相关论文: Mathematical Foundations of Consciousness

In their paper 'Falsification and Consciousness' [1], Kleiner and Hoel introduced a formal mathematical model of the process of generating observable data from experiments and using that data to generate inferences and predictions onto an…

Axiomatic set theory is almost universally accepted as the basic theory which provides the foundations of mathematics, and in which the whole of present day mathematics can be developed. As such, it is the most natural framework for…

We formulate five basic tenets of enactivist cognitive science that we have carefully identified in the relevant literature as the main underlying principles of that philosophy. We then develop a mathematical framework to talk about…

Frege's Grundgesetze was one of the 19th century forerunners to contemporary set theory which was plagued by the Russell paradox. In recent years, it has been shown that subsystems of the Grundgesetze formed by restricting the comprehension…

To make accurate inferences in an interactive setting, an agent must not confuse passive observation of events with having intervened to cause them. The $do$ operator formalises interventions so that we may reason about their effect. Yet…

Although Zermelo-Fraenkel set theory (ZFC) is generally accepted as the appropriate foundation for modern mathematics, proof theorists have known for decades that virtually all mainstream mathematics can actually be formalized in much…

The Machine Consciousness Hypothesis states that consciousness is a substrate-free functional property of computational systems capable of second-order perception. I propose a research program to investigate this idea in silico by studying…

Computational modeling is a critical tool for understanding consciousness, but is it enough on its own? This paper discusses the necessity for an ontological basis of consciousness, and introduces a formal framework for grounding…

We describe a new cognitive ability, i.e., functional conceptual substratum, used implicitly in the generation of several mathematical proofs and definitions. Furthermore, we present an initial (first-order) formalization of this mechanism…

This monograph presents a modular cognitive architecture for artificial intelligence grounded in the formal modeling of belief as structured semantic state. Belief states are defined as dynamic ensembles of linguistic expressions embedded…

A special final coalgebra theorem, in the style of Aczel's, is proved within standard Zermelo-Fraenkel set theory. Aczel's Anti-Foundation Axiom is replaced by a variant definition of function that admits non-well-founded constructions.…

Well-founded fixed points have been used in several areas of knowledge representation and reasoning and to give semantics to logic programs involving negation. They are an important ingredient of approximation fixed point theory. We study…

This paper exposes a contradiction in the Zermelo-Fraenkel set theory with the axiom of choice (ZFC). While Godel's incompleteness theorems state that a consistent system cannot prove its consistency, they do not eliminate proofs using a…

According to Cantor, a set is a collection into a whole of defined and separate (we shall say distinct) objects. So, a natural question is ``How to treat as `sets' collections of indistinguishable objects?". This is the aim of quasi-set…

In this paper, we discuss different models for human logic systems and describe a game with nature. Godel`s incompleteness theorem is taken into account to construct a model of logical networks based on axioms obtained by symmetry breaking.…

We examine the hypothesis that consciousness can be understood as a state of matter, "perceptronium", with distinctive information processing abilities. We explore five basic principles that may distinguish conscious matter from other…

The multifaceted nature of subjective experience poses a challenge to the study of consciousness. Traditional neuroscientific approaches often concentrate on isolated facets, such as perceptual awareness or the global state of consciousness…

We present a system of axioms motivated by a topological intuition: The set of subsets of any set is a topology on that set. On the one hand, this system is a common weakening of Zermelo-Fraenkel set theory ZF, the positive set theory GPK…

We propose an axiomatic foundation of mathematics based on the finite sequence as the foundational concept, rather than based on logic and set, as in set theory, or based on type as in dependent type theories. Finite sequences lead to a…

A logic for specification and verification is derived from the axioms of Zermelo-Fraenkel set theory. The proofs are performed using the proof assistant Isabelle. Isabelle is generic, supporting several different logics. Isabelle has the…