Using Diagrammatic Reasoning for Theorem Proving in a Continuous Domain

Centre for Intelligent Systems and their ApplicationsThis project looks at using diagrammatic reasoning to prove mathematical theorems. The work is motivated by a need for theorem provers whose reasoning is readily intelligible to human beings. It should also have practical applications in mathematics teaching. We focus on the continuous domain of analysis - a geometric subject, but one which is taught using a dry algebraic formalism which many students find hard. The geometric nature of the domain makes it suitable for a diagram-based approach. However it is a difficult domain, and there are several problems, including handling alternating quantifiers, sequences and generalisation. We developed representations and reasoning methods to solve these. Our diagram logic isn't complete, but does cover a reasonable range of theorems. It utilises computers to extend diagrammatic reasoning in new directions – including using animation. This work is tested for soundness, and evaluated empirically for ease of use. We demonstrate that computerised diagrammatic theorem proving is not only possible in the domain of real analysis, but that students perform better using it than with an equivalent algebraic computer system

Digitalisation of the Individual: A Systematic Review from an Affordances-Use-Outcomes Perspective

Digital technology affords individuals to transform several aspects of their everyday lives, leading to different usage patterns with positive and negative outcomes for individuals. While digitalisation is discussed in detail from an organizational perspective, a comprehensive review on outcomes of digitalisation from an individual perspective is currently missing. Therefore, this paper aims to summarize and classify outcomes in lives of individuals that are caused by digitalisation. A structured literature review is conducted. The search string includes the digital individual itself and the digital individual as social being. We discuss the findings of 23 papers on the digitalisation of the individual and present the results in a concept matrix. We identify five types of affordances and differentiate four types of technology use. 25 positive and 31 negative outcomes were reported by existing literature. We contribute a more nuanced understanding of affordances, usage patterns and their outcomes which hold valuable insights for both research and practice

Proof General / Eclipse: A generic interface for interactive proof

Abstract. This paper introduces PG/Eclipse; a sophisticated new interface for interactive theorem provers, offering users a rich set of proof development tools. It is based upon two complementary frameworks. The first is PG/Kit, a generic communication framework for connecting theorem provers and interfaces. PG/Kit should allow straightforward adaptation to most interactive theorem provers. Moreover, by separating interface development from proof engine development, this framework should facilitate the development of both. The second is Eclipse, a sophisticated open source framework for building IDEs. Eclipse is highly modular and extensible, making it a good platform for interface research. Using it has allowed us to provide a rich range of interface features. These frameworks correspond to the twin goals of this project: to define a clear separation between provers and interfaces, and to translate programming development tools to a theorem proving environment

The importance of applying computational creativity to scientific and mathematical domains

Science and mathematics are currently underrepresented in the computational creativity (CC) community. We discuss why the CC community should apply their work to mathematical and scientific domains, and argue that this would be mutually beneficial for the domains in question. We identify a key challenge in Automated Reasoning – that it has not achieved widespread adoption by mathematicians; and one in Automated Scientific Discovery – the need for communicability of automatically generated scientific knowledge. We recommend that CC researchers help to address these two challenges by: (i) applying systems based on cognitive mechanisms to scientific and mathematical domains; (ii) employing experience in building and evaluating interactive systems to this context; and (iii) using expertise in automatically producing framing functionality to enhance the communicability of automatically generated scientific knowledge.EPSRC funded project EP/P017320/1 "Example-driven machine-human collaboration in mathematics

Reconstitution and functional characterization of ion channels from nanodiscs in lipid bilayers

Recent studies have shown that membrane proteins can be efficiently synthesized in vitro before spontaneously inserting into soluble nanoscale lipid bilayers called nanodiscs (NDs). In this paper, we present experimental details that allow a combination of in vitro translation of ion channels into commercially available NDs followed by their direct reconstitution from these nanobilayers into standard bilayer setups for electrophysiological characterization. We present data showing that two model K+ channels, Kcv and KcsA, as well as a recently discovered dual-topology F− channel, Fluc, can be reliably reconstituted from different types of NDs into bilayers without contamination from the in vitro translation cocktail. The functional properties of Kcv and KcsA were characterized electrophysiologically and exhibited sensitivity to the lipid composition of the target DPhPC bilayer, suggesting that the channel proteins were fully exposed to the target membrane and were no longer surrounded by the lipid/protein scaffold. The single-channel properties of the three tested channels are compatible with studies from recordings of the same proteins in other expression systems. Altogether, the data show that synthesis of ion channels into NDs and their subsequent reconstitution into conventional bilayers provide a fast and reliable method for functional analysis of ion channels