Systems that learn: an introduction to learning theory for cognitive and computer scientists
Systems that learn: an introduction to learning theory for cognitive and computer scientists
Identification of unions of languages drawn from an identifiable class
COLT '89 Proceedings of the second annual workshop on Computational learning theory
Inductive inference of monotonic formal systems from positive data
New Generation Computing - Selected papers from the international workshop on algorithmic learning theory,1990
The correct definition of finite elasticity: corrigendum to identification of unions
COLT '91 Proceedings of the fourth annual workshop on Computational learning theory
Inference of Reversible Languages
Journal of the ACM (JACM)
Inductive inference of unbounded unions of pattern languages from positive data
Theoretical Computer Science - Special issue on algorithmic learning theory
Learning algebraic structures from text
Theoretical Computer Science - Algorithmic learning theory
On Approximately Identifying Concept Classes in the Limit
ALT '95 Proceedings of the 6th International Conference on Algorithmic Learning Theory
Mind change complexity of inferring unbounded unions of pattern languages from positive data
ALT'06 Proceedings of the 17th international conference on Algorithmic Learning Theory
Topological Properties of Concept Spaces
ALT '08 Proceedings of the 19th international conference on Algorithmic Learning Theory
Learning Bounded Unions of Noetherian Closed Set Systems Via Characteristic Sets
ICGI '08 Proceedings of the 9th international colloquium on Grammatical Inference: Algorithms and Applications
Theoretical Computer Science
Topological properties of concept spaces (full version)
Information and Computation
Computing characteristic sets of bounded unions of polynomial ideals
JSAI'07 Proceedings of the 2007 conference on New frontiers in artificial intelligence
Inferability of unbounded unions of certain closed set systems
JSAI-isAI'09 Proceedings of the 2009 international conference on New frontiers in artificial intelligence
String extension learning using lattices
LATA'10 Proceedings of the 4th international conference on Language and Automata Theory and Applications
Learning families of closed sets in matroids
WTCS'12 Proceedings of the 2012 international conference on Theoretical Computer Science: computation, physics and beyond
Learning in the limit with lattice-structured hypothesis spaces
Theoretical Computer Science
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In this paper, we generalize previous results showing connections between inductive inference from positive data and algebraic structures by using tools from universal algebra. In particular, we investigate the inferability from positive data of language classes defined by closure operators. We show that some important properties of language classes used in inductive inference correspond closely to commonly used properties of closed set systems. We also investigate the inferability of algebraic closed set systems, and show that these types of systems are inferable from positive data if and only if they contain no infinite ascending chain of closed sets. This generalizes previous results concerning the inferability of various algebraic classes such as the class of ideals of a ring. We also show the relationship with algebraic closed set systems and approximate identifiability as introduced by Kobayashi and Yokomori [11]. We propose that closure operators offer a unifying framework for various approaches to inductive inference from positive data.