Logical Investigation of Reasoning with Tables

In graphical or diagrammatic representations, not only the basic component of a diagram, but also a collection of multiple components can form a unit with semantic significance. We call such a collection a “global object”, and we consider how this can assist in reasoning using diagrammatic representation. In this paper, we investigate reasoning with correspondence tables as a case study. Correspondence tables are a basic, yet widely applied graphical/diagrammatical representation system. Although there may be various types of global objects in a table, here we concentrate on global objects consisting of rows or columns taken as a whole. We investigate reasoning with tables by exploiting not only local conditions, specifying the values in individual table entries, but also global conditions, which specify constraints on rows and columns in the table. This type of reasoning with tables would typically be employed in a task solving simple scheduling problems, such as assigning workers to work on different days of the week, given global conditions such as the number of people to be assigned to each day, as well as local conditions such as the days of the week on which certain people cannot work. We investigate logical properties of reasoning with tables, and conclude, from the perspective of free ride, that the application of global objects makes such reasoning more efficient.