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Inductive learning
Inductive Learning

Wu Xindong,

计算机科学技术学报 , 1993,
Abstract: Machine learning(ML)is a major subfield of artificial intelligence(AI).It has been seen as a feasi- ble way of avoiding the knowledge bottleneck problem in knowledge-based systems development.Re- search on ML has concentrated in the main on inductive learning,a paradigm for inducing rules from unordered sets of exmaples.AQ11 and ID3,the two most widespread algorithms in ML,are both induc- tive.This paper first summarizes AQ11,ID3 and the newly-developed extension matrix approach based HCV algorithm;and then reviews the recent development of inductive learing and automatic knowledge acquisition from data bases.
Cyclic and Inductive Calculi are equivalent  [PDF]
Razvan Voicu,Mengran Li
Computer Science , 2011,
Abstract: Brotherston and Simpson [citation] have formalized and investigated cyclic reasoning, reaching the important conclusion that it is at least as powerful as inductive reasoning (specifically, they showed that each inductive proof can be translated into a cyclic proof). We add to their investigation by proving the converse of this result, namely that each inductive proof can be translated into an inductive one. This, in effect, establishes the equivalence between first order cyclic and inductive calculi.
Regularity of conservative inductive limits
Jan Kucera
International Journal of Mathematics and Mathematical Sciences , 1999, DOI: 10.1155/s0161171299227056
Abstract: A sequentially complete inductive limit of Fr chet spaces is regular, see [3]. With a minor modification, this property can be extended to inductive limits of arbitrary locally convex spaces under an additional assumption of conservativeness.
Sequential completeness of inductive limits  [PDF]
Claudia Gómez,Jan Ku era
International Journal of Mathematics and Mathematical Sciences , 2000, DOI: 10.1155/s0161171200003744
Abstract: A regular inductive limit of sequentially complete spaces is sequentially complete. For the converse of this theorem we have a weaker result: if ind En is sequentially complete inductive limit, and each constituent space En is closed in ind En, then ind En is α-regular.
On sequentially retractive inductive limits
Armando García
International Journal of Mathematics and Mathematical Sciences , 2003, DOI: 10.1155/s0161171203205202
Abstract: Every locally complete inductive limit of sequentially complete locally convex spaces, which satisfies Retakh's condition (M) is regular, sequentially complete and sequentially retractive. A quasiconverse for this theorem and a criterion for sequential retractivity of inductive limits of webbed spaces are given.
The Inductive Kernels of Graphs  [PDF]
Serge Burckel
Mathematics , 2007,
Abstract: It is well known that kernels in graphs are powerful and useful structures, for instance in the theory of games. However, a kernel does not always exist and Chv\'atal proved in 1973 that it is an NP-Complete problem to decide its existence. We present here an alternative definition of kernels that uses an inductive machinery : the inductive kernels. We prove that inductive kernels always exist and a particular one can be constructed in quadratic time. However, it is an NP-Complete problem to decide the existence of an inductive kernel including (resp. excluding) some fixed vertex.
Inductive LS cocategory and localisation  [PDF]
Cristina Costoya,Antonio Viruel
Mathematics , 2011,
Abstract: In this paper we prove that the inductive cocategory of a nilpotent $CW$-complex of finite type $X$, $\indcocat X$, is bounded above by an expression involving the inductive cocategory of the $p$-localisations of $X$. Our arguments can be dualised to LS category improving previous results by Cornea and Stanley. Finally, we show that the inductive cocategory is generic for 1-connected $H_0$-spaces of finite type.
The Prioritized Inductive Logic Programs  [PDF]
Shilong Ma,Yuefei Sui,Ke Xu
Computer Science , 2002,
Abstract: The limit behavior of inductive logic programs has not been explored, but when considering incremental or online inductive learning algorithms which usually run ongoingly, such behavior of the programs should be taken into account. An example is given to show that some inductive learning algorithm may not be correct in the long run if the limit behavior is not considered. An inductive logic program is convergent if given an increasing sequence of example sets, the program produces a corresponding sequence of the Horn logic programs which has the set-theoretic limit, and is limit-correct if the limit of the produced sequence of the Horn logic programs is correct with respect to the limit of the sequence of the example sets. It is shown that the GOLEM system is not limit-correct. Finally, a limit-correct inductive logic system, called the prioritized GOLEM system, is proposed as a solution.
The inductive theory of natural selection  [PDF]
Steven A. Frank
Computer Science , 2014,
Abstract: The theory of natural selection has two forms. Deductive theory describes how populations change over time. One starts with an initial population and some rules for change. From those assumptions, one calculates the future state of the population. Deductive theory predicts how populations adapt to environmental challenge. Inductive theory describes the causes of change in populations. One starts with a given amount of change. One then assigns different parts of the total change to particular causes. Inductive theory analyzes alternative causal models for how populations have adapted to environmental challenge. This chapter emphasizes the inductive analysis of cause.
Inductive algebras and homogeneous shifts  [PDF]
Amritanshu Prasad,M. K. Vemuri
Mathematics , 2009, DOI: 10.1007/s11785-009-0020-6
Abstract: Inductive algebras for the irreducible unitary representations of the universal cover of the group of unimodular two by two matrices are classified. The classification of homogeneous shift operators is obtained as a direct consequence. This gives a new approach to the results of Bagchi and Misra.
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