Boundary logic is a formal diagrammatic system that combines Peirce's Entitative Graphs with Spencer Brown's Laws of Form. Its conceptual basis includes boundary forms composed of non-intersecting closed curves, void-substitution (i.e. deletion) as the primary proof procedure, and semipermeable boundaries that define valid transformations. Boundary logic is first briefly described, and then several new diagrammatic notations for logic derived from geometrical and topological transformation of boundary forms are presented. The calculus and an example proof of modus ponens is provided for textual, enclosure, graph, map, path and block based forms. These new diagrammatic languages for logic convert connectives into configurations of containment, connectivity, contact, conveyance, and concreteness.

The dominant account of the role of diagrams in reasoning, as exemplified by the work of Barwise and associates, is that they are "sentences" in a 2-D language, with specialized rules of inference that generate new diagrams. We discuss a larger variety of roles for diagrams in helping with reasoning, focusing in particular on their role as physical models of states of affairs, much like an architectural model of a building or a 3-D molecular model of a chemical compound. We discuss the concept of a physical model for a logical sentence, and the role played by the causal structure of the physical medium in making the given sentence as well as a set of implied sentences true. When the physical model is prototypical, it supports the inference of certain other sentences for which it provides a model as well. We also informally discuss a proposal that diagrams and similar physical models help to explicate a certain sense of relevance in inference, an intuition that so-called Relevance Logics attempt to capture.

This paper discusses the types of communicative signals that frequently appear in bar charts and how we exploit them as evidence in our system for inferring the intended message of an information graphic. Through a series of examples, we demonstrate the impact that various types of communicative signals, namely salience, captions and estimated perceptual task effort, have on the intended message inferred by our implemented system.

This paper describes the evaluation of ERST, an adaptive system which is designed to improve its users' external representation (ER) selection accuracy on a range of database query tasks. The design of the system was informed by the results of experimental studies. Those studies examined the interactions between the participants' background knowledge-of-external representations, their preferences for selecting particular information display forms, and their performance across a range of tasks involving database queries. The paper describes how ERST's adaptation is based on predicting users' ER-to-task matching skills and performance at reasoning with ERs, via a Bayesian user model. The model drives ERST's adaptive interventions in two ways - by 1. hinting to the user that particular representations be used, and/or 2. by removing from the user the opportunity to select display forms which have been associated with prior poor performance for that user. The results show that ERST does improve an individual's ER reasoning performance. The system is able to successfully predict users' ER-to-task matching skills and their ER reasoning performance via its Bayesian user model.

Illustrating a dynamic process with an arrow-containing diagram is a widespread convention in people's daily communications. In order to build a basis for capturing the structure and semantics of such arrow-containing diagrams, this paper formalizes the topological relations between two arrow symbols in such a diagram and discusses the influence of topological relations on the diagram's semantics. Topological relations of arrow symbols are established by two types of links, intersections and common references, which are further distinguished into nine types based on the combination of the linked parts of two arrow symbols. The topological relations are captured by the existence/non-existence of these nine types of intersections and common references. Then, this paper demonstrates that arrow symbols with different types of intersections illustrate two actions with different interrelations, whereas those with common references illustrate a pair of semantics that may be mutually exclusive or synchronized.

Drawings of water are the earliest, least abstract forms of flow diagram. Representations of ideal or generalised sequences for manufacturing or actual paths for materials between machines came next. Subsequently documentation of production and information flow become subjects for graphical representation. A similar level of abstraction was necessary for representations of invisible flows such as electricity. After initial use to define control, flow diagrams became a general purpose tool for planning automated computation at all levels of composition. Proliferation of syntax variants and the need for a common language for documentation were the motivations behind standardisation efforts. Public communication of metalevel systems information superseded private comprehension of detailed algorithmic processes as a primary function. Changes to programming language structures and their associated processes caused the initial demise of flow diagrams in software engineering.

This experiment examines how learners integrate and understand an animation about a mechanical complex three pulleys system (Hegarty & Just, 1993; Hegarty, 2004). We tested two populations of learners, with high mechanical and spatial abilities and with low spatial and mechanical abilities. For all subjects, their task consisted to understand an animated three pulleys system. Two variables were manipulated: the controllability of the animations and the orientation of the attention of the learners. During the inspection of the animation by the subjects, we recorded their eye tracking to carry on line information about dynamic cognitive processing. After the inspection of the animation, the subjects answered to a comprehension test about the pulleys system. We distinguished three different levels of integration of the system: configuration, local kinematics and entire functional model. The comprehension test results indicated a positive effect of a full controllable animation and also a positive effect of a specific orientation of attention, on the functional model and on local kinematics. The eye tracking data indicated that the learners process highly the areas of the animations where a great amount of motion is involved along the causal chain of events. We show an effect of the controllability of the system and of a specific orientation of attention of the learner on the amount of eye fixations and on the number of transitions between areas that included the causal chain. With a specific orientation of their attention on the kinematics and on the entire functional model, learners watched less the irrelevant areas of the animated diagram for the integration of the causal chain.

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 compare these metrics 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. Finally, we consider how our notions of clutter relate to concrete nesting of Euler diagrams.

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.

Although the ability to select an appropriate diagram to suit the task at hand is one important aspect of graphic literacy, novices have been shown to have a problem with this. To examine how it might be possible to bridge the gap between experts and novices that has been identified in previous research, the present study investigated whether teaching sessions involving active comparison of diagrams and review of lessons leant from problem solving sessions would facilitate the development of participants’ abstract conditional knowledge and use of appropriate diagrams in subsequent problem solving. Fifty-eight 8th grade participants were assigned one of the two conditions and were provided with instruction and assessment sessions over five days. In both experimental and control conditions, traditional math classes were provided in which diagrams were used in explaining how to solve various math word problems. However, the experimental group was additionally provided with sessions to actively compare diagrams used and review lessons learnt from problem solving. The results of subsequent assessments showed that participants in the experimental condition constructed more appropriate diagrams in solving math word problems. In an assessment of conditional knowledge, these participants also provided more abstract and detailed descriptions about the uses of diagrams in problem solving. Implications for diagrams research and student math instruction are discussed.

We propose a case-based method for constructing a structural model of a schematic diagram of a physical system through analogical mapping and transfer. A source case may contain (1) a 2-D vector-graphics line drawing of a physical device, (2) a specification of the shapes and spatial relations in the drawing, and (3) a specification of the components and connections of the device depicted in this diagram. Given an input of a target 2-D vector graphics line drawing and a description of the shapes and spatial relations in it, we ask how an agent might align the two drawings and transfer the relevant structural elements over to the new drawing, giving as output a specification of the components and connections depicted in the input drawing. The domain is engineering design of kinematic devices that convert translational motion into rotational motion, such as a piston and crankshaft device. The Archytas system implements this method for situations in which the drawings in the source case and the target problem are very similar.

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.