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Learning First-Order Definitions of Functions

J. R. Quinlan
1996 The Journal of Artificial Intelligence Research  
In this paper, a particular first-order learning system is modified to customize it for finding definitions of functional relations.  ...  First-order learning involves finding a clause-form definition of a relation from examples of the relation and relevant background information.  ...  The learned de nition is ordered and every clause ends with a cut.  ... 
doi:10.1613/jair.308 fatcat:5qqnivvfqbexvjqf4p2rz62bty

Learning First-Order Definitions of Functions [article]

J. R. Quinlan
1996 arXiv   pre-print
In this paper, a particular first-order learning system is modified to customize it for finding definitions of functional relations.  ...  First-order learning involves finding a clause-form definition of a relation from examples of the relation and relevant background information.  ...  List processing functions (Section 5.1)  ... 
arXiv:cs/9610102v1 fatcat:3x5ziuf7nvgu5n3h7wwamspfw4

Learnability of constrained logic programs [chapter]

Sašo Džeroski, Stephen Muggleton, Stuart Russell
1993 Lecture Notes in Computer Science  
More specifically, k-literal predicate definitions consisting of constrained, function-free, nonrecursive program clauses are polynomially PAC-learnable under arbitrary distributions.  ...  We then derive some positive results concerning the learnability of these restricted classes of logic programs, by reduction to a standard propositional learning problem.  ...  Acknowledgements The work reported in this paper is part of the ESPRIT BRA Project 6020 Inductive Logic Programming. Thanks to Luc De Raedt for his comments on the paper.  ... 
doi:10.1007/3-540-56602-3_148 fatcat:yjwrdw5hvjcbzo6fkspjq6dhcu

Page 1056 of Neural Computation Vol. 7, Issue 5 [page]

1995 Neural Computation  
In Definition 2.2 we will give a precise definition of the refinement of the PAC learning model that we consider in this paper.  ...  We will prove in Theorem 2.1 that for arbitrarily complex first-order neural nets N’ with piecewise linear activation functions there exists an efficient and provably successful learning algorithm for  ... 

Varied ways to teach the definite integral concept

Iiris Attorps, Kjell Björk, Mirko Radic, Timo Tossavainen
2013 IEJME-Mathematics Education  
In the following, we discuss how we managed to promote students' conceptual learning by varying the treatment of the object of learning (the concept of definite integral and the Fundamental Theorem of  ...  The analysis of learning results revealed some critical aspects of the definite integral concept and patterns of variations that seem to be effective to a significant degree.  ...  In order to understand what variations a teacher should use, he or she must first become aware of the varying ways students may experience the object of learning.  ... 
doi:10.29333/iejme/275 fatcat:xprnbhgbkvdc5jwyekjp52d6su

Decoupling Learning Rules from Representations [article]

Philip S. Thomas and Christoph Dann and Emma Brunskill
2017 arXiv   pre-print
., what parameterized function should be used) and what learning rule should be used to search through the resulting set of representable functions.  ...  In the artificial intelligence field, learning often corresponds to changing the parameters of a parameterized function.  ...  This leads to the more general definition of j-order covariance: Definition 4 (j-Order Covariant Learning Rule with Respect to a Sequence and Set).  ... 
arXiv:1706.03100v1 fatcat:7lkegq3qqje7hoeihg3hsp62ia

Strongly typed inductive concept learning [chapter]

P. A. Flach, C. Giraud-Carrier, J. W. Lloyd
1998 Lecture Notes in Computer Science  
In this paper we argue that the use of a language with a type system, together with higher-order facilities and functions, provides a suitable basis for knowledge representation in inductive concept learning  ...  To illustrate the point, we take some learning tasks from the machine learning and ILP literature and represent them in Escher, a typed, higher-order, functional logic programming language being developed  ...  Antony Bowers is implementing the learning system. Discussions with Nada Lavrac greatly helped to improved the presentation of the paper, as did the comments of the referees.  ... 
doi:10.1007/bfb0027322 fatcat:cnbhcmvlrfdlvh5dnf6dy73ui4

Adaptive feature descriptor selection based on a multi-table reinforcement learning strategy

Monica Piñol, Angel D. Sappa, Ricardo Toledo
2015 Neurocomputing  
The behavior of the reinforcement learning with different state definitions is evaluated. Additionally, a method that combines all these states is formulated in order to select the optimal state.  ...  The goal of the proposed framework is to learn the best descriptor for each image in a given database. This goal is reached by means of a reinforcement learning process using the minimum information.  ...  In concrete, the method joins the RL and a first order logic technique to recognize objects. In [17] a method that learns the features of the image in order to recognize objects is presented .  ... 
doi:10.1016/j.neucom.2014.03.080 fatcat:7fcfutosvfg5lbjttt2jtt2tze

Learning higher-order logic programs [article]

Andrew Cropper and Rolf Morel and Stephen H. Muggleton
2019 arXiv   pre-print
A key feature of inductive logic programming (ILP) is its ability to learn first-order programs, which are intrinsically more expressive than propositional programs.  ...  Our theoretical results show that learning higher-order programs, rather than first-order programs, can reduce the textual complexity required to express programs which in turn reduces the size of the  ...  Inductive functional programming Functional program induction approaches often support learning higher-order programs.  ... 
arXiv:1907.10953v1 fatcat:vfi6o64vnrfqrit6ig3s725d2q

STUDENTS' DIFFICULTIES AND MISCONCEPTIONS OF THE FUNCTION CONCEPT

Ashebir Sidelil Sebsibe, Bereket Telemos Dorra, Bude Wako Beressa
2019 International journal of research - granthaalayah  
A test that included tasks given in different representations, about definition, about examples of functions in word description and applications of properties of functions was administered.  ...  Whereas, a relation is a function if it has algebraic expression, overgeneralization that a representation is a functions if it is symbolized as an ordered pairs, and considering every point of discontinuity  ...  Acknowledgement The authors thankful to Wachemo University research and community service vice president office for providing found for the successful completion of this study.  ... 
doi:10.29121/granthaalayah.v7.i8.2019.656 fatcat:sddtki4xhzadvcuij2ti7dr2uy

STUDENTS' DIFFICULTIES AND MISCONCEPTIONS OF THE FUNCTION CONCEPT

Ashebir Sidelil Sebsibe, Bereket Telemos Dorra, Bude Wako Beressa
2019 Zenodo  
A test that included tasks given in different representations, about definition, about examples of functions in word description and applications of properties of functions was administered.  ...  Whereas, a relation is a function if it has algebraic expression, overgeneralization that a representation is a functions if it is symbolized as an ordered pairs, and considering every point of discontinuity  ...  Acknowledgement The authors thankful to Wachemo University research and community service vice president office for providing found for the successful completion of this study.  ... 
doi:10.5281/zenodo.3381159 fatcat:knhcpxhqvzd2plwspxl6evtr4m

Probabilistic Inductive Inference:a Survey [article]

Andris Ambainis
1999 arXiv   pre-print
Inductive inference is a recursion-theoretic theory of learning, first developed by E. M. Gold (1967). This paper surveys developments in probabilistic inductive inference.  ...  We mainly focus on finite inference of recursive functions, since this simple paradigm has produced the most interesting (and most complex) results.  ...  Other recently studied models are probabilistic language learning with monotonicity restrictions [27] and probabilistic learning up to a small set of errors [22] .  ... 
arXiv:cs/9902026v1 fatcat:2qplun5agrhddkucf7kq4nq7aq

A STUDY ON LIMITS TEACHING IN THE COLLEGE ANALYSIS MAJOR

Hye Young Oh
2014 Korean Journal of Mathematics  
In this study, we consider the informal and formal definition of limit on the basis of middle and high school curriculum, and then analyze the reason of difficulties experienced when sophomores learn the  ...  formal definition( -δ procedure) of limit.  ...  The objects of this research are sophomores of N university, who learn the formal definition of limit ( -δ procedure) first. The period of research was from the middle of March to April.  ... 
doi:10.11568/kjm.2014.22.1.169 fatcat:udmop6u4qvgbfpqvddnywnc3x4

Learning higher-order logic programs

Andrew Cropper, Rolf Morel, Stephen Muggleton
2019 Machine Learning  
A key feature of inductive logic programming is its ability to learn first-order programs, which are intrinsically more expressive than propositional programs.  ...  Specifically, we extend meta-interpretive learning (MIL) to support learning higher-order programs by allowing for higher-order definitions to be used as background knowledge.  ...  To extend MIL to support learning higher-order programs we introduce higher-order definitions: Definition 2 (Higher-order definition) A higher-order definition is a set of higher-order Horn clauses where  ... 
doi:10.1007/s10994-019-05862-7 fatcat:ppudvtskw5fwbkytc5bpgpdkm4

Ten Open Problems in Grammatical Inference [chapter]

Colin de la Higuera
2006 Lecture Notes in Computer Science  
They cover the areas of polynomial learning models, learning from ordered alphabets, learning deterministic Pomdps, learning negotiation processes, learning from context-free background knowledge.  ...  We propose 10 different open problems in the field of grammatical inference. In all cases, problems are theoretically oriented but correspond to practical questions.  ...  Acknowledgements Thanks to Jose Oncina for different discussions that led to several definitions and problems from sections 4 and 6.  ... 
doi:10.1007/11872436_4 fatcat:5snm4lpumbhw5e7ffh5vwxzhum
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