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A Unifying Logic

About: This article is published in The Ruffin Series in Business Ethics.The article was published on 1995-04-01. It has received 1 citations till now. The article focuses on the topics: Philosophy of logic.
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Journal ArticleDOI
TL;DR: This paper shows that the ''texts'' or ''positive presentations'' of concepts in inductive inference can be viewed as special cases of the ''admissible representations'' of computable analysis.
Abstract: Based on the observation that the category of concept spaces with the positive information topology is equivalent to the category of countably based T"0 topological spaces, we investigate further connections between the learning in the limit model of inductive inference and topology. In particular, we show that the ''texts'' or ''positive presentations'' of concepts in inductive inference can be viewed as special cases of the ''admissible representations'' of computable analysis. We also show that several structural properties of concept spaces have well known topological equivalents. In addition to topological methods, we use algebraic closure operators to analyze the structure of concept spaces, and we show the connection between these two approaches. The goal of this paper is not only to introduce new perspectives to learning theorists, but also to present the field of inductive inference in a way more accessible to domain theorists and topologists.

38 citations


Cites background from "A Unifying Logic"

  • ...We do require that the learner decrement its counter after every change of hypothesis, because we feel that the theory becomesmoremathematically natural thisway (see [22] for further support for this approach tomind-change complexity)....

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  • ...It is well known among learning theorists that there are many connections between topology and inductive inference [17,22], and that some important notions in inductive inference can be easily formalized by introducing the positive information topology onto a concept space [19]....

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References
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Journal ArticleDOI
TL;DR: This paper shows that the ''texts'' or ''positive presentations'' of concepts in inductive inference can be viewed as special cases of the ''admissible representations'' of computable analysis.
Abstract: Based on the observation that the category of concept spaces with the positive information topology is equivalent to the category of countably based T"0 topological spaces, we investigate further connections between the learning in the limit model of inductive inference and topology. In particular, we show that the ''texts'' or ''positive presentations'' of concepts in inductive inference can be viewed as special cases of the ''admissible representations'' of computable analysis. We also show that several structural properties of concept spaces have well known topological equivalents. In addition to topological methods, we use algebraic closure operators to analyze the structure of concept spaces, and we show the connection between these two approaches. The goal of this paper is not only to introduce new perspectives to learning theorists, but also to present the field of inductive inference in a way more accessible to domain theorists and topologists.

38 citations