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2010.3: Uniformity principle for $\Sigma$-definability

2010.3: Korovina Margarita and Kudinov Oleg (2009) Uniformity principle for $\Sigma$-definability. Journal of Logic and Computation, 19 (1). pp. 159-174. ISSN 0955-792X

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DOI: 10.1093/logcom/exn033

Abstract

The main goal of this research is to develop logical tools and techniques for effective reasoning about continuous data based on $\Sigma$-definability. In this article we invent the Uniformity Principleand prove it for $\Sigma$-definability over the real numbers extended by open predicates. Using the Uniformity Principle, we investigate different approaches to enrich the language of {Sigma}-formulas in such a way that simplifies reasoning about computable continuous data without enlarging the class of $\Sigma$-definable sets. In order to do reasoning about computability of certain continuous data we have to pick up an appropriate language of a structure representing these continuous data. We formulate several major conditions how to do that in a right direction. We also employ the Uniformity Principleto argue that our logical approach is a good way for formalization of computable continuous data in logical terms.

Item Type:Article
Uncontrolled Keywords:CICADA,$\Sigma$-Definability, Uniformity Principle, effective reasoning about continuous data, continuous data types, computable analysis
Subjects:MSC 2000 > 03 Mathematical logic and foundations
MSC 2000 > 68 Computer science
MIMS number:2010.3
Deposited By:Dr Margarita Korovina
Deposited On:08 January 2010

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