Algebra. Addison-Wesley, Reading, Massachusetts, 1982. [Freivalds et al., 1995] R. Freivalds, E. Kinber, & C. H. Smith. On the Intrinsic Complexity of Learning. Information and Computation, 123(1):64--71, 1995. [Fuhrmann, 1991] A. Fuhrmann. Theory contraction through base contraction. Journal of Philosophical Logic, 20:175--203, 1991. [Fulk & Jain, 1994] M. Fulk & S. Jain. Approximate inference and scientific method. Information and Computation, 114--2:179--191, 1994. [Fulk et al., 1994] M. Fulk, S. Jain, & D. Osherson. Open Problems in systems that learn. Journal of Computer and System Sciences, 49(3):589 -- 604, 1994. BIBLIOGRAPHY 123 [Fulk, 1988] M. Fulk. Saving the phenomenon: Requirements that inductive machines not contradict known data. Inform. Comput., 79:193--209, 1988. [Fulk, 1990] M. Fulk. Prudence and other conditions on formal language learning. Information and Computation, 85(1):1--11, 1990. [Gaifman & Snir, 1982] H. Gaifman & M. Snir. Probabilities over rich langu...

In designing learning algorithms it seems quite reasonable to construct them in a way such that all data the algorithm already has obtained are correctly and completely reflected in the hypothesis the algorithm outputs on these data. However, this approach may totally fail, i.e., it may lead to the unsolvability of the learning problem, or it may exclude any efficient solution of it. In particular, we present a natural learning problem and prove that it can be solved in polynomial time if and only if the algorithm is allowed to ignore data.

. Planning is investigated in an area where classical Strips- like approaches usually fail. The application domain is therapy (i.e. repair) for complex dynamic processes. The peculiarities of this domain are discussed in some detail for convincingly developing the characteristics of the inductive planning approach presented. Plans are intended to be run for process therapy. Thus, plans are programs. Because of the unavoidable vagueness and uncertainty of information about complex dynamic processes in the case of disturbance, therapy plan generation turns out to be inductive program synthesis. There is developed a graph-theoretically based approach to inductive therapy plan generation. This approach is investigated from the inductive inference perspective. Particular emphasis is put on consistent and incremental learning of therapy plans. Basic application scenarios are developed and compared to each other. The inductive inference approach is invoked to develop and investigate a couple...

this paper initiates a study in which it is demonstrated that certain concepts (represented by functions) can be learned, but only in the event that certain relevant subconcepts (also represented by functions) have been previously learned. In other words, the Soar project presents empirical evidence that learning how to learn is viable for computers and this paper proves that doing so is the only way possible for computers to make certain inferences.

U-shaped learning behaviour in cognitive development involves learning, unlearning and relearning. It occurs, for example, in learning irregular verbs. The prior cognitive science literature is occupied with how humans do it, for example, general rules versus tables of exceptions. This paper is mostly concerned with whether Ushaped learning behaviour may be necessary in the abstract mathematical setting of inductive inference, that is, in the computational learning theory following the framework of Gold. All notions considered are learning from text, that is, from positive data. Previous work showed that U-shaped learning behaviour is necessary for behaviourally correct learning but not for syntactically convergent, learning in the limit ( = explanatory learning). The present paper establishes the necessity for the hierarchy of classes of vacillatory learning where a behaviourally correct learner has to satisfy the additional constraint that it vacillates in the limit between at most b grammars, where b ∈ {2, 3,...,∗}. Non U-shaped vacillatory learning is shown to be restrictive: every non U-shaped vacillatorily learnable class is already learnable in the limit. Furthermore, if vacillatory learning with the parameter b = 2 is possible then non U-shaped behaviourally correct learning is also possible. But for b = 3, surprisingly, there is a class witnessing that this implication fails.

Gold [Gol67] discovered a fundamental enumeration technique, the so-called identification-by-enumeration, a simple but powerful class of algorithms for learning from examples (inductive inference). We introduce a variety of more sophisticated (and more powerful) enumeration techniques and characterize their power. We conclude with the thesis that enumeration techniques are even universal in that each solvable learning problem in inductive inference can be solved by an adequate enumeration technique. This thesis is technically motivated and discussed. Keywords: Learning from examples, learning by search, identification by enumeration, enumeration techniques. Role of Search 1 1 Introduction The role of search, for learning from examples, is examined in a theoretical setting. Gold's seminal paper [Gol67] on inductive inference introduced a simple but powerful learning technique which became known as identificationby -enumeration. Identification-by-enumeration begins with an infi...

. In any learnability setting, hypotheses are conjectured from some hypothesis space. Studied herein are the effects on learnability of the presence or absence of certain control structures in the hypothesis space. First presented are control structure characterizations of some rather specific but illustrative learnability results. Then presented are the main theorems. Each of these characterizes the invariance of a learning class over hypothesis space V (and a little more about V ) as: V has suitable instances of all denotational control structures. 1 Introduction In any learnability setting, hypotheses are conjectured from some hypothesis space, for example, in [OSW86] from general purpose programming systems, in [ZL95, Wie78] from subrecursive systems, and in [Qui92] from very simple classes of classificatory decision trees. 3 Much is known theoretically about the restrictions on learning power resulting from restricted hypothesis spaces [ZL95]. In the present paper we begin to...

Algebra. Addison-Wesley, Reading, Massachusetts, 1982. [Freivalds et al., 1995] R. Freivalds, E. Kinber, & C. H. Smith. On the Intrinsic Complexity of Learning. Information and Computation, 123(1):64--71, 1995. [Fuhrmann, 1991] A. Fuhrmann. Theory contraction through base contraction. Journal of Philosophical Logic, 20:175--203, 1991. [Fulk & Jain, 1994] M. Fulk & S. Jain. Approximate inference and scientific method. Information and Computation, 114--2:179--191, 1994. [Fulk et al., 1994] M. Fulk, S. Jain, & D. Osherson. Open Problems in systems that learn. Journal of Computer and System Sciences, 49(3):589 -- 604, 1994. BIBLIOGRAPHY 123 [Fulk, 1988] M. Fulk. Saving the phenomenon: Requirements that inductive machines not contradict known data. Inform. Comput., 79:193--209, 1988. [Fulk, 1990] M. Fulk. Prudence and other conditions on formal language learning. Information and Computation, 85(1):1--11, 1990. [Gaifman & Snir, 1982] H. Gaifman & M. Snir. Probabilities over rich langu...

A consistent learner is required to correctly and completely reflect in its actual hypothesis all data received so far. Though this demand sounds quite plausible, it may lead to the unsolvability of the learning problem. Therefore, in the present paper several variations of consistent learning are introduced and studied. These variations allow a so-called δ –delay relaxing the consistency demand to all but the last δ data. Additionally, we introduce the notion of coherent learning (again with δ – delay) requiring the learner to correctly reflect only the last datum (only the n − δ th datum) seen. Our results are manyfold. First, it is shown that all models of coherent learning with δ –delay are exactly as powerful as their corresponding consistent learning models with δ –delay. Second, we provide characterizations for consistent learning with δ –delay in terms of complexity and computable numberings. Finally, we establish strict hierarchies for all consistent learning models with δ –delay in dependence on δ.

Studying the learnability of classes of recursive functions has attracted considerable interest for at least four decades. Starting with Gold’s (1967) model of learning in the limit, many variations, modifications and extensions have been proposed. These models differ in some of the following: the mode of convergence, the requirements intermediate hypotheses have to fulfill, the set of allowed learning strategies, the source of information available to the learner during the learning process, the set of admissible hypothesis spaces, and the learning goals. A considerable amount of work done in this field has been devoted to the characterization of function classes that can be learned in a given model, the influence of natural, intuitive postulates on the resulting learning power, the incorporation of randomness into the learning process, the complexity of learning, among others. On the occasion of Rolf Wiehagen’s 60th birthday, the last four decades of research in that area are surveyed, with a special focus on Rolf Wiehagen’s work, which has made him one of the most influential scientists in the theory of learning recursive functions.