相关论文: Mathematical Foundations of Consciousness

Bridging continuous perceptual signals and discrete symbolic reasoning is a fundamental challenge in AI systems that must operate under uncertainty. We present a neuro-symbolic framework that explicitly models and propagates uncertainty…

We introduce a general theory of functions called Flow. We prove ZF, non-well founded ZF and ZFC can be immersed within Flow as a natural consequence from our framework. The existence of strongly inaccessible cardinals is entailed from our…

General intelligence must reorganize experience into internal structures that enable prediction and action under finite resources. Existing systems implicitly presuppose fixed primitive units -- tokens, subwords, pixels, or predefined…

The aim of this paper is twofold: (1) to assess whether the construct of neural representations plays an explanatory role under the variational free-energy principle and its corollary process theory, active inference; and (2) if so, to…

Reasoning is fundamental to human intelligence, and critical for problem-solving, decision-making, and critical thinking. Reasoning refers to drawing new conclusions based on existing knowledge, which can support various applications like…

Recently Feferman (Rev. Symb. Logic 6: 6-15, 2013) has outlined a program for the development of a foundation for naive category theory. While Ernst (ibid. 8: 306-327, 2015) has shown that the resulting axiomatic system is still…

A theory of recursive definitions has been mechanized in Isabelle's Zermelo-Fraenkel (ZF) set theory. The objective is to support the formalization of particular recursive definitions for use in verification, semantics proofs and other…

We present a definition of cause and effect in terms of decision-theoretic primitives and thereby provide a principled foundation for causal reasoning. Our definition departs from the traditional view of causation in that causal assertions…

We study a new proof principle in the context of constructive Zermelo-Fraenkel set theory based on what we will call "non-deterministic inductive definitions". We give applications to formal topology as well as a predicative justification…

In this paper I propose the idea to establish a clear distinction between the foundations of truth and the foundations of meaning in Mathematics. I explore on the most basic example, the mathematical line, the possibility that the…

Humans understand the world through the integration of multiple sensory modalities, enabling them to perceive, reason about, and imagine dynamic physical processes. Inspired by this capability, multimodal foundation models (MFMs) have…

In our understanding, a mind-map is an adaptive engine that basically works incrementally on the fundament of existing transactional streams. Generally, mind-maps consist of symbolic cells that are connected with each other and that become…

This is a proof of the strong AI hypothesis, i.e. that machines can be conscious. It is a phenomenological proof that pattern-recognition and subjective consciousness are the same activity in different terms. Therefore, it proves that…

Control was from its very beginning an important concept in cybernetics. Later on, with the works of W. Ross Ashby, for example, biological concepts such as adaptation were interpreted in the light of cybernetic systems theory. Adaptation…

Recent advances in theoretical biology suggest that basal cognition and sentient behaviour are emergent properties of in vitro cell cultures and neuronal networks, respectively. Such neuronal networks spontaneously learn structured…

A cognitive architecture aimed at cumulative learning must provide the necessary information and control structures to allow agents to learn incrementally and autonomously from their experience. This involves managing an agent's goals as…

Mathematicians and philosophers have appealed to categoricity arguments in a surprisingly varied range of contexts. One familiar example calls on second-order categoricity in an attempt to show that the Continuum Hypothesis, despite its…

This contribution examines two radically different explanations of our phenomenal intuitions, one reductive and one strongly non-reductive, and identifies two germane ideas that could benefit many other theories of consciousness. Firstly,…

This paper introduces function alignment, a novel theory of mind and intelligence that is both intuitively compelling and structurally grounded. It explicitly models how meaning, interpretation, and analogy emerge from interactions among…

We develop a modal logic to capture partial awareness. The logic has three building blocks: objects, properties, and concepts. Properties are unary predicates on objects; concepts are Boolean combinations of properties. We take an agent to…