Related papers: Ludics without Designs I: Triads
In this paper, we use braiding diagrams to present rules of shapes and designs. That is, we design colour, design size, design brightness, design codes by means of braiding.
We show upper and lower bounds for angles in iterations of trisections of certain triangulations.
Conceptors provide an elementary neuro-computational mechanism which sheds a fresh and unifying light on a diversity of cognitive phenomena. A number of demanding learning and processing tasks can be solved with unprecedented ease,…
We introduce the concept of protometric and present some properties of protometrics.
We develop a theory of modulus triples, for future motivic applications.
By investigating a recurrence relation about functions, we first give alternative proofs of various identities on Fibonacci numbers and Lucas numbers, and then, make certain well known identities visible via certain trivalent graph…
The article proposes a new technique for proving the undefinability of logical connectives through each other and illustrates the technique with several examples. Some of the obtained results are new proofs of the existing theorems, others…
The aim of this paper is to introduce a logic in which nouns and verbs are handled together as a deductive reasoning, and also to observe the relationship between nouns and verbs as well as between logics and conversations.
In this paper, we introduce round and sleek topological spaces and study their properties.
This is a brief introduction to the basic concepts of topology. It includes the basic constructions, discusses separation properties, metric and pseudometric spaces, and gives some applications arising from the use of topology in computing.
A new methodological approach for the study of topology for shapes made of arrangements of lines, planes or solids is presented. Topologies for shapes are traditionally built on the classical theory of point-sets. In this paper, topologies…
We offer an axiomatic presentation of three-dimensional projective space that adopts the line as its fundamental element and renders automatic the principle of duality.
As an attempt to uncover the topological nature of composition of strategies in game semantics, we present a ``topological'' game for Multiplicative Additive Linear Logic without propositional variables, including cut moves. We recast the…
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…
The rationalizability concept was introduced in \cite{Ber84} and \cite{Pea84} to assess what can be inferred by rational players in a non-cooperative game in the presence of common knowledge. However, this notion can be defined in a number…
This paper introduces and outlines a new integrative field, Ideometrics. It is the systematic science of generating, evaluating, and prioritising ideas, based on the proposed sense of ideas and assigning value to information by the brain.…
In this paper, we propose to connect Prawitz's theory of grounds with Girard's Ludics. This connection is carried out on two levels. On a more philosophical one, we highlight some differences between Prawitz's and Girard's approaches, but…
Magic squares are well-known arrangements of integers with common row, column, and diagonal sums. Various other magic shapes have been proposed, but triangles have been somewhat overlooked. We introduce certain triangular arrangements of…
We invent the notion of a derived and fluid variety. Fluid variety has no proper derived variety as its subvariety. We examine some properties of fluid and derived varieties. Examples of such varieties of bands are presented.
This paper surveys, in the first place, some basic facts from the classification theory of normal complex singularities, including details for the low dimensions 2 and 3. Next, it describes how the toric singularities are located within the…