Towards the Spatial Database Specification for GIS using Z-Notations Farooq Ahmad, Salahuddin Khan and Sher Afzal Khan Abstract—Formal methods are mathematical techniques use in design, development and verification of software and hard- ware system. Geographic information systems GIS use to collect, store, analyze and present spatial informations. GIS databases are usually very complex to design. Formal methods can play an important role in their design. In the paper, the authors investigate an approach of formal specification of spatial databases for GIS systems using Z notation (a formal language with a powerful structuring mechanism). For the purpose, we use an example from the context of GIS and spatial database to draw Entity Relationship Diagram ERD. Further the paper presents transformation from Entity Relationship Diagram ERD to formal specification that shows all the entities and their relationships in Z notation. In this paper we exhibit that the approach is applicable for spatial database designing. Consequently this leads to unambiguous, consistent and verified GIS system. Index Terms—Formal Methods, Z-Notations, GIS, Spatial databases, Conceptual design. I. I NTRODUCTION G EOGRAPHIC Information Systems GIS are extremely complex software, hence specification methods are very important for their quality especially for: consistency of data models, different component interfaces, and in database architecture [3]. Existing methods offer large amounts of text and diagrams, which often creates ambiguity and problems to scale up large problems where the greater amount of documentation require. Due to these problems, it is argued to develop software model for designing GIS. For this there are many useful models of GIS, which are designed by using informal approaches in ad-hoc fashion. Consequently, it is difficult for GIS designer to fully capture Modularity and to remove ambiguous, inconsistency and to verify step by step to a system. In order to remove such errors we propose formal approach based upon transformation of ERD diagram to Z- notation. This would help GIS designer to verify his system early at the design level. According to Woodcock et al. [11] Z is model-oriented approach, and has a powerful structuring mechanism. It can be used to specify information systems in combination with natural language. The formal method Z is based on discrete mathematics such as predicate logic, set theory, functions and relations. It is used for specifying the behavior of abstract data 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 travel grant for this work is supported by the Higher Education Commission of Pakistan for oral presentation. Farooq Ahmad is with the Faculty of Information Technology, University of Central Punjab, lahore, Pakistan e-mail:dr.farooq@ucp.edu.pk. Salahuddin Khan is with the Department of Computer Sciences, SZABIST- Islamababd, Pakistan e-mail:salahuddin209@yahoo.com. Sher Afzal Khan is with the Department of Computer Sciences, Abdul Wali Khan University, Mardan, Pakistan e-mail:sher.afzal@awkum.edu.pk. called schemas. The schema consists of three parts; the first one is the schema name which is in the top line, the second part between the first and second line is the schema signature which is the set of names and types of entities introduced in a schema. The third part under the middle line is called the schema predicate which is used for the set of properties and shows the relationships between the entities and the variables defined in the schema signature. These schemas can be combined to produce the overall description of the system. The paper address schemas in the specification part of the paper. The Z-specification cannot typically be executed by computers, but the standard tools are available which are used for checking syntax and proof of the formal specification, leads to quality of specification and this allows mistakes to be detected and corrected sooner in the design life cycle. Formalization is the process of the design of representations of infinite phenomena by a finite set of distinct symbols, [4]. The use of formalization process basically facilitates to understand the underlying structure and theory in the model [1]. The organization of the paper is as follows: Section 2 describes Geographic Information Systems GIS, spatial databases and their conceptual model. Section 3 describes related work that has been done regarding use of formal methods in GIS and spatial databases. In section 4, Formal specifications of conceptual design of spatial databases are demonstrated using Z-notations. In Section 5, we present the proof and verification of syntax used in our proposed approach. In the end, we give conclusion and references. II. GEOGRAPHIC I NFORMATION SYSTEMS GIS In the past, efforts have been made to define GIS from a variety of angles. This diversity of perceptions has lead to innumerable definitions for GIS, based on the type of user and application domain. In view of current capabilities of GIS, it can be defined as ”an information system used to store, organize, retrieve, analyze, output and update spatially referenced data, in order to support decision making for planning and management of activities like natural resources and environmental management, transportation and telecom- munication utilities, commerce and business affairs, defense services, and various administrative management”, Debashis Chakraborty 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 difference in regard to geospatial data. Before GIS, geospatial data were poorly maintained. The process of data retrieval, data security, 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