To adequately model mathematical arguments the analyst must be able to represent the mathematical objects under discussion and the relationships between them, as well as inferences drawn about these objects and relationships as the discourse unfolds. We introduce a framework with these properties, which has been used to analyse mathematical dialogues and expository texts. The framework can recover salient elements of discourse at, and within, the sentence level, as well as the way mathematical content connects to form larger argumentative structures. We show how the framework might be used to support computational reasoning, and argue that it provides a more natural way to examine the process of proving theorems than do Lamport's structured proofs.

Building on a survey of previous theories of serendipity and creativity, we advance a sequential model of serendipitous occurrences. We distinguish between serendipity as a service and serendipity in the system itself, clarify the role of invention and discovery, and provide a measure for the serendipity potential of a system. While a system can arguably not be guaranteed to be serendipitous, it can have a high potential for serendipity. Practitioners can use these theoretical tools to evaluate a computational system's potential for unexpected behaviour that may have a beneficial outcome. In addition to a qualitative features of serendipity potential, the model also includes quantitative ratings that can guide development work. We show how the model is used in three case studies of existing and hypothetical systems, in the context of evolutionary computing, automated programming, and (next-generation) recommender systems. From this analysis, we extract recommendations for practitioners working with computational serendipity, and outline future directions for research.

We sketch the process of creating a novel video game by blending two video games specified in the Video Game Description Language (VGDL), following the COINVENT computational model of conceptual blending. We highlight the choices that need to be made in this process, and discuss the prospects for a computational game designer based on blending.