The Fourth Conceptual Structures Tool Interoperability Workshop (CS-TIW 2009) was held in Moscow, Russia on the 26th of July 2009, collocated with the 17th International Conference on Conceptual Structures (ICCS 2009) “Leveraging Semantic Technologies”. Information about the workshop is available at the webpage: http://www.kde.cs.uni-kassel.de/ws/cs-tiw2009. The title of this year's workshop, “Vision and Applications” was chosen to emphasize the new challenges, problems and issues that have appeared in the context of knowledge representation that involve the visual manipulation of information by domain experts. Furthermore, such knowledge has to be manipulated with fast results within a logic based framework. In this context conceptual structure tools play a crucial role as their graph based foundations allow for (1) rigorous algorithmic reasoning and (2) user validation for both reasoning and representation. It is a unique environment for integrated research in discrete mathematics, human computer interaction, cognitive science and engineering. The workshop brought together researchers from diverse communities with the common goal of a fruitful discussion on the above mentioned interoperability issues by raising mutual awareness of ongoing research and existing technologies from which each community could benefit. We wish in full to express our appreciation to all the authors of submitted papers and to the members of the Program Committee for all their work and valuable comments.