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Quantum Physics and Linguistics最新文献

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An alternative Gospel of structure: order, composition, processes 另一种结构福音:秩序、组成、过程
Quantum Physics and Linguistics Pub Date : 2013-07-15 DOI: 10.1093/acprof:oso/9780199646296.003.0001
B. Coecke
{"title":"An alternative Gospel of structure: order, composition, processes","authors":"B. Coecke","doi":"10.1093/acprof:oso/9780199646296.003.0001","DOIUrl":"https://doi.org/10.1093/acprof:oso/9780199646296.003.0001","url":null,"abstract":"We survey some basic mathematical structures, which arguably are more primitive than the structures taught at school. These structures are orders, with or without composition, and (symmetric) monoidal categories. We list several `real life' incarnations of each of these. This paper also serves as an introduction to these structures and their current and potentially future uses in linguistics, physics and knowledge representation.","PeriodicalId":273067,"journal":{"name":"Quantum Physics and Linguistics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128563183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 18
Types and forgetfulness in categorical linguistics and quantum mechanics 范畴语言学和量子力学中的类型和遗忘
Quantum Physics and Linguistics Pub Date : 2013-03-13 DOI: 10.1093/acprof:oso/9780199646296.003.0008
P. Hines
{"title":"Types and forgetfulness in categorical linguistics and quantum mechanics","authors":"P. Hines","doi":"10.1093/acprof:oso/9780199646296.003.0008","DOIUrl":"https://doi.org/10.1093/acprof:oso/9780199646296.003.0008","url":null,"abstract":"The role of types in categorical models of meaning is investigated. A general scheme for how typed models of meaning may be used to compare sentences, regardless of their grammatical structure is described, and a toy example is used as an illustration. Taking as a starting point the question of whether the evaluation of such a type system 'loses information', we consider the parametrized typing associated with connectives from this viewpoint. \u0000The answer to this question implies that, within full categorical models of meaning, the objects associated with types must exhibit a simple but subtle categorical property known as self-similarity. We investigate the category theory behind this, with explicit reference to typed systems, and their monoidal closed structure. We then demonstrate close connections between such self-similar structures and dagger Frobenius algebras. In particular, we demonstrate that the categorical structures implied by the polymorphically typed connectives give rise to a (lax unitless) form of the special forms of Frobenius algebras known as classical structures, used heavily in abstract categorical approaches to quantum mechanics.","PeriodicalId":273067,"journal":{"name":"Quantum Physics and Linguistics","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117308846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 11
From Sentence to Concept 从句子到概念
Quantum Physics and Linguistics Pub Date : 2012-10-11 DOI: 10.1093/acprof:oso/9780199646296.003.0009
A. Preller
{"title":"From Sentence to Concept","authors":"A. Preller","doi":"10.1093/acprof:oso/9780199646296.003.0009","DOIUrl":"https://doi.org/10.1093/acprof:oso/9780199646296.003.0009","url":null,"abstract":"The compositional functional logical models of natural language are recast as compact closed categories. Composition is based on the geometrical representation of information flow characteristic for these categories. The functional logical interpretation of (strings of) words is carried over to projectors in a finite tensor product of 2-dimensional spaces such that the truth of a sentence is equivalent to the truth of the corresponding projector. Examples include sentences with compound noun phrases involving quantifiers, adjectives and negation.","PeriodicalId":273067,"journal":{"name":"Quantum Physics and Linguistics","volume":"661 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122965553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Hopf algebras - Variant notions and reconstruction theorems Hopf代数。变异体概念和重构定理
Quantum Physics and Linguistics Pub Date : 2012-02-16 DOI: 10.1093/acprof:oso/9780199646296.003.0005
J. Vercruysse
{"title":"Hopf algebras - Variant notions and reconstruction theorems","authors":"J. Vercruysse","doi":"10.1093/acprof:oso/9780199646296.003.0005","DOIUrl":"https://doi.org/10.1093/acprof:oso/9780199646296.003.0005","url":null,"abstract":"Hopf algebras are closely related to monoidal categories. More precise, $k$-Hopf algebras can be characterized as those algebras whose category of finite dimensional representations is an autonomous monoidal category such that the forgetful functor to $k$-vectorspaces is a strict monoidal functor. This result is known as the Tannaka reconstruction theorem (for Hopf algebras). Because of the importance of both Hopf algebras in various fields, over the last last few decades, many generalizations have been defined. We will survey these different generalizations from the point of view of the Tannaka reconstruction theorem.","PeriodicalId":273067,"journal":{"name":"Quantum Physics and Linguistics","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117029889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 13
Modular Categories 模块化的类别
Quantum Physics and Linguistics Pub Date : 2012-01-31 DOI: 10.1093/acprof:oso/9780199646296.003.0006
Michael Mueger
{"title":"Modular Categories","authors":"Michael Mueger","doi":"10.1093/acprof:oso/9780199646296.003.0006","DOIUrl":"https://doi.org/10.1093/acprof:oso/9780199646296.003.0006","url":null,"abstract":"• Modular categories serve as input datum for the Reshetikhin-Turaev construction of topological quantum field theories in 2+1 dimensions and therefore give rise to invariants of smooth 3-manifolds. This goes some way towards making Witten’s interpretation of the Jones polynomial via Chern-Simons QFT rigorous. (But since there still is no complete rigorous non-perturbative construction of the Chern-Simons QFTs by conventional quantum field theory methods, there also is no proof of their equivalence to the RT-TQFTs constructed using the representation theory of quantum groups.)","PeriodicalId":273067,"journal":{"name":"Quantum Physics and Linguistics","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121491276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 30
Proof nets for the Lambek-Grishin calculus Lambek-Grishin微积分的证明网
Quantum Physics and Linguistics Pub Date : 2011-12-01 DOI: 10.1093/acprof:oso/9780199646296.003.0010
M. Moortgat, R. Moot
{"title":"Proof nets for the Lambek-Grishin calculus","authors":"M. Moortgat, R. Moot","doi":"10.1093/acprof:oso/9780199646296.003.0010","DOIUrl":"https://doi.org/10.1093/acprof:oso/9780199646296.003.0010","url":null,"abstract":"Grishin's generalization of Lambek's Syntactic Calculus combines a non-commutative multiplicative conjunction and its residuals (product, left and right division) with a dual family: multiplicative disjunction, right and left difference. Interaction between these two families takes the form of linear distributivity principles. We study proof nets for the Lambek-Grishin calculus and the correspondence between these nets and unfocused and focused versions of its sequent calculus.","PeriodicalId":273067,"journal":{"name":"Quantum Physics and Linguistics","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127345857","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 16
Algebras over a field and semantics for context based reasoning 字段上的代数和基于上下文推理的语义
Quantum Physics and Linguistics Pub Date : 2011-11-07 DOI: 10.1093/acprof:oso/9780199646296.003.0011
Daoud Clarke
{"title":"Algebras over a field and semantics for context based reasoning","authors":"Daoud Clarke","doi":"10.1093/acprof:oso/9780199646296.003.0011","DOIUrl":"https://doi.org/10.1093/acprof:oso/9780199646296.003.0011","url":null,"abstract":"This paper introduces context algebras and demonstrates their application to combining logical and vector-based representations of meaning. Other approaches to this problem attempt to reproduce aspects of logical semantics within new frameworks. The approach we present here is different: We show how logical semantics can be embedded within a vector space framework, and use this to combine distributional semantics, in which the meanings of words are represented as vectors, with logical semantics, in which the meaning of a sentence is represented as a logical form.","PeriodicalId":273067,"journal":{"name":"Quantum Physics and Linguistics","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121309279","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Scalars, Monads, and Categories 标量、单子和类别
Quantum Physics and Linguistics Pub Date : 2010-03-02 DOI: 10.1093/acprof:oso/9780199646296.003.0007
Dion Coumans, B. Jacobs
{"title":"Scalars, Monads, and Categories","authors":"Dion Coumans, B. Jacobs","doi":"10.1093/acprof:oso/9780199646296.003.0007","DOIUrl":"https://doi.org/10.1093/acprof:oso/9780199646296.003.0007","url":null,"abstract":"This chapter describes interrelations between: (1) algebraic structure on sets of scalars, (2) properties of monads associated with such sets of scalars, and (3) structure in categories (esp. Lawvere theories) associated with these monads. These interrelations will be expressed in terms of \"triangles of adjunctions\", involving for instance various kinds of monoids (non-commutative, commutative, involutive) and semirings as scalars. It will be shown to which kind of monads and categories these algebraic structures correspond via adjunctions.","PeriodicalId":273067,"journal":{"name":"Quantum Physics and Linguistics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126441383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 35
Type-Driven Syntax and Semantics for Composing Meaning Vectors 组成意义向量的类型驱动语法和语义
Quantum Physics and Linguistics Pub Date : 1900-01-01 DOI: 10.1093/acprof:oso/9780199646296.003.0013
S. Clark
{"title":"Type-Driven Syntax and Semantics for Composing Meaning Vectors","authors":"S. Clark","doi":"10.1093/acprof:oso/9780199646296.003.0013","DOIUrl":"https://doi.org/10.1093/acprof:oso/9780199646296.003.0013","url":null,"abstract":"A draft chapter for the OUP book on Compositional methods in Physics and Linguistics. This draft formatted on 27th February 2012.","PeriodicalId":273067,"journal":{"name":"Quantum Physics and Linguistics","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124290854","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 28
Distributional Semantic Models 分布语义模型
Quantum Physics and Linguistics Pub Date : 1900-01-01 DOI: 10.1093/acprof:oso/9780199646296.003.0012
S. Pulman
{"title":"Distributional Semantic Models","authors":"S. Pulman","doi":"10.1093/acprof:oso/9780199646296.003.0012","DOIUrl":"https://doi.org/10.1093/acprof:oso/9780199646296.003.0012","url":null,"abstract":"","PeriodicalId":273067,"journal":{"name":"Quantum Physics and Linguistics","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126553866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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