Formal Modelling

wasonIn contrast to many artificial systems, humans do not use quantitative representations (such as meters, angles, coordinates), but rather a qualitative representation of knowledge. The best characterization might be found in Moratz & Ragni (2008):

“Qualitative spatial reasoning (QSR) abstracts metrical details of the physical world and enables computers to make predic- tions about spatial relations even when precise quantitative information is unavailable (Cohn, 1997). From a practical viewpoint QSR is an abstraction that summarizes similar quantitative states into one qualitative characterization. A complementary view from the cognitive perspective is that the qualitative method compares features within the object domain rather than by measuring them in terms of some artificial external scale (Freksa, 1992). This is why qualitative descriptions are quite natural for humans.”

In the following several qualitative calculi are presented and investigated. Especially wrt. the computational complexity of combinations of such calculi for relevant and important domains such as spatial, temporal, spatio-temporal, and causal reasoning. It is necessary to show how we can define a useful language to analyze computational properties and to develop more complex languages, i.e., that consist of combinations of such calculi. The latter is relevant as a limitation of most calculi is that they are not expressive enough to represent human reasoning.


  • Combining Topological and Orientation Information
    Ragni, M., & Wölfl, S. (2008). Reasoning about Topological and Positional Information in Dynamic Settings. In D. Wilson & H. C. Lane (Eds.), Proceedings of the Twenty- First International Florida Artificial Intelligence Research Society Conference (pp. 606–611). Menlo Park, CA: AAAI Press.
  • Branching Allen:
    Ragni, M., & Wölfl, S. (2004). Branching Allen: Reasoning with intervals in branching time. In C. Freksa, M. Knauff, B. Krieg-Brückner, B. Nebel, & T. Barkowsky (Eds.), Spatial Cognition IV – Reasoning, Action, Interaction (pp. 330–351). Berlin: Springer.
  • Dependency Calculus:
    Ragni, M., & Scivos, A. (2005a). The dependency calculus: Reasoning in a General Point Relation Algebra. In U. Furbach (Ed.), Advances in Artificial Intelligence: Pro- ceedings of the 28th Annual German Conference on AI (pp. 49–63). Berlin: Springer.
  • Temporalizing Cardinal Directions:
    Ragni, M., & Wölfl, S. (2005). Temporalizing spatial calculi: On generalized neighborhood graphs. In U. Furbach (Ed.), Advances in Artificial Intelligence, Proceedings of the 28th Annual German Conference on AI (pp. 64–78). Berlin: Springer.
  • Nonmonotonic Logic: Suppression: Dietz, E.-A., Hölldobler, S., & Ragni, M. (2012a). A Computational Approach to the Suppression Task. In N. Miyake, D. Peebles, & R. Cooper (Eds.), Proceedings of the 34th Annual Conference of the Cognitive Science Society (pp. 1500–1505). Austin, TX: Cognitive Science Society.
  • Nonmonotonic Logic: Wason Selection Task:
    Dietz, E. A., Hölldobler, S., & Ragni, M. (2012b). A Simple Model for the Wason Selection Task. In T. Barkowsky, M. Ragni, & F. Stolzenburg (Eds.), Report Series of the Transregional Collaborative Research Center SFB/TR 8 Spatial Cognition.
  • Nonmonotonic Logic: Abstract and Social Case:
    Dietz, E.-A., Hölldobler, S., & Ragni, M. (2013). A Computational Logic Approach to the Abstract and the Social Case of the Selection Task.