{"title":"Functorial semiotics for creativity","authors":"G. Mazzola","doi":"10.1080/17459737.2019.1675193","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2020-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematics and Music","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/17459737.2019.1675193","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 1
Abstract
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.
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.
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