Spatial Relations in Reasoning: a Computational Model

Jury:
Laure Vieu - Université de Toulouse / IRIT
Valeria Giardino - École Normale Supérieure / IJN
Igor Douven - Université Paris 1 / IHPST
Carl Schultz - Aarhus University / ECE
Salvador Mascarenhas - École Normale Supérieure / IJN
Paul Égré - École Normale Supérieure / IJN (Directeur de thèse)
 

Abstract: The psychology of spatial reasoning often limits its studies to positioning problems such as "A is to the left of B, C is to the right of B, where is A compared to C?". The computational model PRISM, developed within the model-based approach, simulates in detail the psychological processes that enable us to solve this kind of problem, especially by including relevant cognitive elements such as attentional limits. However, no computational model seems to exist for our way of reasoning about other types of relations, such as circle inclusion, or those used in geometry.

To fill this gap, it is first shown that the mental representations underlying spatial reasoning must be diagrammatic in nature in order to justify our inferential abilities without resorting to rules in the mind. Then, the computational tool Answer Set Programming Modulo Theories for the Qualitative Spatial domain ASPMT(QS), recently proposed in artificial intelligence, is used to take into account all the geometric constraints that govern the creation and variation of these mental representations. By combining these possibilities with the psychological principles already present in PRISM, it is finally possible to propose the computational model EPRISM (‘E’ for Extended) that simulates our psychological reasoning for all types of spatial relational problems.

Moreover, several theories of cognitive science seem to ground cognitive capacities in our ability to think spatially, as is particularly the case for cognitive linguistics, which proves that abstract expressions and concepts are understood by means of spatial mental representations. This opens up the possibility to extend the use of EPRISM to other topics in cognitive science, such as the modulation process of the theory of mental models or the study of conditional reasoning.

Zoom link : send an email to François Olivier (fcs.olivier@gmail.com)