixConversion.com/arra y-ont#" > <owl:Ontology rdf:about=""> <rdfs:label>Matrix conversion</rdfs:label> <rdfs:comment></rdfs:comment> <owl:versionInfo>$Id:matrixConversionont.owl,v 1.0 Sat Apr 19 01:37:10 EEST 2007 Exp$</owl:versionInfo> </owl:Ontology> <MatrixDimensions rdf:ID="MatrixDimensions"> <hasValue rdf:datatype="&xsd;string">3</hasValue> </MatrixDimensions> <MatrixType rdf:ID="MatrixType"> <hasValue rdf:datatype="&xsd;string">float</hasValue> </MatrixType> <MatrixName rdf:ID="MatrixName"> <hasValue rdf:datatype="&xsd;string">MyArray</hasValue> </MatrixName> <MatrixDim rdf:ID="MatrixDim"> <hasValue rdf:datatype="&xsd;string">2,3,4</hasValue> </MatrixDim> <MatrixIndexes rdf:ID="MatrixIndexes"> <Index[0,0,0] rdf:datatype="&xsd;string">3.2</Index[0,0,0]> <Index[0,0,1] rdf:datatype="&xsd;string">5.7</Index[0,0,1]> <Index[0,0,2] rdf:datatype="&xsd;string">90.45</Index[0,0,2] > <Index[0,0,3] rdf:datatype="&xsd;string">32.5</Index[0,0,3]> <Index[0,1,0] rdf:datatype="&xsd;string">2.2</Index[0,1,0]> <Index[0,1,1] rdf:datatype="&xsd;string">7.7</Index[0,1,1]> <Index[0,1,2] rdf:datatype="&xsd;string">4.3</Index[0,1,2]> <Index[0,1,3] rdf:datatype="&xsd;string">6.0</Index[0,1,3]> <Index[0,2,0] rdf:datatype="&xsd;string">5.1</Index[0,2,0]> <Index[0,2,1] rdf:datatype="&xsd;string">7.4</Index[0,2,1]> <Index[0,2,2] rdf:datatype="&xsd;string">8.9</Index[0,2,2]> <Index[0,2,3] rdf:datatype="&xsd;string">0.3</Index[0,2,3]> <Index[1,0,0] rdf:datatype="&xsd;string">6.7</Index[1,0,0]> <Index[1,0,1] rdf:datatype="&xsd;string">90.2</Index[1,0,1]> <Index[1,0,2] rdf:datatype="&xsd;string">5.1</Index[1,0,2]> <Index[1,0,3] rdf:datatype="&xsd;string">7.8</Index[1,0,3]> <Index[1,1,0] rdf:datatype="&xsd;string">8.2</Index[1,1,0]> <Index[1,1,1] rdf:datatype="&xsd;string">4.4</Index[1,1,1]> <Index[1,1,2] rdf:datatype="&xsd;string">23.2</Index[1,1,2]> <Index[1,1,3] rdf:datatype="&xsd;string">6.3</Index[1,1,3]> <Index[1,2,0] rdf:datatype="&xsd;string">5.5</Index[1,2,0]> <Index[1,2,1] rdf:datatype="&xsd;string">3.0</Index[1,2,1]> <Index[1,2,2] rdf:datatype="&xsd;string">7.0</Index[1,2,2]> <Index[1,2,3] rdf:datatype="&xsd;string">80.3</Index[1,2,3]> </rdf:RDF> Fig. 3. Entering values in matrix cells IV. EMBEDDING THE MATRIX ONTOLOGY IN MATH SOFTWARE Math software generally support matrices represented as C data structures. Moreover, other keywords can be represented with the convertor module to be suitable for specific math software. At this step the same matrix which already is in terms of OWL ontology file will be converted to programming language syntaxes to be useful for math software. At this part a simple and tiny program converts the above OWL file into .m and .c files for MATLAB and C compilers. The following output is generated using the given OWL file for MATLAB. Note that in MATLAB the indices start from 1 by default. MyArray=zeros(2,3,4); MyArray(1,1,1)=3.2; MyArray(1,1,2)=5.7; MyArray(1,1,3)=90.45; MyArray(1,1,4)=32.5; MyArray(1,2,1)=-2.2; MyArray(1,2,2)=7.7; MyArray(1,2,3)=-4.3; MyArray(1,2,4)=6.0; MyArray(1,3,1)=5.1; MyArray(1,3,2)=7.4; MyArray(1,3,3)=8.9; MyArray(1,3,4)=0.3; MyArray(2,1,1)=-6.7; MyArray(2,1,2)=90.2; MyArray(2,1,3)=5.1; MyArray(2,1,4)=7.8; MyArray(2,2,1)=8.2; MyArray(2,2,2)=4.4; MyArray(2,2,3)=-23.2; MyArray(2,2,4)=6.3; MyArray(2,3,1)=5.5; MyArray(2,3,2)=-3.0; MyArray(2,3,3)=7.0; MyArray(2,3,4)=80.3; Additionally for C: void main(void){ float MyArray [2][3][4]; MyArray[0][0][0]=3.2; MyArray[0][0][1]=5.7; MyArray[0][0][2]=90.45; MyArray[0][0][3]=32.5; MyArray[0][1][0]=-2.2; MyArray[0][1][1]=7.7; MyArray[0][1][2]=-4.3; MyArray[0][1][3]=6.0; MyArray[0][2][0]=5.1; MyArray[0][2][1]=7.4; MyArray[0][2][2]=8.9; MyArray[0][2][3]=0.3; MyArray[1][0][0]=-6.7; MyArray[1][0][1]=90.2; MyArray[1][0][2]=5.1; MyArray[1][0][3]=7.8; MyArray[1][1][0]=8.2; MyArray[1][1][1]=4.4; MyArray[1][1][2]=-23.2; MyArray[1][1][3]=6.3; MyArray[1][2][0]=5.5; MyArray[1][2][1]=-3.0; MyArray[1][2][2]=7.0; MyArray[1][2][3]=80.3; } V. TESTING THE DEVELOPED SCHEME Solving the mathematical queries in math software requires some change in matrix. Therefore a reverse mechanism is also required to prepare output from matrices represented in a MATLAB file as OWL ontology file. The result was successful using a very simple convertor we developed. A case study for the developed scheme is presenting a sample map showing the traffic network among a few junctions. The created ontology file can be optimized for redundancy reduction and then it can be represented as programming languages syntaxes suitable for math software to satisfy a query such as shortest path between two node using intersection nodes. VI. CONCLUSIONS In this paper we presented embedding matrices ontology into math software engines to support reasoning and mission oriented calculation. This is used as base of developing a framework for in developing real-time semantic agents and human interactive communication. The way of representation of traffic network data and labyrinth matrix and its optimization for being represented in term of ontology data were covered. Moreover, the ontology data was represented in form of programming language data structure to be embedded into math software. Within this scope, future researches will be developing other bases for the mentioned framework such as prolog data and UML information representation as OWL ontology files. REFERENCES [1] Elçi and B. Rahnama; Considerations on a New Software Architecture for Distributed Environments Using Autonomous Semantic Agents, Proc. 2nd International Workshop on Software Cybernetics IWSC2005, 29th IEEE COMPSAC 2005, IEEE publications, pp.133-138. [2] Elçi and B. Rahnama; Intelligent Junction: Improving the Quality of Life for Mobile Citizens through better Traffic Management, Proc. YvKB 2006, 8-9 June 2006, Ankara, Turkey, TBD Publications (in Turkish). [3] H. Takahashi; H. Nishi; K. 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