相关论文: Mathematical Foundations of Consciousness

The science of consciousness has been successful over the last decades. Yet, it seems that some of the key questions remain unanswered. Perhaps, as a science of consciousness, we cannot move forward using the same theoretical commitments…

We introduce a semantics for epistemic logic exploiting a belief base abstraction. Differently from existing Kripke-style semantics for epistemic logic in which the notions of possible world and epistemic alternative are primitive, in the…

Plato is well-known in mathematics for the eponymous foundational philosophy Platonism based on ideal objects. Plato's allegory of the cave provides a powerful visual illustration of the idea that we only have access to shadows or…

Inspired by Zermelo's quasi-categoricity result characterizing the models of second-order Zermelo-Fraenkel set theory $\text{ZFC}_2$, we investigate when those models are fully categorical, characterized by the addition to $\text{ZFC}_2$…

We develop an axiomatic framework for fractal analysis and fractal number theory grounded in hierarchies of definability. Central to this approach is a sequence of formal systems F_n, each corresponding to a definability level S_n contained…

Accretive and monotone operator theory are central branches of nonlinear functional analysis and constitute the abstract study of set-valued mappings between function spaces. This paper deals with the computational properties of certain…

We propose a simple cognitive model where qualitative and quantitative com- parisons enable animals to identify objects, associate them with their properties held in memory and make naive inference. Simple notions like equivalence re-…

Knowledge graphs and ontologies are becoming increasingly important as technical solutions for Findable, Accessible, Interoperable, and Reusable data and metadata (FAIR Guiding Principles). We discuss four challenges that impede the use of…

In the process of evolution, the brain has achieved such perfection that artificial intelligence systems do not have and which needs its own mathematics. The concept of cognitome, introduced by the academician K.V. Anokhin, as the cognitive…

We propose a new interpretability method for neural networks, which is based on a novel mathematico-philosophical theory of reasons. Our method computes a vector for each neuron, called its reasons vector. We then can compute how strongly…

Graphs are a central representation in biomedical research, capturing molecular interaction networks, gene regulatory circuits, cell--cell communication maps, and knowledge graphs. Despite their importance, currently there is not a broadly…

As a discipline cybernetics has a long and rich history. In its first generation it not only had a worldwide span, in the area of computer modelling, for example, its proponents such as John von Neumann, Stanislaw Ulam, Warren McCulloch and…

The notion of argumentation and the one of belief stand in a problematic relation to one another. On the one hand, argumentation is crucial for belief formation: as the outcome of a process of arguing, an agent might come to (justifiably)…

We further develop the theoretical framework of proof mining, a program in mathematical logic that seeks to quantify and extract computational information from prima facie `non-computational' proofs from the mainstream mathematical…

Humans have the ability to report the contents of their subjective experience - we can say to each other, "I am aware of X". The decision processes that support these reports about mental contents remain poorly understood. In this article I…

There are different meanings of foundation of mathematics: philosophical, logical, and mathematical. Here foundations are considered as a theory that provides means (concepts, structures, methods etc.) for the development of whole…

The notion of equality (identity) is simple and ubiquitous, making it a key case study for broader questions about the representations supporting abstract relational reasoning. Previous work suggested that neural networks were not suitable…

In this paper we propose an interpretation for self-referential propositions in a "meta-model" N* of ZF. This meta-model N* is considered as an informal model of arithmetic that mathematicians often use when working with number theory.…

The study and understanding of human behaviour is relevant to computer science, artificial intelligence, neural computation, cognitive science, philosophy, psychology, and several other areas. Presupposing cognition as basis of behaviour,…

This article focuses on elucidating the concept of consciousness from a relational and post-phenomenological theory of non-human communication agents (ANHC). Specifically, we explore the contributions of Thomas Metzinger s Self Model…