Negation in Spatial Reasoning
In recent years a lot of research has been done in order to determine factors of complexity in spatial relational reasoning, like the number of models, the wording of conclusion or the influence of relational complexity. But research so far focused on affirmative statements only, i. e. negated expressions have not yet been investigated. In spatial reasoning and in human machine interaction, however, negation plays a fundamental role. Central questions are: How are negated statements represented? What happens in multiple-model cases? Which effects have different reference frames? We conducted three experiments to show that humans (i) negate a relation by using the opposite relation, (ii) construct preferred mental models and use an economic principle, and (iii) have more difficulties in reasoning with negated relations. The goal is to extend our cognitive and computational model – the SRM.
KeywordsSpatial Reasoning Knowledge Representation and Reasoning Cognitive modeling
Unable to display preview. Download preview PDF.
- 1.Gabbay, D., Wansing, H.: What is Negation? Oxford University Press, Oxford (1999)Google Scholar
- 2.Gapp, K.P.: Angle, distance, shape and their relationship to projective relations. In: Moore, J.D., Lehman, J.F. (eds.) Proceedings of the Seventeenth Annual Conference of the Cognitive Science Society, pp. 112–117. Lawrence Erlbaum Associates Inc. (1995)Google Scholar
- 3.Hasson, U., Glucksberg, S.: Does understanding negation entail affirmation? an examination of negated metaphors. Journal of Pragmatics (forthcoming)Google Scholar
- 4.Johnson-Laird, P.N., Byrne, R.M.J.: Deduction. Erlbaum, Hillsdale, NJ (1991)Google Scholar
- 6.Knauff, M.: Deduktion und logisches Denken. In: Funke, J. (ed.) Denken und Problemlösen. Enzyklopädie der Psychologie, vol. 8, Hogrefe, Göttingen (2006)Google Scholar
- 7.Mani, K., Johnson-Laird, P.N.: The mental representation of spatial descriptions. Memory & Cognition 10(2), 181–187 (1982)Google Scholar
- 8.Ragni, M., Fangmeier, T., Webber, L., Knauff, M.: Complexity in spatial reasoning. In: Proceedings of the 28th Annual Cognitive Science Conference, Mahwah, NJ, Lawrence Erlbaum Associates, Mahwah (2006)Google Scholar
- 9.Ragni, M., Knauff, M., Nebel, B.: A computational model for spatial reasoning with mental models, pp. 1064–1070. Erlbaum, Mahwah, NJ (2005)Google Scholar
- 10.Ragni, M., Steffenhagen, F.: An implementation of the srm-model. Technical report 011-09/2006, SFB/TR 8 Spatial Cognition (2006), http://www.sfbtr8.uni-bremen.de
- 12.Russell, S., Norvig, P.: Artificial Intelligence: A Modern Approach, 2nd edn. Prentice-Hall, Englewood Cliffs (2003)Google Scholar
- 13.Vandierendonck, A., Dierckx, V., Vooght, G.D.: Mental model construction in linear reasoning: Evidence for the construction of initial annotated models. The Quarterly Journal of Experimental Psychology 57A, 1369–1391 (2004)Google Scholar