Qualitative spatial representation and reasoning are among the important capabilities in intelligent geospatial information system development. Although a large contribution to the study of moving objects has been attributed to the quantitative use and analysis of data, such calculations are ineffective when there is little inaccurate data on position and geometry or when explicitly explaining events rather than presenting numerical results is needed. In some cases, the computational complexity of quantitative methods is a factor in their weakness. In such a situation, the ideas of expressing and presenting moving objects relationships in qualitative and explicit forms and using logical and rational methods instead of computational and analytical ones have been proposed. This paper presents the application and extension of the remarkable Qualitative Trajectory Calculus (QTC) framework to represent and reason about moving point objects in GIS network paths by considering the concept of accessibility. QTC extension and reasoning paradigm were theoretically defined based on basic relationships such as moving one object toward another, moving one object away from another, moving one object following on another, and so on, allowing one object to access another along a specified path. The important properties of the developed methodology were discussed by examining the conceptual neighborhood of relationships and introducing and proving a number of inference rules. The obtained rules, which are mainly presented in the form of a composition table, formed a knowledge base for logical inference. Also, some of the extracted relationships showed features such as being inverse, symmetric, and transitive. For the purpose of practical implementation, examples of inference and query were tested by employing Prolog language to develop a deduction system using logical rules and facts. In this implementation, eight moving agents were considered. The existing facts of the spatial and movement situations complementing the knowledge base were expressed in terms of seven logical sentences. In addition to these facts, five items from the whole derivation rules, defined in the theoretical part, were selected and rewritten in the form of first-order logic. According to these facts and derivation rules, some example queries were proposed including 1. Which of the following agents does agent A have access to? 2. To which agents do agent A move? 3. What agents does agent A move away from? 4. Does agent A reach agent D? 5. Does agent A move away from agent H? The SWI Prolog system was then used to answer the queries. The output of the queries from the logical inference system was compared with the output of the queries from a conventional relational database. Due to the inference capability, the logical inference system provided results that were not recoverable from the initial information in the database. For example, a regular survey of a database found that only agent B was available for agent A, but the results of the inference on the knowledge base showed that in addition to B, the factors E, C, and D were also available for A. Comparing the results of queries from the above framework with the output of the contemporary relational databases enhanced the findings of this research eventually.