Related papers: Ludics without Designs I: Triads
Constructions and exploration of plane algebraic curves has received a new push with the development of automated methods, whose algorithms are continuously improved and implemented in various software packages. We use them to explore the…
This paper examines the role that enchantment plays in the design of AI things by constructing a taxonomy of design approaches that increase or decrease the perception of magic and enchantment. We start from the design discourse surrounding…
Lens design uses a calculation of the lens' surfaces that permit to obtain an image from a given object. A set of general rules and laws permits to calculate the essential points of the optical system such as distances, thickness, pupils,…
We present a complete system of inequalities for the inradius, circumradius, and diameter in the $3$-dimensional Euclidean space. To do so, we prove quasiconcavity of the inradius evaluated over $n$-simplices with a common facet…
We suggest a method of solving the problem of existence of a triangle with prescribed two bisectors and one third element which can be taken as one of the angles, the sides, the heights or the medians, or the third bisector.
In this paper, we introduce Linear Logic with a nondeterministic facility, which has a self-dual additive connective. In the system the proof net technology is available in a natural way. The important point is that nondeterminism in the…
Universal Design (UD), an approach to accessibility that was first conceptualized in architecture to make buildings physically accessible, has since been applied to curriculum design to make classrooms accessible for a larger range of…
A relatively common sight in graphic designs is a planar arrangement of three gears in contact. However, since neighboring gears must rotate in opposite directions, none of the gears can move. We give a non-planar, and non-frozen,…
Every sport needs rules. Tournament design refers to the rules that determine how a tournament, a series of games between a number of competitors, is organized. This study aims to provide an overview of the tournament design literature from…
Gamification has been widely employed in the educational domain over the past eight years when the term became a trend. However, the literature states that gamification still lacks formal definitions to support the design and analysis of…
We introduce ologisms. They generate from ologs by extending their logical expressivity, from the possibility of considering constraints of equational nature only to the possibility of considering constraints of syllogistic nature, in…
In this paper, we consider a game beginning with a multiset of elements from a group. On a move, two elements are replaced by their sum. This is a no strategy game, and can be modeled as a graded poset with the rank of a node equal to the…
Can artificial intelligence discover, from raw experience and without human supervision, concepts that humans have discovered? One challenge is that human concepts themselves are fluid: conceptual boundaries can shift, split, and merge as…
This paper shows the initial stages of development, from first principles, of a formal logic to characterise and then explore issues in a broadly defined idea of Veracity, which includes properties of demonstrability, truth, trust and…
We introduce an inductive logic programming approach that combines classical divide-and-conquer search with modern constraint-driven search. Our anytime approach can learn optimal, recursive, and large programs and supports predicate…
The aim of this short lecture series is to expose the students to the beautiful theory of lattices by, on one hand, demonstrating various basic ideas that appear in this theory and, on the other hand, formulating some of the celebrated…
In this note, we provide a generalization for the definition of a trisection of a 4-manifold with boundary. We demonstrate the utility of this more general definition by finding a trisection diagram for the Cacime Surface, and also by…
In this paper we introduce distinct approaches to loop braid groups, a generalisation of braid groups, and unify all the definitions that have appeared so far in literature, with a complete proof of the equivalence of these definitions.…
This paper presents a type theory in which it is possible to directly manipulate $n$-dimensional cubes (points, lines, squares, cubes, etc.) based on an interpretation of dependent type theory in a cubical set model. This enables new ways…
This paper provides an introduction to Kundt spaces, clarifying several important properties, many of which are typically scattered across the mathematical literature or presented without explicit reference to Kundt terminology. While not…