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
Learning context-free grammars from structural data in polynomial time
Theoretical Computer Science
Types of monotonic language learning and their characterization
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
Towards a mathematical theory of machine discovery from facts
Theoretical Computer Science - Special issue on algorithmic learning theory
A Guided Tour Across the Boundaries of Learning Recursive Languages
Algorithmic Learning for Knowledge-Based Systems, GOSLER Final Report
Inductive Inference Machines That Can Refute Hypothesis Spaces
ALT '93 Proceedings of the 4th International Workshop on Algorithmic Learning Theory
Machine Discovery in the Presence of Incomplete or Ambiguous Data
AII '94 Proceedings of the 4th International Workshop on Analogical and Inductive Inference: Algorithmic Learning Theory
Inductive Inference of an Approximate Concept from Positive Data
AII '94 Proceedings of the 4th International Workshop on Analogical and Inductive Inference: Algorithmic Learning Theory
On Approximately Identifying Concept Classes in the Limit
ALT '95 Proceedings of the 6th International Conference on Algorithmic Learning Theory
Language Learning from Membership Queries and Characteristic Examples
ALT '95 Proceedings of the 6th International Conference on Algorithmic Learning Theory
Inferring a System from Examples with Time Passage
ALT '97 Proceedings of the 8th International Conference on Algorithmic Learning Theory
Progress in Discovery Science, Final Report of the Japanese Discovery Science Project
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In their previous paper, Mukouchi and Arikawa discussed both refutability and inferability of a hypothesis space from examples. If a target language is a member of the hypothesis space, then an inference machine should identify it in the limit, otherwise it should refute the hypothesis space itself in a finite time. They pointed out the necessity of refutability of a hypothesis space from a view point of machine discovery. Recently, Mukouchi focused sequences of examples successively generated by a certain kind of system. He call such a sequence an observation with time passage, and a sequence extended as long as possible a complete observation. Then the set of all possible complete observations is called a phenomenon of the system. In this paper, we introduce phenomena generated by rewriting systems known as 0L systems and pure grammars, and investigate their inferability in the limit from positive examples as well as refutable inferability from complete examples. First, we show that any phenomenon class generated by 0L systems is inferable in the limit from positive examples. We also show that the phenomenon class generated by pure grammars such that left hand side of each production is not longer than a fixed length is inferable in the limit from positive examples, while the phenomenon class of unrestricted pure grammars is shown not to be inferable. We also obtain the result that the phenomenon class of pure grammars such that the number of productions and that of axioms are not greater than a fixed number is inferable in the limit from positive examples as well as refutably inferable from complete examples.