A cognitive exploration of the “non-visual” nature of geometric proofs

Why are Geometric Proofs (Usually) “Non-Visual”? We asked this question as a way to explore the similarities and differences between diagrams and text (visual thinking versus language thinking). Traditional text-based proofs are considered (by many to be) more rigorous than diagrams alone. In this paper we focus on human perceptual-cognitive characteristics that may encourage textual modes for proofs because of the ergonomic affordances of text relative to diagrams. We suggest that visual-spatial perception of physical objects, where an object is perceived with greater acuity through foveal vision rather than peripheral vision, is similar to attention navigating a conceptual visual-spatial structure. We suggest that attention has foveal-like and peripheral-like characteristics and that textual modes appeal to what we refer to here as foveal-focal attention, an extension of prior work in focused attention

Mechanised Uniform Interpolation for Modal Logics K, GL, and iSL

The uniform interpolation property in a given logic can be understood as the definability of propositional quantifiers. We mechanise the computation of these quantifiers and prove correctness in the Coq proof assistant for three modal logics, namely: (1) the modal logic K, for which a pen-and-paper proof exists; (2) Gödel-Löb logic GL, for which our formalisation clarifies an important point in an existing, but incomplete, sequent-style proof; and (3) intuitionistic strong Löb logic iSL, for which this is the first proof-theoretic construction of uniform interpolants. Our work also yields verified programs that allow one to compute the propositional quantifiers on any formula in this logic

Mechanised Uniform Interpolation for Modal Logics K, GL, and iSL

The uniform interpolation property in a given logic can be understood as the definability of propositional quantifiers. We mechanise the computation of these quantifiers and prove correctness in the Coq proof assistant for three modal logics, namely: (1) the modal logic K, for which a pen-and-paper proof exists; (2) Gödel-Löb logic GL, for which our formalisation clarifies an important point in an existing, but incomplete, sequent-style proof; and (3) intuitionistic strong Löb logic iSL, for which this is the first proof-theoretic construction of uniform interpolants. Our work also yields verified programs that allow one to compute the propositional quantifiers on any formula in this logic

The discourse in early digital type design technologies

This thesis is concerned with the development of digital type design technologies and the discourse around them through new environments during a period of radical change and transition in the type manufacturing industry. It maps the emergence of a new field by exploring environments of discourse such as trade associations, academic institutions and the publication landscape, established as a response to new communities and identifies them as catalysts of change. The research considers different numerical models of letterform description devised through academic research, corporate research and commercial endeavours during a phase of type manufacturing that spans from the zenith of phototype setting to the introduction of office-based laserprinting, covering most of the 1970s and 1980s. A particular event, identified as a highpoint in this discourse and as a main catalyst of change, is the Association Typographique Internationale’s working seminar hosted at Stanford University in the summer of 1983. It marks a focus point in these discussions during a period of several linear and concurrent developments, and it reflects issues that maintained their relevance after the introduction of the digital PostScript format, which followed the period surveyed in this thesis. Although more than a dozen digital type design systems were developed by 1983, this study is particularly concerned with five systems considered for presentation at the Stanford working seminar. While some of these systems found no particular use, others had some commercial success or even became well established among an international list of type manufacturers. All five encapsulate the relevant issues discussed at Stanford; from a research standpoint they are equally significant in providing information on the challenges type designers faced at the time. As this research investigates a relatively short and recent period, it is characterised by a lack of certain archival material. In addition to a handful of academic archives, this thesis heavily draws on primary source material, on records and artefacts from personal collections, on oral history as a method to record the voices of contemporary witnesses, and uses these sources as an opportunity to discover hidden figures that have been overlooked in the past. This thesis explores debated issues such as maintaining standards, while introducing new ones; shared responsibilities, collaborations as well as conflicts between designers and engineers; challenges and opportunities for established manufacturers versus an emerging generation of independent designers; as well as implications that new technologies had on the essentials of designing and digitizing type, from learning new terminology to measuring quality, dealing with compatibility and the introduction of automated and parametric design

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

CLiFF Notes: Research in the Language Information and Computation Laboratory of The University of Pennsylvania

This report takes its name from the Computational Linguistics Feedback Forum (CLIFF), an informal discussion group for students and faculty. However the scope of the research covered in this report is broader than the title might suggest; this is the yearly report of the LINC Lab, the Language, Information and Computation Laboratory of the University of Pennsylvania. It may at first be hard to see the threads that bind together the work presented here, work by faculty, graduate students and postdocs in the Computer Science, Psychology, and Linguistics Departments, and the Institute for Research in Cognitive Science. It includes prototypical Natural Language fields such as: Combinatorial Categorial Grammars, Tree Adjoining Grammars, syntactic parsing and the syntax-semantics interface; but it extends to statistical methods, plan inference, instruction understanding, intonation, causal reasoning, free word order languages, geometric reasoning, medical informatics, connectionism, and language acquisition. With 48 individual contributors and six projects represented, this is the largest LINC Lab collection to date, and the most diverse