Search results for "Inductive reasoning"
showing 10 items of 54 documents
Inductive synthesis of dot expressions
2005
We consider the problem of the synthesis of algorithms by sample computations. We introduce a formal language, namely, the so-called dot expressions, which is based on a formalization of the intuitive notion of ellipsis (‘...’). Whilst formally the dot expressions are simply a language describing sets of words, on the other hand, it can be considered as a programming language supporting quite a wide class of programs. Equivalence and asymptotical equivalence of dot expressions are defined and proved to be decidable. A formal example of a dot expression is defined in the way that, actually, it represents a sample computation of the program presented by the given dot expression. A system of s…
On Inductive Generalization in Monadic First-Order Logic With Identity
1966
Publisher Summary The chapter examines the results obtained by means of a system when the relation of identity is used in addition to monadic predicates. The chapter compares the new system of inductive logic sketched by Jaakko Hintikka with Carnap's system. The main advantage of Hintikka's system is that it gives natural degrees of confirmation to inductive generalizations, whereas Carnap's confirmation function c * enables one to deal satisfactorily with singular inductive inference only. According to Carnap's system, general sentences that are not logically true receive nonnegligible degrees of confirmation only if the evidence contains a large part of the individuals in the whole univer…
Closedness properties in team learning of recursive functions
1997
This paper investigates closedness properties in relation with team learning of total recursive functions. One of the first problems solved for any new identification types is the following: “Does the identifiability of classes U1 and U2 imply the identifiability of U1∪U2?” In this paper we are interested in a more general question: “Does the identifiability of every union of n−1 classes out of U1,...,Un imply the identifiability of U1∪...∪Un?” If the answer is positive, we call such identification type n-closed. We show that n-closedness can be equivalently formulated in terms of team learning. After that we find for which n team identification in the limit and team finite identification t…
On Duality in Learning and the Selection of Learning Teams
1996
AbstractPrevious work in inductive inference dealt mostly with finding one or several machines (IIMs) that successfully learn collections of functions. Herein we start with a class of functions and considerthe learner setof all IIMs that are successful at learning the given class. Applying this perspective to the case of team inference leads to the notion ofdiversificationfor a class of functions. This enable us to distinguish between several flavours of IIMs all of which must be represented in a team learning the given class.
Ordinal mind change complexity of language identification
1997
The approach of ordinal mind change complexity, introduced by Freivalds and Smith, uses constructive ordinals to bound the number of mind changes made by a learning machine. This approach provides a measure of the extent to which a learning machine has to keep revising its estimate of the number of mind changes it will make before converging to a correct hypothesis for languages in the class being learned. Recently, this measure, which also suggests the difficulty of learning a class of languages, has been used to analyze the learnability of rich classes of languages. Jain and Sharma have shown that the ordinal mind change complexity for identification from positive data of languages formed…
Efficient learning of regular expressions from good examples
1994
We consider the problem of restoring regular expressions from expressive examples. We define the class of unambiguous regular expressions, the notion of the union number of an expression showing how many union operations can occur directly under any single iteration, and the notion of an expressive example. We present a polynomial time algorithm which tries to restore an unambiguous regular expression from one expressive example. We prove that if the union number of the expression is 0 or 1 and the example is long enough, then the algorithm correctly restores the original expression from one good example. The proof relies on original investigations in theory of covering symbol sequences (wo…
Optimization problem in inductive inference
1995
Algorithms recognizing to which of n classes some total function belongs are constructed (n > 2). In this construction strategies determining to which of two classes the function belongs are used as subroutines. Upper and lower bounds for number of necessary strategies are obtained in several models: FIN- and EX-identification and EX-identification with limited number of mindchanges. It is proved that in EX-identification it is necessary to use n(n−1)/2 strategies. In FIN-identification [3n/2 − 2] strategies are necessary and sufficient, in EX-identification with one mindchange- n log2n+o(n log2n) strategies.
Learning with belief levels
2008
AbstractWe study learning of predicate logics formulas from “elementary facts,” i.e. from the values of the predicates in the given model. Several models of learning are considered, but most of our attention is paid to learning with belief levels. We propose an axiom system which describes what we consider to be a human scientist's natural behavior when trying to explore these elementary facts. It is proved that no such system can be complete. However we believe that our axiom system is “practically” complete. Theorems presented in the paper in some sense confirm our hypothesis.
Self-learning inductive inference machines
1991
Self-knowledge is a concept that is present in several philosophies. In this article, we consider the issue of whether or not a learning algorithm can in some sense possess self-knowledge. The question is answered affirmatively. Self-learning inductive inference algorithms are taken to be those that learn programs for their own algorithms, in addition to other functions. La connaissance de soi est un concept qui se retrouve dans plusieurs philosophies. Dans cet article, les auteurs s'interrogent a savoir si un algorithme d' apprentissage peut dans une certaine mesure posseder la connaissance de soi. lis apportent une reponse positive a cette question. Les algorithmes d'inference inductive a…
Learning formulae from elementary facts
1997
Since the seminal paper by E.M. Gold [Gol67] the computational learning theory community has been presuming that the main problem in the learning theory on the recursion-theoretical level is to restore a grammar from samples of language or a program from its sample computations. However scientists in physics and biology have become accustomed to looking for interesting assertions rather than for a universal theory explaining everything.