Related papers: Visual thinking and simplicity in proof
Space time cube representation is an information visualization technique where spatiotemporal data points are mapped into a cube. Fast and correct analysis of such information is important in for instance geospatial and social visualization…
We try to bring to light some combinatorial structure underlying formal proofs in logic. We do this through the study of the Craig Interpolation Theorem which is properly a statement about the structure of formal derivations. We show that…
The visualization of argumentation frameworks (AFs) is crucial for enabling a wide applicability of argumentative tools. However, their visualization is often considered only as an accompanying part of tools for computing semantics and…
The paper analizes a set of issues related to analogy and analogical reasoning, namely: 1) The problem of analogy and its duplicity; 2) The role of analogy in demonstrative reasoning; 3) The role of analogy in non-demonstrative reasoning;…
We establish new and different kinds of proofs of properties that arise due to the orthogonal decomposition of the Hilbert space, including projections, over the unit interval of one dimension. We also see angles between functions,…
Uncertainty visualizations often emphasize point estimates to support magnitude estimates or decisions through visual comparison. However, when design choices emphasize means, users may overlook uncertainty information and misinterpret…
This paper explores and proves the one-seventh area triangle using a purely algebraic approach as opposed to a geometric one. A triangle set purely in the complex plane is used so that we can utilise features of the complex number system to…
Diagrammatic, analogical or iconic representations are often contrasted with linguistic or logical representations, in which the shape of the symbols is arbitrary. The aim of this paper is to make a case for the usefulness of diagrams in…
Scene viewing is used to study attentional selection in complex but still controlled environments. One of the main observations on eye movements during scene viewing is the inhomogeneous distribution of fixation locations: While some parts…
In traditional justification logic, evidence terms have the syntactic form of polynomials, but they are not equipped with the corresponding algebraic structure. We present a novel semantic approach to justification logic that models…
The impressive results of modern neural networks partly come from their non linear behaviour. Unfortunately, this property makes it very difficult to apply formal verification tools, even if we restrict ourselves to networks with a…
Pre-college mathematics modeling instruction often frames mathematics as being separated from reasoning about the real world -- and commonly treats reasoning mathematically and reasoning about the real-world context as separate stages of a…
This paper investigates how global decision problems over arithmetically represented domains acquire reflective structure through class-quantification. Arithmetization forces diagonal fixed points whose verification requires reflection…
Images usually convey richer detail than text, but often include redundant information, which potentially downgrades multimodal reasoning performance. When faced with lengthy or complex messages, humans tend to employ abstract thinking to…
When presented with questions involving visual thinking, humans naturally switch reasoning modalities, often forming mental images or drawing visual aids. Large language models have shown promising results in arithmetic and symbolic…
The importance of an element in a visual stimulus is commonly associated with the fixations during a free-viewing task. We argue that fixations are not always correlated with attention or awareness of visual objects. We suggest to filter…
Current multimodal large language models (MLLMs) still face significant challenges in complex visual tasks (e.g., spatial understanding, fine-grained perception). Prior methods have tried to incorporate visual reasoning, however, they fail…
Visual modes of communication are ubiquitous in modern life --- from maps to data plots to political cartoons. Here we investigate drawing, the most basic form of visual communication. Participants were paired in an online environment to…
Learning robust representations that allow to reliably establish relations between images is of paramount importance for virtually all of computer vision. Annotating the quadratic number of pairwise relations between training images is…
Linear probes and sparse autoencoders consistently recover meaningful structure from transformer representations -- yet why should such simple methods succeed in deep, nonlinear systems? We show this is not merely an empirical regularity…