Going Beyond the Data as the Patching (Sheaving) of Local Knowledge

On the Design of Social Robots Using Sheaf Theory and Smart Contracts

The incorporation of robots in the social fabric of our society has taken giant leaps, enabled by advances in artificial intelligence and big data. As these robots become increasingly adept at parsing through enormous datasets and making decisions where humans fall short, a significant challenge lies in the analysis of robot behavior. Capturing interactions between robots, humans and IoT devices in traditional structures such as graphs poses challenges in the storage and analysis of large data sets in dense graphs generated by frequent activities. This paper proposes a framework that uses the blockchain for the storage of robotic interactions, and the use of sheaf theory for analysis of these interactions. Applications of our framework for social robots and swarm robots incorporating imperfect information and irrationality on the blockchain sheaf are proposed. This work shows the application of such a framework for various blockchain applications on the spectrum of human-robot interaction, and identifies key challenges that arise as a result of using the blockchain for robotic applications.

Sheaving-a universal construction for semantic compositionality

Semantic compositionality—the way that meanings of complex entities obtain from meanings of constituent entities and their structural relations—is supposed to explain certain concomitant cognitive capacities, such as systematicity. Yet, cognitive scientists are divided on mechanisms for compositionality: e.g. a language of thought on one side versus a geometry of thought on the other. Category theory is a field of (meta)mathematics invented to bridge formal divides. We focus on sheaving—a construction at the nexus of algebra and geometry/topology, alluding to an integrative view, to sketch out a category theory perspective on the semantics of compositionality. Sheaving is a universal construction for making inferences from local knowledge, where meaning is grounded by the underlying topological space. Three examples illustrate how topology conveys meaning, in terms of the inclusion relations between the open sets that constitute the space, though the topology is not regarded as the only source of semantic information. In this sense, category (sheaf) theory provides a general framework for semantic compositionality.

This article is part of the theme issue ‘Towards mechanistic models of meaning composition’.