Catálogo de publicaciones - libros

Logical studies of diagrammatic reasoning—indeed, mathematical reasoning in general—are typically oriented towards proof-theory. The underlying idea is that a reasoning agent computes diagrammatic objects during the execution of a reasoning task. These diagrammatic objects, in turn, are assumed to be very much like sentences. The logician accordingly attempts to specify these diagrams in terms of a recursive syntax. Subsequently, he defines a relation ⊢ between sets of diagrams in terms of several rules of inference (or between sets of sentences and/or diagrams in case of so-called heterogeneous logics). Thus, diagrammatic reasoning is seen as being essentially a form of logical derivation. This proof-theoretic approach towards diagrammatic reasoning has been worked out in some detail, but only in a limited number of cases. For example, in case of reasoning with Venn diagrams and Euler diagrams (Shin [5] and Hammer [2]).

We conducted eye-tracking studies of subjects solving the problem of finding shortest paths in a graph using a known procedure (Dijkstra’s algorithm). The goal of these studies was to investigate how people reason about and solve graphically presented problems. First, we compared performance when the graphical display was animated to when the display was static. Second, we compared performance when the display was initially sparse, with detailed information being progressively revealed, to when the display presented all information simultaneously. Results suggest that while animation of the procedure or algorithm does not improve accuracy, animation coupled with progressively revealing objects of interest on the display does improve accuracy and other process measures of problem solving.

Visual focus and mental focus in diagram-based problem solving have been shown to be often interrelated with respect to cognitive and visuo-perceptual representational and procedural properties. A problem solver’s visual focus can be used for a rough detection of mental focus in diagrammatic reasoning – sufficient to distinguish certain problem solving modes. An integration of visual focus over time can reveal characteristic patterns of problem solving strategies or solutions models. Such patterns hold formidable potential for computer-assisted and collaborative human-computer reasoning with diagrams.

Researchers in all areas of science recognize the value of graphical displays and research on graphs has focused on determining which graphical elements enhance readability. To date, no research has examined the physiological processing of graphs. The purpose of this project was to examine the event-related potentials (ERPs) associated with the processing of bivariate scatterplots. Participants viewed scatterplots depicting different linear relationships (positive and negative; strong and weak) and their ERPs were analyzed. Results indicate interesting differences in how scatterplots are processed. Overall, there was differential processing in posterior, medial, and anterior brain sites. Sites on the left and right sides of the brain showed different patterns of activity in response to the scatterplots. In addition, results suggest that different relationships are processed differently in the brain (confirming previous research that has suggested that the perception of covariation is dependent upon the type of relationship depicted on a scatterplot).

The process of member validation requires researchers to present their findings back to the communities that have been studied to gain their appraisal of the work. By depicting subject matter that ranges from the physical to the conceptual, diagrams provide a valuable alternative to the written documents traditionally used in member validation. This paper reports on a study in which diagram-based member validation was used to assess the accuracy and acceptability of the researchers’ interpretations. The manner in which the technique was implemented, the benefits that were realized and possible directions for future work are all discussed.

Research on explanations shows how category prototypicality can affect the the framing of comparative information about social groups. Spontaneous explanations of group differences focus on the attributes of atypical groups and treat the attributes of prototypical groups as the norm. Thus, gender differences are attributed to women more than men (Miller, Taylor, & Buck, 1991), and sexual orientation differences to lesbians/gay men more than straight women and men (Hegarty & Pratto, 2001). When group differences are explained within an overarching category for which the atypical group is more prototypical (e.g., sexual orientation differences among gay and straight men living with HIV/AIDS), these patterns are not observed (Miller et al., 1991, Experiment 3; Hegarty & Pratto, 2001, Experiment 2).

Euler diagrams are an effective and intuitive way of representing relationships between sets. As the number of sets represented grows, Euler diagrams can become ‘cluttered’ and lose some of their intuitive appeal. In this paper we consider various measures of ‘clutter’ for abstract Euler diagrams and show that they compare well with results obtained from an empirical study. We also show that all abstract Euler diagrams can be constructed inductively by inserting a contour at a time and we relate this inductive description to the clutter metrics.

Many graphical representation systems apparently support derivative meanings , namely, meaning relations not directly legitimized by the systems’ semantic conventions. Practitioners and researchers of graphical communication have long realized the functional importance of the generative nature of graphical meaning, yet no systematic attempts have been made to clarify the informational mechanism behind it. In this project, we develop a mathematical framework in which meaning derivation properties of graphical systems are explicitly modeled and accounted for.

We argue that a comprehensive model of graph comprehension must include spatial cognition. We propose that current models of graph comprehension have not needed to incorporate spatial processes, because most of the task/graph combinations used in the psychology laboratory are very simple and can be addressed using perceptual processes. However, data from our own research in complex domains that use complex graphs shows extensive use of spatial processing. We propose an extension to current models of graph comprehension in which spatial processing occurs a) when information is not explicitly represented in the graph and b) when simple perceptual processes are inadequate to extract that implicit information. We apply this model extension to some previously published research on graph comprehension from different labs, and find that it is able to account for the results.