The work deals with the extension of the Explorer of Semantics of First-Order Logic with new components, which represent a completely different view of practicing the structures of first-order logic than the original application offered so far. The application is extended mainly by a graph view, in which the elements of the domain, symbols of constants, ternary and quaternary relations are expressed by means of graph vertices and binary relations are expressed by means of edges. Subsequently, it is possible to define expressions (formulas and terms), which the application evaluates according to the created structure. The original view of the structures is preserved in the application and it is possible to easily switch between the old and the new view. To do this, it was necessary to ensure consistency of data between views. The application is primarily programmed using the React, Redux and React Diagrams libraries. It was tested by students of the subject Mathematics (4) - Logic for computer science. Keywords: first-order logic, satisfaction in finite structure, client-side web application