In this article I present and discuss some criteria to provide a diagrammatic classification. Such a classification is of use for exploring in detail the domain of diagrammatic reasoning. Diagrams can be classified in terms of the use we make of them—static or dynamic—and of the correspondence between their space and the space of the data they are intended to represent. The investigation is not guided by the opposition visual vs. non-visual, but by the idea that there is a continuous interaction between diagrams and language. Diagrammatic reasoning is characterized by a duality, since it refers both to an object, the diagram, having its spatial characteristics, and to a subject, the user, who interprets them. A particular place in the classification is occupied by constructional diagrams, which exhibit for the user instructions for the application of some procedures.

This paper presents a graph-based knowledge representation and reasoning language. This language benefits from an important syntactic operation, which is called a graph homomorphism. This operation is sound and complete with respect to logical deduction. Hence, it is possible to do logical reasoning without using the language of logic but only graphical, thus visual, notions. This paper presents the main knowledge constructs of this language, elementary graph-based reasoning mechanisms, as well as the graph homomorphism, which encompasses all these elementary transformations in one global step. We put our work in context by presenting a concrete semantic annotation application example.

Biologists depend on visual representations, and their use of diagrams has drawn the attention of philosophers, historians, and sociologists interested in understanding how these images are involved in biological reasoning. These studies, however, proceed from identification of diagrams on the basis of their spare visual appearance, and do not draw on a foundational theory of the nature of diagrams as representations. This approach has limited the extent to which we understand how these diagrams are involved in biological reasoning. In this paper, I characterize three different kinds of figures among those previously identified as diagrams. The features that make these figures distinctive as representational types, furthermore, illuminate the ways in which they are involved in biological reasoning.

Industrial design processes can be described as human design problem solving, incorporating the acquisition, evaluation, production and transfer of specific knowledge. In this paper, we will describe the connection and interaction between visualization and reasoning during different stages of the design process. Thereby we focus on three early stages of this process: clarifying the task, concepting and designing an overall solution.

This paper provides a rather general description of design processes and more detailed remarks on design knowledge and design actions. It specifically focuses on design concepts as visual key elements in industrial design processes. We will address the importance of externalization and visualization as means for thinking and knowledge generation and transfer in industrial design in general.

The design process is described as an interplay of the parallel and iterative developments of three domains: knowledge, concept and design. In contrast to linear schemes, this paper proposes a design process scheme focusing on iterative circles and parallel processing possibilities. Industrial design knowledge will be described and compared to relevant knowledge in other disciplines, in particular, engineering design knowledge. We will describe the strong link between the designer's individual biographies, design knowledge and the outcome of design processes.

Design concepts will be discussed as extremely compact representations of core characteristics of the artifacts to be designed, serving as a guide to the design process.

Design actions as described in this paper are characterized by the simultaneous occurrence of thought and externalization processes. Different kinds of visualization are discussed in regard of their role in reasoning during industrial design processes.

This paper concludes by sketching two perspectives. One addresses the need for interdisciplinary research on new visualization tools with regard to human reasoning in design processes. The second one gives an impression of how visualization tools and methods of industrial design can supplement other disciplines.

The concept of manipulative abduction is devoted to capture the role of action in many interesting cognitive situations: action provides otherwise unavailable information that enables the agent to solve problems by starting and performing a suitable abductive process of generation or selection of hypotheses. We observe that many external things, usually inert from an epistemological point of view, can be transformed into epistemic mediators. I will present some details derived from the history of the discovery of the non-Euclidean geometries that illustrate the relationships between strategies for anomaly resolution and visual thinking. Geometrical diagrams are external representations that play both a mirror role (to externalize rough mental models) and an unveiling role (as gateways to imaginary entities). I describe them as epistemic mediators able to perform various explanatory, non-explanatory, and instrumental abductive tasks (discovery of new properties or new propositions/hypotheses, provision of suitable sequences of models as able to convincingly verifying theorems, etc.). I am also convinced that they can be exploited and studied in everyday non-mathematical applications also to the aim of promoting new trends in artificial intelligence modeling of various aspects of hypothetical reasoning: finding routes, road signs, buildings maps, for example, in connection with various zooming effects of spatial reasoning. I also think that the cognitive activities of optical, mirror, and unveiling diagrams can be studied in other areas of manipulative and model-based reasoning, such as the ones involving creative, analogical, and spatial inferences, both in science and everyday situations so that this can extend the epistemological, computational, and the psychological theory.

In this paper I tackle the question of what basic form an analytical method for articulating and ultimately assessing visual representations should take. I start from the assumption that scientific images, being less prone to interpretive complication than artworks, are ideal objects from which to engage this question. I then assess a recent application of Nelson Goodman's aesthetics to the project of parsing scientific images, Laura Perini's ‘The truth in pictures’. I argue that, although her project is an important one, her Goodmanian conventionalism produces a method of analysis that is incapable of adequately parsing a certain class of pictures and her focus on truth is unnecessary. This speaks against the promise of Goodman's analytical strategy for elucidating visual content and reasoning in the sciences and elsewhere. As an alternative, I develop John Willats’ analytical method and compare it to Perini's through engaging three of her examples—a chemical diagram, a graph and an electron micrograph. Ultimately, a space remains open for a mixed system where Willats’ account provides pictorial analysis and the Goodman–Perini approach parses visual languages.

Visuo is an implemented Python program that models visual reasoning. It takes as input a description of a scene in words (e.g. ‘small dog on a sunny street’) and produces estimates of the quantitative magnitudes of the qualitative input (e.g. the size of the dog and the brightness of the street). We claim that reasoners transfer quantitative knowledge to new concepts from distributions of familiar concepts in memory. We also claim that visuospatial magnitudes should be stored as distributions over fuzzy sets. We show that Visuo successfully predicts quantitative knowledge to new concepts.

Research into visual reasoning up to now has focused on images that are literal depictions of their objects. I argue in this article that an important further mode of visual reasoning operates on images that depict objects metaphorically. Such images form part of the class of expressive symbols: they are found, for example, in allegorical representations in works of visual art, studied by iconology. They were also a common way of encapsulating insights about the universe in natural philosophy in the Renaissance. Many writers assume that expressive symbols have vanished from modern science, but I argue in the second part of the article that mathematical law statements in present-day physics should be seen, in part, as images that constitute expressive symbols of the world. In support of this view, I offer evidence that law statements relate to their objects metaphorically and that physicists engage with them primarily through visual inspection and visual reasoning.