Please use this identifier to cite or link to this item:
Title: Unifying logic, topology and learning in Parametric logic
Authors: Martin, E.
Sharma, A.
Stephan, F. 
Keywords: Borel and difference hierarchies
Inductive inference
Inductive logic
Weak forms of compactness
Issue Date: 18-Jan-2006
Source: Martin, E., Sharma, A., Stephan, F. (2006-01-18). Unifying logic, topology and learning in Parametric logic. Theoretical Computer Science 350 (1) : 103-124. ScholarBank@NUS Repository.
Abstract: Many connections have been established between learning and logic, or learning and topology, or logic and topology. Still, the connections are not at the heart of these fields. Each of them is fairly independent of the others when attention is restricted to basic notions and main results. We show that connections can actually be made at a fundamental level, and result in a logic with parameters that needs topological notions for its early developments, and notions from learning theory for interpretation and applicability. One of the key properties of first-order logic is that the classical notion of logical consequence is compact. We generalize the notion of logical consequence, and we generalize compactness to β-weak compactness where β is an ordinal. The effect is to stratify the set of generalized logical consequences of a theory into levels, and levels into layers. Deduction corresponds to the lower layer of the first level above the underlying theory, learning with less than β mind changes to layer β of the first level, and learning in the limit to the first layer of the second level. Refinements of Borel-like hierarchies provide the topological tools needed to develop the framework. © 2005 Elsevier B.V. All rights reserved.
Source Title: Theoretical Computer Science
ISSN: 03043975
DOI: 10.1016/j.tcs.2005.10.018
Appears in Collections:Staff Publications

Show full item record
Files in This Item:
There are no files associated with this item.


checked on Feb 28, 2018


checked on Feb 20, 2018

Page view(s)

checked on Feb 27, 2018

Google ScholarTM



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.