创造力的功能符号学

IF 0.5 2区数学 Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematics and Music Pub Date : 2020-01-02 DOI:10.1080/17459737.2019.1675193

G. Mazzola

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引用次数: 1

摘要

在本文中，我们发展了一个数学上的符号学理论。这个项目似乎对未来的计算创造力科学至关重要，因为创造力过程的结果必须为给定的符号学背景添加新的符号。数学框架建立在函子的范畴上，特别是从有向图的路径范畴和Gabriel-Zisman分数演算中推导出的线性化范畴。这种方法中的语义被扩展到由Yoneda引理支持的许多“全局”结构，包括上同调结构。这种方法的结论是对所提出的功能符号学方面的创造力类别进行了简短的讨论。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Functorial semiotics for creativity

In this paper, we develop a mathematically conceived semiotic theory. This project seems essential for a future computational creativity science since the outcome of the process of creativity must add new signs to given semiotic contexts. The mathematical framework is built upon categories of functors, in particular linearized categories deduced from path categories of digraphs and the Gabriel–Zisman calculus of fractions. Semantics in this approach is extended to a number of “global” constructions enabled by the Yoneda Lemma, including cohomological constructions. This approach concludes with a short discussion of classes of creativity with respect to the proposed functorial semiotics.

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来源期刊

Journal of Mathematics and Music 数学-数学跨学科应用

CiteScore

1.90

自引率

18.20%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Mathematics and Music aims to advance the use of mathematical modelling and computation in music theory. The Journal focuses on mathematical approaches to musical structures and processes, including mathematical investigations into music-theoretic or compositional issues as well as mathematically motivated analyses of musical works or performances. In consideration of the deep unsolved ontological and epistemological questions concerning knowledge about music, the Journal is open to a broad array of methodologies and topics, particularly those outside of established research fields such as acoustics, sound engineering, auditory perception, linguistics etc.