Search results for "Inductive reasoning"
showing 10 items of 54 documents
On the power of inductive inference from good examples
1993
Abstract The usual information in inductive inference available for the purposes of identifying an unknown recursive function f is the set of all input/output examples (x,f(x)),n eN. In contrast to this approach we show that it is considerably more powerful to work with finite sets of “good” examples even when these good examples are required to be effectively computable. The influence of the underlying numberings, with respect to which the identification has to be realized, to the capabilities of inference from good examples is also investigated. It turns out that nonstandard numberings can be much more powerful than Godel numberings.
On the impact of forgetting on learning machines
1995
People tend not to have perfect memories when it comes to learning, or to anything else for that matter. Most formal studies of learning, however, assume a perfect memory. Some approaches have restricted the number of items that could be retained. We introduce a complexity theoretic accounting of memory utilization by learning machines. In our new model, memory is measured in bits as a function of the size of the input. There is a hierarchy of learnability based on increasing memory allotment. The lower bound results are proved using an unusual combination of pumping and mutual recursion theorem arguments. For technical reasons, it was necessary to consider two types of memory : long and sh…
An inductive inference approach to classification
1992
In this paper, we introduce a formal framework for investigating the relationship of inductive inference and the task of classification. We give the first results on the relationship between functions that can be identified in the limit and functions that can be acquired from unclassified objects only. Moreover, we present results on the complexity of classification functions and the preconditions necessary in order to allow the computation of such functions.
On the Influence of Technology on Learning Processes
2014
Probabilistic computations and frequency computations were invented for the same purpose, namely, to study possible advantages of technology involving random choices. Recently several authors have discovered close relationships of these generalizations of deterministic computations to computations taking advice. Various forms of computation taking advice were studied by Karp and Lipton [1], Damm and Holzer [2], and Freivalds [3]. In the present paper, we apply the nonconstructive, probabilistic, and frequency methods to an inductive inference paradigm originally due to Gold [4] and investigate their impact on the resulting learning models. Several trade-offs with respect to the resulting l…
Incorporating hypothetical knowledge into the process of inductive synthesis
1996
The problem of inductive inference of functions from hypothetical knowledge is investigated in this paper. This type of inductive inference could be regarded as a generalization of synthesis from examples that can be directed not only by input/output examples but also by knowledge of, e. g., functional description's syntactic structure or assumptions about the process of function evaluation. We show that synthesis of this kind is possible by efficiently enumerating the hypothesis space and illustrate it with several examples.
Learning small programs with additional information
1997
This paper was inspired by [FBW 94]. An arbitrary upper bound on the size of some program for the target function suffices for the learning of some program for this function. In [FBW 94] it was discovered that if “learning” is understood as “identification in the limit,” then in some programming languages it is possible to learn a program of size not exceeding the bound, while in some other programming languages this is not possible.
The power of procrastination in inductive inference: How it depends on used ordinal notations
1995
We consider inductive inference with procrastination. Usually it is defined using constructive ordinals. For constructive ordinals there exist many different systems of notations. In this paper we study how the power of inductive inference depends on used system of notations.
Inductive inference of recursive functions: Qualitative theory
2005
This survey contains both old and very recent results in non-quantitative aspects of inductive inference of total recursive functions. The survey is not complete. The paper was written to stress some of the main results in selected directions of research performed at the University of Latvia rather than to exhaust all of the obtained results. We concentrated on the more explored areas such as the inference of indices in non-Goedel computable numberings, the inference of minimal Goedel numbers, and the specifics of inference of minimal indices in Kolmogorov numberings.
Towards A Twitter Observatory: A Multi-Paradigm Framework For Collecting, Storing And Analysing Tweets
2016
International audience; In this article we show how a multi-paradigm framework can fulfil the requirements of tweets analysis and reduce the waiting time for researchers that use computational resources and storage systems to support large-scale data analysis. The originality of our approach is to combine concerns about data harvesting, data storage, data analysis and data visualisation into a framework that supports inductive reasoning in multidisciplinary scientific research. Our main contribution is a polyglot storage system with a generic data model to support logical data independence and a set of tools that can provide a suitable solution for mixing different types of algorithms in or…
Pattern languages with and without erasing
1994
The paper deals with the problems related to finding a pattern common to all words in a given set. We restrict our attention to patterns expressible by the use of variables ranging over words. Two essentially different cases result, depending on whether or not the empty word belongs to the range. We investigate equivalence and inclusion problems, patterns descriptive for a set, as well as some complexity issues. The inclusion problem between two pattern languages turns out to be of fundamental theoretical importance because many problems in the classical combinatorics of words can be reduced to it.