Related papers: Formal Ways for Measuring Relations between Concep…
On the basis of the general character and operation of the process of perception, a formalism is sought to mathematically describe the subjective or abstract/mental process of perception. It is shown that the formalism of orthodox quantum…
Symmetries and isomorphisms play similar conceptual roles when we consider how models represent physical situations, but they are formally distinct, as two models related by symmetries are not typically isomorphic. I offer a rigorous…
Despite the remarkable success of large large-scale neural networks, we still lack unified notation for thinking about and describing their representational spaces. We lack methods to reliably describe how their representations are…
Conceptualization, a fundamental element of human cognition, plays a pivotal role in human generalizable reasoning. Generally speaking, it refers to the process of sequentially abstracting specific instances into higher-level concepts and…
Connectedness, path connectedness, and uniform connectedness are well-known concepts. In the traditional presentation of these concepts there is a substantial difference between connectedness and the other two notions, namely connectedness…
A rigorous mathematical theory of dimensional analysis, systematically accounting for the use of physical quantities in science and engineering, perhaps surprisingly, was not developed until relatively recently. We claim that this has…
We develop a general formalism for representing and understanding structure in complex systems. In our view, structure is the totality of relationships among a system's components, and these relationships can be quantified using information…
We show that the dimension of the geometric shape formed by the phenomenologically valid points inside a multi-dimensional parameter space can be used to characterise different new physics models and to define a quantitative measure for the…
The concept of synthetic dimensions has emerged as a powerful framework in photonics and atomic physics, enabling the exploration of high-dimensional physics beyond conventional spatial constraints. Originally developed for quantum…
The last decade has seen huge progress in the development of advanced machine learning models; however, those models are powerless unless human users can interpret them. Here we show how the mind's construction of concepts and meaning can…
Rational agents acting as observers use ``knowables'' to construct a vision of the outside world. Thereby, they are bound by the information exchanged with what they consider to be objects. The cartesian cut or, in modern terminology, the…
We propose a deep semantic characterization of space and motion categorically from the viewpoint of grounding embodied human-object interactions. Our key focus is on an ontological model that would be adept to formalisation from the…
A generalization of metric space is presented which is shown to admit a theory strongly related to that of ordinary metric spaces. To avoid the topological effects related to dropping any of the axioms of metric space, first a new, and…
We investigate the space efficiency of a Propositional Knowledge Representation (PKR) formalism. Intuitively, the space efficiency of a formalism F in representing a certain piece of knowledge A, is the size of the shortest formula of F…
Spatial relationships between objects represent key scene information for humans to understand and interact with the world. To study the capability of current computer vision systems to recognize physically grounded spatial relations, we…
How does scientific knowledge grow? This question has occupied a central place in the philosophy of science, stimulating heated debates, but yielding no clear consensus. Many explanations can be understood in terms of whether and how they…
Ontologies enable knowledge sharing and interdisciplinary collaboration by providing standardized, structured vocabularies for diverse communities. While logical axioms are a cornerstone of ontology design, natural language elements such as…
Automated decision making is often complicated by the complexity of the knowledge involved. Much of this complexity arises from the context sensitive variations of the underlying phenomena. We propose a framework for representing…
Large scale neural models show impressive performance across a wide array of linguistic tasks. Despite this they remain, largely, black-boxes - inducing vector-representations of their input that prove difficult to interpret. This limits…
We introduce a new form of logical relation which, in the spirit of metric relations, allows us to assign each pair of programs a quantity measuring their distance, rather than a boolean value standing for their being equivalent. The…