A Graphical Formalism for Reasoning about Substitution in Resource Transforming Procedures

Abstract

The ability to repurpose and substitute materials and resources when necessary is an important aspect of human reasoning and activity. In particular, substitution plays a vital role in resource consuming and artifact producing activities – purposeful, goal directed procedures that transform resources from raw materials into finished products, the descriptions of which we refer to here as recipes. To see this, consider how adaptable humans are when we encounter constraints, such as limited resources, when making, manufacturing and constructing. In spite of this there has been comparatively little work given to developing representations for substitution within such contexts in a formal reasoning framework. We address this gap by proposing a graphical formalisation that captures consumables and the actions on them in the form of labelled bipartite graphs. Using examples such as “do it yourself" (DIY) instructions, manufacturing processes and cooking recipes to illustrate, we then propose formal definitions for comparing recipes, for composing recipes from subrecipes, and for deconstructing recipes into subrecipes. We then introduce and compare two formal definitions for substitution which are required when there are missing consumables, or some actions are not possible, or because there is some need to change the final product. We illustrate how automated reasoning about recipes in this context may be achieved by implementing our definitions in answer set programming (ASP).