arXiv cs.AI· Simon Hegelich, Bardh Prenkaj, Habiba Sarhan, Morteza Shahrezaye, Kolja Hegelich, Erik Cambria, Christian Montag·· 12 小时前AI 评分18
Co-Recursive Semantic Self-Extension：开放-ended 智能的数学基础
Co-Recursive Semantic Self-Extension: A Mathematical Foundation for Open-Ended Intelligence
AI 导读
研究者提出“语义自我扩展”设计原则，主张智能不应只在既有语义内消解歧义，而要把未解决结构转化为新的意义空间。借助 Kolmogorov 复杂度，作者证明任何具有固定状态描述、转移机制和初始条件的架构都无法生成包含不可约算法信息的历史，有限智能体耦合也无法突破该界限。扩展需依赖保存语义内容与历史坐标的持久外部记忆，集体生成能力取决于迁移所需重叠与生成所需差异之间的平衡。
正文 · 原文
Abstract:Artificial intelligence has advanced through scale, data, and computation, yet remains bounded by its representational framework. We ask what makes intelligence open-ended. Every inferential system selects meaningful distinctions, limiting what it can learn. Within a fixed purpose, performance reaches a ceiling set by its semantic domain. Teleological succession, in which purposes arise from earlier ones, faces a similar limit: Boolean-closed purpose-transformations exhaust their reachable semantic territory. We shift from purposes to inferential systems. Drawing on Kant and Gödel, we model cognitive states as partial evaluations over a formal language. Unresolved propositions may be undecided or undecidable. Reasoning can resolve the former but not the latter, leaving a frontier for extension. Non-trivial reductions of undecidable propositions expose undecidable intermediate premises whose reflective reification supports multiple decisive extensions. Finite trace-guided generation remains fallible, requiring meta-level selection and polycontextural exploration. Using Kolmogorov complexity, we show that no architecture with a fixed state description, transition mechanism, and initial condition can generate histories incorporating irreducible algorithmic information. Because physical systems are fixed in this sense, we examine collectives. Coupling finitely many finite agents does not remove the bound. Extension requires persistent external memory preserving semantic content and historical coordinates. Collective generative capacity depends on balancing overlap for transfer with difference for generation. We propose semantic self-extension as a design principle: intelligence should not merely resolve ambiguity within existing meanings, but transform unresolved structures into new spaces of meaning, generating new distinctions, questions, representations, and purposes.
| Subjects: | Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2610.31097 [cs.AI] |
| (or arXiv:2610.31097v2 [cs.AI] for this version) | |
| https://doi.org/10.48550/arXiv.2610.31097 arXiv-issued DOI via DataCite |
Submission history
From: Bardh Prenkaj [view email]
[v1]
Thu, 22 Oct 2026 11:12:17 UTC (64 KB)
[v2]
Fri, 23 Oct 2026 09:17:57 UTC (64 KB)
来源：arXiv cs.AI · arxiv.org