抽象超结构范式：走向结构归纳理论
Abstraction Super-structuring Normal Forms: Towards a Theory of Structural Induction
摘要：
归纳是一个过程，通过这个过程，我们获得了世界的预测性定律、理论或模型。我们考虑归纳的结构方面。我们回答的问题，我们是否可以找到一个有限的和minmalistic一套操作的结构元素，任何理论可以表示。我们识别抽象（将相似的实体分组）和超结构（在拓扑上组合，例如，时空接近的实体）作为归纳过程中的基本结构操作。我们表明，只有两个结构操作，即反向抽象和反向超结构（抽象和超结构的抽象）足以充分利用图灵等价生成语法的全部权力归纳。我们探讨了这个定理的含义与隐变量的性质，激进的实证主义和2个世纪前大卫休谟关于概念之间的联系原则的主张。
英文摘要：
Induction is the process by which we obtain predictive laws or theories or models of the world. We consider the structural aspect of induction. We answer the question as to whether we can find a finite and minmalistic set of operations on structural elements in terms of which any theory can be expressed. We identify abstraction (grouping similar entities) and super-structuring (combining topologically e.g., spatio-temporally close entities) as the essential structural operations in the induction process. We show that only two more structural operations, namely, reverse abstraction and reverse super-structuring (the duals of abstraction and super-structuring respectively) suffice in order to exploit the full power of Turing-equivalent generative grammars in induction. We explore the implications of this theorem with respect to the nature of hidden variables, radical positivism and the 2-century old claim of David Hume about the principles of connexion among ideas.
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