towards the spatial database speciﬁcation for gis … databases for gis systems using z notation...

Towards the Spatial Database Specification forGIS using Z-Notations

Farooq Ahmad, Salahuddin Khan and Sher Afzal Khan

Abstract—Formal methods are mathematical techniques usein design, development and verification of software and hard-ware system. Geographic information systems GIS use tocollect, store, analyze and present spatial informations. GISdatabases are usually very complex to design. Formal methodscan play an important role in their design. In the paper,the authors investigate an approach of formal specification ofspatial databases for GIS systems using Z notation (a formallanguage with a powerful structuring mechanism). For thepurpose, we use an example from the context of GIS and spatialdatabase to draw Entity Relationship Diagram ERD. Furtherthe paper presents transformation from Entity RelationshipDiagram ERD to formal specification that shows all the entitiesand their relationships in Z notation. In this paper we exhibitthat the approach is applicable for spatial database designing.Consequently this leads to unambiguous, consistent and verifiedGIS system.

Index Terms—Formal Methods, Z-Notations, GIS, Spatialdatabases, Conceptual design.

I. INTRODUCTION

GEOGRAPHIC Information Systems GIS are extremelycomplex software, hence specification methods are

very important for their quality especially for: consistency ofdata models, different component interfaces, and in databasearchitecture [3]. Existing methods offer large amounts of textand diagrams, which often creates ambiguity and problemsto scale up large problems where the greater amount ofdocumentation require. Due to these problems, it is arguedto develop software model for designing GIS. For this thereare many useful models of GIS, which are designed by usinginformal approaches in ad-hoc fashion. Consequently, it isdifficult for GIS designer to fully capture Modularity andto remove ambiguous, inconsistency and to verify step bystep to a system. In order to remove such errors we proposeformal approach based upon transformation of ERD diagramto Z- notation. This would help GIS designer to verify hissystem early at the design level.

According to Woodcock et al. [11] Z is model-orientedapproach, and has a powerful structuring mechanism. It canbe used to specify information systems in combination withnatural language. The formal method Z is based on discretemathematics such as predicate logic, set theory, functions andrelations. It is used for specifying the behavior of abstractdata type and sequential programs. The Z-specification di-vides the specification of complex system in different states

Manuscript received June 05, 2012; revised July 12, 2012. The travelgrant for this work is supported by the Higher Education Commission ofPakistan for oral presentation.

Farooq Ahmad is with the Faculty of Information Technology, Universityof Central Punjab, lahore, Pakistan e-mail:[email protected].

Salahuddin Khan is with the Department of Computer Sciences,SZABIST- Islamababd, Pakistan e-mail:[email protected].

Sher Afzal Khan is with the Department of Computer Sciences, AbdulWali Khan University, Mardan, Pakistan e-mail:[email protected].

called schemas. The schema consists of three parts; the firstone is the schema name which is in the top line, the secondpart between the first and second line is the schema signaturewhich is the set of names and types of entities introducedin a schema. The third part under the middle line is calledthe schema predicate which is used for the set of propertiesand shows the relationships between the entities and thevariables defined in the schema signature. These schemas canbe combined to produce the overall description of the system.The paper address schemas in the specification part of thepaper. The Z-specification cannot typically be executed bycomputers, but the standard tools are available which are usedfor checking syntax and proof of the formal specification,leads to quality of specification and this allows mistakes tobe detected and corrected sooner in the design life cycle.Formalization is the process of the design of representationsof infinite phenomena by a finite set of distinct symbols,[4]. The use of formalization process basically facilitates tounderstand the underlying structure and theory in the model[1].

The organization of the paper is as follows: Section2 describes Geographic Information Systems GIS, spatialdatabases and their conceptual model. Section 3 describesrelated work that has been done regarding use of formalmethods in GIS and spatial databases. In section 4, Formalspecifications of conceptual design of spatial databases aredemonstrated using Z-notations. In Section 5, we presentthe proof and verification of syntax used in our proposedapproach. In the end, we give conclusion and references.

II. GEOGRAPHIC INFORMATION SYSTEMS GIS

In the past, efforts have been made to define GIS from avariety of angles. This diversity of perceptions has lead toinnumerable definitions for GIS, based on the type of userand application domain. In view of current capabilities ofGIS, it can be defined as ”an information system used tostore, organize, retrieve, analyze, output and update spatiallyreferenced data, in order to support decision making forplanning and management of activities like natural resourcesand environmental management, transportation and telecom-munication utilities, commerce and business affairs, defenseservices, and various administrative management”, DebashisChakraborty and Rabi N. Sahoo (2007).

The major functional units of typical geographic informa-tion systems GIS consist of Data Input Unit, Data Model,Data Manipulation Capabilities, and Result Presentation Fa-cilities [6].

The evolution of GIS has created a great differencein regard to geospatial data. Before GIS, geospatial datawere poorly maintained. The process of data retrieval, datasecurity, and data sharing were imprecise and not useful.

Proceedings of the World Congress on Engineering and Computer Science 2012 Vol I WCECS 2012, October 24-26, 2012, San Francisco, USA

ISBN: 978-988-19251-6-9 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)

WCECS 2012

But now with the evolution of GIS, spatial data is bettermaintained, easy to search, analyze and represent, and canbe shared safely along-with simple updating mechanisms,Debashis Chakraborty and Rabi N. Sahoo (2007). Due to this,a significant amount of time and money is saved, efficiency isimproved and most importantly, now we can expect a betterdecision-making ability.

A few examples of use of GIS technology are that bymapping the locations of school-age children can help toknow where school is needed, mapping crime incidents helpsto know need for increased police patrol, mapping customer’shome and work locations can help bank place ATM machinesto provide better service, mapping properties of city can helpusers to locate a specific address or property owner and GISsystems also helps businessmen or marketers to find newprospects.

There are many popular commercial GIS software butGIS products by Environmental Systems Research InstituteESRI have made it a world leader in GIS industry. Its GISsolutions like ArcInfo, ArcView, and ArcGIS have becomea de facto standard for those who want to model spatialsystems using maps, topological and remote sensing data [7].

III. RELATED WORK

According to Andrew et al. [3] formalization of geographicspace in Geographic Information Systems GIS is considered.Formalization is the representation of model of the world bymeans of formal language. It is also proposed that relationaldatabases can be considered as representations of formalmodels. Tables are representations of the extension of aparticular relation. In order to perform query processing,algebraic operations on the rows and columns in the tableare performed. It is also proposed that by viewing GISas implementations of formal theories of the geometry ofgeographic space, we can consider the spatial databasesas representations of formal models of formal theories ofgeographic space and GIS operations as model based proofprocedures.

Belussi et al.[5] proposed a Layered Spatial Data ModelLSDM for the representation of geographical information indifferent layers and maps. The data model is based on theconcept of feature type which are roads, lakes, etc. Themain feature of the proposed data model is the ability torepresent maps in which the geometry of its objects is notcompletely known. A language for querying layered maps isalso presented. The proposed model and language have beenimplemented on top of a commercial object-relational spatialdatabase system.

Jianchun et al. [10] proposed a formal specification datamodel FSM using the formal specification languages andtechniques, which is a representation for describing thesemantics of objects and their relationships. The purpose ofgiving this FSM is to generate common framework schemaintegration in multidatabase systems and solve the schematicconflicts among local schemas. The FSM provides types andproperties to model the real-world objects. Alejandro et al.[2] formally defined dimension predicate and a method fordiscovering all the valid dimension predicates between twospatial objects of any type and complexity is presented. Theconcept of dimension predicates turns out to be useful not

only in high-level applications but also as part of a develop-ment hierarchy that includes robust geometric primitives RGPwhich represent building blocks of the well known complexspatial data types like point, line and region. Applying di-mension predicates to RGPs during development may benefitcorrectness of the implemented data type model. Huiqing etal. [9] explored a method based on an apartment web serviceapplication, which uses geospatial data to improve accuracyand quality of online information. The great strength of thespatial data is to query about the location and direction ofspatial objects. A simple fuzzy model for direction query isintroduced. Querying examples in the paper have shown thecapabilities of a spatial database to support fuzzy directionalqueries.

IV. FORMAL SPECIFICATION FOR CONCEPTUAL MODELOF SPATIAL DATABASE

In order to show use of formal specification in spa-tial databases of GIS, we will use an example of spatialapplication domain. This application will map the parks,schools, road accessing the schools and parks, and bus-stopsadjacent to these roads. This application will help the CityDevelopment Authority to recognize the need of more greenspace, schools, roads accessing the parks and schools, andbus-stops at suitable places. There are managers for parks andschools who look after and manage the activities there. Parksand Schools are accessed by roads and each road has bus-stops adjacent to it. City Development Authority providesdifferent facilities to parks and schools. Education Authorityoffice monitors the standard and activities of schools.

A. Business Rules

Business Rules are statements that describe and confineaspects of the business and state business structure. Thebusiness rules for our spatial application domain are asfollows;

• Each PARK has a MANAGER, and a MANAGER canmanage only one PARK. No two PARKs have sameMANAGER.

• Each PARK has one or more TRACKs for walk.• Each PARK is accessed by one or many ROADs, and aROAD can access one or more PARKs.

• DEV. AUTHORITY provides facilities to all PARKsand each PARK get facilities from DEV. AUTHORITY.

• Each SCHOOL is managed by a PRINCIPAL, and aPRINCIPAL can manage only one SCHOOL.

• Each SCHOOL is accessed by one or many ROADs, anda ROAD can access one or many SCHOOLs.

• DEV. AUTHORITY provides facilities to allSCHOOLs and each SCHOOL get facilities fromDEV. AUTHORITY.

• EDUCATION AUTHORITY monitors the activities ofall SCHOOLs, and each SCHOOL is accountable toEDUCATION AUTHORITY.

• There are many BUS-STOPs adjacent to a ROAD, anda particular BUS-STOP is located aside of only oneROAD.



WCECS 2012

B. Entity Relationship Diagram of Example

Next, on the basis of above mentioned business rules,we will draw Conceptual model or Entity Relationshipsdiagram ERD with pictograms for our spatial application.The conceptual model of our spatial database is shown inthe entity relationship diagram in Figure 1.

C. Formal Specification for entities of Entity RelationshipDiagram (ERD)

Now, we will use formal methods to define the Formalschemas for entities of above mentioned Entity RelationshipDiagram in Z-Notation by using Z/EVES tool. Schema isa two-dimensional notation in which declarations for theobjects appear in the upper part and constraints on theobjects appear in the lower part. In Z, when a variable isintroduced for the first time in a specification documents itstype must be given which is just a collection of objects. Thebasic type is enclosed in square brackets when it is beingintroduced. So in all the schemas below, first line which isin bracket, introduces basic types. Then objects of those typesand functions are declared in upper portion of schema andconstraints in lower portion as described above.

[Parkid, Parkname, Parkarea, Parkaddress]

ParkPid : PParkidPname : PParknameParea : PParkareaPaddress : PParkaddressParkattribrel : Parkid � Parkname× Parkname

×Parkarea× Parkaddress

Pid = dom Parkattribrel

[Trackid, Tracklength, Lineid]

TrackTid : PTrackidTlength : PTracklengthLid : PLineidTrackattribrel : Trackid � Tracklength× Lineid

Tid = dom Trackattribrel

[Roadid, Roadname, RNumoflanes]

RoadRid : PRoadidRname : PRoadnameNumoflanes : PRNumoflanesLineid : PLineidRoadattribrel : Roadid � Roadname

×RNumoflanes× Lineid

Rid = dom Roadattribrel

[Schoolid, Schoolname, Schooladdress, Pointid]

SchoolSid : P SchoolidSname : P SchoolnameSaddress : P SchooladdressPointid : PPointidSchoolattribrel : Schoolid � Schoolname

×Schooladdress× Pointid

Sid = dom Schoolattribrel

[Principalid, Principalname, Gender, Age]

PrinciaplPlid : PPrincipalidPlname : PPrincipalnamePlgender : PGenderPage : PAgePrincipalattribrel : Principalid � Principalname

×Gender × Age

Plid = dom Principalattribrel

[Managerid, Managername]

ManagerMid : PManageridMname : PManagernameMgender : PGenderMage : PAgeManagerattribrel : Managerid � Managername

×Gender × Age

Mid = dom Managerattribrel

[Standid, Standname]

BusStandStandid : P StandidStandname : P StandnamePointid : PPointidBusstopattribrel : Standid � Standname× Pointid

Standid = dom Busstopattribrel

[DevAuthorityName, DevAuthorityAddress]

DevelopmentAuthorityAuthorityname : PDevAuthorityNameAuthorityaddress : PDevAuthorityAddressPointid : PPointidDevattribrel : DevAuthorityName �

(DevAuthorityAddress× Pointid)

Authorityname = dom Devattribrel

[EduofficeName, EduofficeAddress]

EducationDepttofficeEduoffname : PEduofficeNameEduoffaddress : PEduofficeAddressPointid : PPointidEduattribrel : EduofficeName �

(EduofficeAddress× Pointid)

Eduoffname = dom Eduattribrel



WCECS 2012

Fig. 1. Conceptual model of spatial application

D. Formal Specification for relations between entities ofEntity Relationship Diagram (ERD)

Now, we will define the Formal schemas for relationshipsbetween entities of above mentioned Entity RelationshipDiagram in Z-Notation by using Z/EVES tool.

[Parks, Managers, Tracks, Roads, DevAuthority, Schools,Principals, EduOffice, BusStops]

ParkManagementCityparks : PParksCitypmanagers : PManagersManage : Parks � Managers

Cityparks = dom ManageCitypmanagers = ran Manage

ParkDescriptionΞParkManagementCityptracks : PTracksContained : Parks↔ Tracks

Cityparks = dom ContainedCityptracks = ran Contained

AccessParkΞParkManagementCityroads : PRoadsPaccess : Parks↔ Roads

Cityparks = dom PaccessCityroads = ran Paccess

ParkFacilitationΞParkManagementCityAuthority : PDevAuthorityProvidef acilities : Parks 7→ DevAuthority

Cityparks = dom Providef acilitiesCityAuthority = ran Providef acilities

SchoolManagementCityschools : P SchoolsCitysprincipals : PPrincipalsManage : Schools � Principals

Cityschools = dom ManageCitysprincipals = ran Manage



WCECS 2012

SchoolMonitoringΞSchoolManagementCityEduoffice : PEduOfficeMonitors : Schools 7→ EduOffice

Cityschools = dom MonitorsCityEduoffice = ran Monitors

AccessSchoolSchoolManagementCityroads : PRoadsSaccess : Schools↔ Roads

SchoolfacilitiesΞSchoolManagementCityAuthority : PDevAuthorityGetfacilities : Schools↔ DevAuthority

Cityschools = dom GetfacilitiesCityAuthority = ran Getfacilities

RoadBusStopsΞAccessSchoolCitybusstops : PBusStopsAdjacentto : Roads↔ BusStops

Cityroads = dom AdjacenttoCitybusstops = ran Adjacentto

It is clear from above mentioned formal specification thatit is unambiguous and understandable by only one way. Theuse of this formal specification will be helpful in a great dealfor designer of complex spatial databases to perform furtherdesign processes.

V. VERIFICATION OF SPECIFICATION

The formal schemas mentioned in previous section areimplemented and verified by Z/EVES tool. Some of thesnapshots of verification of these schemas are shown infollowing fligure 2(a) shows schemas for description of enti-ties and figure 2(b) shows schemas for relationship betweenentities. The main screen consists of three columns. Firstcolumns shows the verification of syntax, Second columnshows verification of proof, and Third column contains thespecification.

VI. CONCLUSIONS

In this paper, a brief introduction of Formal methodsand Geographic Information Systems GIS is given alongwith the application of formal methods in spatial databasesdevelopment. It is showed that conceptual models of spatialdatabases can be formalized in formal systems. The databaseconcept is vital component of all GIS systems and differ-entiates it from other simple computer supported mappingsystems, which may produce good quality maps but canneither highlight the important relationships between featuresnor provide any form of analysis. By using formal methods, amodel is considered as an algebraic structure which consistsof sets of individuals, relations, and functions. Relations and

(a)

(b)

Fig. 2. Z/EVES verification of Z- specification

functions of the model correspond to relations, properties,and processes in the world. These models use some formallanguage to represent conceptual models. In this paper, I haveused Z -notation that has powerful structuring mechanismand is based upon set theory and mathematical logic. Themain reason of using Formal methods in Conceptual designwas that they provide a compact description of the entitiesand relationships between them.

REFERENCES

[1] Adrijana Car and Andrew U. Frank 1995: Formalization of ConceptualModels for GIS using GOFER. In Proceedings of GIS/LIS ’95 CentralEurope, in Budapest, Hungary, pp: 8

[2] Alejandro Pauly, Mark McKenney, Reasey Praing, and Markus Schnei-der 2005: Dimension Refined Topological Predicates. In Proceedings ofthe 13th annual ACM international workshop on Geographic informa-tion systems

[3] Andrew U. Frank and Werner Kuhn1995: Specifying Open GIS withFunctional Languages. In 4th International Symposium on Large SpatialDatabases, SSD’95, in Portland, USA, 184-195

[4] Andrew U. Frank and Thomas Bittner 1997: An Introduction to theApplication of Formal Theories to GIS. In Proceedings of AngewandteGeographische Informationsverarbeitung IX (AGIT), (Dollinger, F., andStrobl, J., eds.), in Salzburg, Published by Institut fuer Geographie,Universitaet Salzburg, Salzburger Geographische Materialien, Vol. Heft26, 11-22



WCECS 2012

[5] A. Belussi, B. Catania, and E. Bertino November 2003: A ReferenceFramework for Integrating Multiple Representations of GeographicalMaps. Proceedings of the 11th ACM international symposium onAdvances in geographic information systems GIS ’03

[6] Brajesh Goyal, Shashi Shekhar, Mark Coyle, Duen-Ren Liu, andShyamsundar Sarkar 1997: Data Models in Geographic InformationSystems. Communication ACM 40(4): 103-111

[7] David G. Jenkins and Lisa A. MacCauley 2006: GIS, SINKS, FILL,and Disappearing Wetlands: Unintended Consequences in AlgorithmDevelopment and Use, Symposium on Applied Computing 2006: Pro-ceedings of the 2006 ACM symposium on Applied computing, Pages277-282

[8] Debashis Chakraborty and Rabi N. Sahoo 2007: Fundamentals ofGeographic Information System, Viva Books Private Limited

[9] Huiqing H. Yang, Geoffrey L. Tranard 2006: An Online InformationSystem for Apartment Services with Fuzzy Spatial Queries. IKE’06:Proceedings

[10] Jianchun Zhang 1994: A Formal Specification Model and Its Applica-tion in Multidatabase Systems. In Proceedings of the 1994 conferenceof the Centre for Advanced Studies on Collaborative research

[11] Jim Woodcock and Jim Davies 1996: Using Z Specification Refine-ment and Proof. Prentice Hall (ISBN 0-13-948472-8)



WCECS 2012

towards the spatial database speciﬁcation for gis … databases for gis systems using z notation...

Documents