Review Causal knowledge and reasoning by cognitive maps: Pursuing a holistic approach Alejandro Pen ˜a a,b,c, * , Humberto Sossa c , Agustı ´n Gutie ´rrez c a WOLNM, 31 Julio 1859 # 1099-B, Leyes Reforma, DF 09310, Mexico b UPIICSA, National Polytechnic Institute, Te 950, Granjas Mexico, DF 08400, Mexico c Centre for Computer Research, National Polytechnic Institute, Juan de Dios Batiz s/n, Nva. Industrial Vallejo, DF 07738, Mexico Abstract Due to the lack of an integral study about cognitive maps (CM) that focus on the causal phenomenon, this paper introduces the underlying concepts towards a holistic conceptual model, enhanced by a profile of several versions. We illustrate the use of CM through their application into the Web-based Education Systems (WBES). From the causal perspective, CM depict and simulate the systems dynamics based upon qualitative knowledge about a specific domain. A CM is a visual digraph that identifies the concepts of a given subject of analysis. CM show causal-effect relationships among the concepts and outline complex structures. This tool aims to predict the evolution of a model through causal inference. This kind of inference estimates the degree of significance of change of the concepts in the context of the whole system. The behavior of a CM is given away during iterations that update the variation of the concept state values until reach a stable point in a search space, a pattern of states or a chaotic region. The purpose of this research is to share its findings, depict the work done and promote the use of CM in a broad spectrum of domains. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Cognitive maps; causality; concepts; causal relations; qualitative model; causal inference 1. Introduction CM is a term with a broad and deep meaning that has been used to focus on specific subjects. The first work done under this term was the psychology research about spatial learning in human beings and animals in the 19th century (Koulouriotis, Diakoulakis, Emiris, Antonidakis, & Kalia- katsos, 2003). Afterwards, Trowbridge in 1913 and Tolman in 1948 enhanced the former findings (Pen ˜a & Gutie ´rrez, 2004a). Later on Tolman (1948) found out that: In the course of learning something like a field map of the envi- ronment is established in the Hippocampus. So in 1973, Downs and Stea (1973) defined the cognitive mapping pro- cess as: The result of psychological transformations by which an individual acquires, codes, stores, recalls and decodes information about his/her spatial environment. With this baseline, different works have been achieved like: The modeling of topological maps regarding to the physi- cal space where a mobile robot navigates (Fillenbaum & Rapport, 1971; Hafner, 2000) and the sketch of virtual worlds that people experienced (Billinghurst & Weghorst, 1993). Also, CM have inspired memorizing techniques (Belleza, 1999) and teaching–learning methods by tracing data relations of any domain as spatial relations. This kind of approaches takes advantage of the innate abilities to understand and remember data about the objects that sur- rounded a physical place (Johns & Blake, 2001). In addition to the spatial connotation, some CM-based models and techniques have been outlined for representing and eliciting cognitive structures. For instance, Barlett (1932) proposes the schema as the knowledge structure 0957-4174/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2007.06.016 * Corresponding author. Address: WOLNM, 31 Julio 1859 # 1099-B, Leyes Reforma, DF 09310, Mexico. Tel./fax: +52 55 5694 0916, +52 55 5454 2611 (mobile). E-mail addresses: apenaa@ipn.mx (A. Pen ˜ a), hsossa@cic.ipn.mx (H. Sossa), atornes@cic.ipn.mx (A. Gutie ´rrez). www.elsevier.com/locate/eswa Expert Systems with Applications 35 (2008) 2–18 Expert Systems with Applications