We argue that there are mutually beneficial connections to be made between ideas in argumentation theory and the philosophy of mathematics, and that these connections can be suggested via the process of producing computational models of theories in these domains. We discuss Lakatos’s work (Proofs and Refutations, 1976) in which he championed the informal nature of mathematics, and our computational representation of his theory. In particular, we outline our representation of Cauchy’s proof of Euler’s conjecture, in which we use work (...) by Haggith on argumentation structures, and identify connections between these structures and Lakatos’s methods. (shrink)

We describe recent developments in research on mathematical practice and cognition and outline the nine contributions in this special issue of topiCS. We divide these contributions into those that address (a) mathematical reasoning: patterns, levels, and evaluation; (b) mathematical concepts: evolution and meaning; and (c) the number concept: representation and processing.

Computational Creativity, Concept Invention, and General Intelligence in their own right all are flourishing research disciplines producing surprising and captivating results that continuously influence and change our view on where the limits of intelligent machines lie, each day pushing the boundaries a bit further. By 2014, all three fields also have left their marks on everyday life – machine-composed music has been performed in concert halls, automated theorem provers are accepted tools in enterprises’ R&D departments, and cognitive architectures are being (...) integrated in pilot assistance systems for next generation airplanes. Still, although the corresponding aims and goals are clearly similar (as are the common methods and approaches), the developments in each of these areas have happened mostly individually within the respective community and without closer relationships to the goings-on in the other two disciplines. In order to overcome this gap and to provide a common platform for interaction and exchange between the different directions, the International Workshops on “Computational Creativity, Concept Invention, and General Intelligence” (C3GI) have been started. At ECAI-2012 and IJCAI-2013, the first and second edition of C3GI each gathered researchers from all three fields, presenting recent developments and results from their research and in dialogue and joint debates bridging the disciplinary boundaries. The chapters contained in this book are based on expanded versions of accepted contributions to the workshops and additional selected contributions by renowned researchers in the relevant fields. Individually, they give an account of the state-of-the-art in their respective area, discussing both, theoretical approaches as well as implemented systems. When taken together and looked at from an integrative perspective, the book in its totality offers a starting point for a (re)integration of Computational Creativity, Concept Invention, and General Intelligence, making visible common lines of work and theoretical underpinnings, and pointing at chances and opportunities arising from the interplay of the three fields. (shrink)

We describe how Intuitionistic Linear Logic can be used to provide a unified logical account for agents to find and execute plans. This account supports the modelling of agent interaction, including dialogue; allows agents to be robust to unexpected events and failures; and supports significant reuse of agent specifications. The framework has been implemented and several case studies have been considered. Further applications include human–computer interfaces as well as agent interaction in the semantic web.

The target article by Cohen Kadosh & Walsh (CK&W) raises questions as to the precise nature of the notion of abstractness that is intended. We note that there are various uses of the term, and also more generally in mathematics, and suggest that abstractness is not an all-or-nothing property as the authors suggest. An alternative possibility raised by the analysis of numerical representation into automatic and intentional codes is suggested.