Mathematics as a Game of Types
AUTOR(ES)
Jackson William Marques de Carvalho
FONTE
IBICT - Instituto Brasileiro de Informação em Ciência e Tecnologia
DATA DE PUBLICAÇÃO
08/04/2005
RESUMO
This thesis presents a grammar-based approach to the specification of mathematical notation. The method introduced is based on a meta-strueture that uses attributed context-free grammars for capturing the meaning of mathematical concepts. This structure supports the creation of multi-purpose documents and allows the specification of mathematical notation in a dynamical way. In the context of this thesis, multi-purpose documents refer to documents that may be rendered or used in different ways, some of which might not be known at the time the document is created. By dynamical it is understood that the meaning associated with syntax is allowed to be modified. The proposal described in this thesis is based on an authoring model which addresses the user needs as a fundamental requirement. This characteristic is structured around a scope mechanism that allows the mapping between semantics and syntax to be modified at any time during authoring. This process supports the dynamic characteristics of the meaning-to-syntax binding necessary during the authoring of mathematical concepts. The multi-purpose property is supported by a semantics-based mark-up that provides the possibility for the mathematical concepts to be processed according to the specific requirements of applications. Modular grammar fragments characterized by a one-to-one mapping between mathematical concept and grammar representation provide the adequate support for the definition of the various scopes. An incremental update process is defined as a way to modify the necessary grammar fragments to support the changes proposed during the authoring process.
ASSUNTO(S)
rendering matematica da computacao types interfaces metasystem notation authoring multimodal user-oriented mathematics grammars
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