How can Euler diagrams support non-consequence inferences? Although an inference to non-consequence, in which people are asked to judge whether no valid conclusion can be drawn from the given premises, is one of the two sides of logical inference, it has received remarkably little attention in research on human diagrammatic reasoning; how diagrams are really manipulated for such inferences remains unclear. We hypothesized that people naturally make these inferences by enumerating possible diagrams, based on the logical notion of self-consistency, in (...) which every Euler diagram is true in a set-theoretical interpretation. The work is divided into three parts, each exploring a particular condition or scenario. In condition 1, we asked participants to directly manipulate diagrams with size-fixed circles as they solved syllogistic tasks, with the result that more reasoners used the enumeration strategy. In condition 2, another type of size-fixed diagram was used. The diagram layout change interfered with accurate task performances and with the use of the enumeration strategy; however, the enumeration strategy was still dominant for those who could correctly perform the tasks. In condition 3, we used size-scalable diagrams, which reduced the interfering effect of diagram layout and enhanced participants’ selection of the enumeration strategy. These results provide evidence that non-consequence inferences can be achieved by diagram enumeration, exploiting the self-consistency of Euler diagrams. An alternate strategy based on counter-example construction with Euler diagrams, as well as effects of diagram layout in inferential processes, are also discussed. (shrink)

This paper explores the question of what makes diagrammatic representations effective for human logical reasoning, focusing on how Euler diagrams support syllogistic reasoning. It is widely held that diagrammatic representations aid intuitive understanding of logical reasoning. In the psychological literature, however, it is still controversial whether and how Euler diagrams can aid untrained people to successfully conduct logical reasoning such as set-theoretic and syllogistic reasoning. To challenge the negative view, we build on the findings of modern diagrammatic logic and introduce (...) an Euler-style diagrammatic representation system that is designed to avoid problems inherent to a traditional version of Euler diagrams. It is hypothesized that Euler diagrams are effective not only in interpreting sentential premises but also in reasoning about semantic structures implicit in given sentences. To test the hypothesis, we compared Euler diagrams with other types of diagrams having different syntactic or semantic properties. Experiment compared the difference in performance between syllogistic reasoning with Euler diagrams and Venn diagrams. Additional analysis examined the case of a linear variant of Euler diagrams, in which set-relationships are represented by one-dimensional lines. The experimental results provide evidence supporting our hypothesis. It is argued that the efficacy of diagrams in supporting syllogistic reasoning crucially depends on the way they represent the relational information contained in categorical sentences. (shrink)

In this special issue of Minds and Machines ("Situations and Artificial Intelligence") we take a close look at recent situation-theoretic research which has mostly originated within a philosophical framework but promises to have strong connotations for Artificial Intelligence workers. The seven papers which make up this special issue (three of the papers appear in Minds and Machines 9(1)) demonstrate the advantages of the situation-based approach towards problems with a definite AI flavor.