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1

Lubarsky, Robert S. "μ-definable sets of integers". Journal of Symbolic Logic 58, № 1 (1993): 291–313. http://dx.doi.org/10.2307/2275338.

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Inductive definability has been studied for some time already. Nonetheless, there are some simple questions that seem to have been overlooked. In particular, there is the problem of the expressibility of the μ-calculus.The μ-calculus originated with Scott and DeBakker [SD] and was developed by Hitchcock and Park [HP], Park [Pa], Kozen [K], and others. It is a language for including inductive definitions with first-order logic. One can think of a formula in first-order logic (with one free variable) as defining a subset of the universe, the set of elements that make it true. Then “and” correspo
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2

Bosch, Carlos, and Jan Kučera. "Closed bounded sets in inductive limits of $\Cal K$-spaces." Czechoslovak Mathematical Journal 43, no. 2 (1993): 221–23. http://dx.doi.org/10.21136/cmj.1993.128401.

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3

Bell, John L. "Finite sets and frege structures." Journal of Symbolic Logic 64, no. 4 (1999): 1552–56. http://dx.doi.org/10.2307/2586795.

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Call a family of subsets of a set E inductive if and is closed under unions with disjoint singletons, that is, ifA Frege structure is a pair (E, ν) with ν a map to E whose domain dom(ν) is an inductive family of subsets of E such thatIn [2] it is shown in a constructive setting that each Frege structure determines a subset which is the domain of a model of Peano's axioms. In this note we establish, within the same constructive setting, three facts. First, we show that the least inductive family of subsets of a set E is precisely the family of decidable Kuratowski finite subsets of E. Secondly,
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CURI, GIOVANNI. "ABSTRACT INDUCTIVE AND CO-INDUCTIVE DEFINITIONS." Journal of Symbolic Logic 83, no. 2 (2018): 598–616. http://dx.doi.org/10.1017/jsl.2018.13.

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AbstractIn [G. Curi, On Tarski’s fixed point theorem. Proc. Amer. Math. Soc., 143 (2015), pp. 4439–4455], a notion of abstract inductive definition is formulated to extend Aczel’s theory of inductive definitions to the setting of complete lattices. In this article, after discussing a further extension of the theory to structures of much larger size than complete lattices, as the class of all sets or the class of ordinals, a similar generalization is carried out for the theory of co-inductive definitions on a set. As a corollary, a constructive version of the general form of Tarski’s fixed poin
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ARCISZEWSKI, TOMASZ, and WOJCIECH ZIARKO. "Inductive Learning in Civil Engineering: Rough Sets Approach." Computer-Aided Civil and Infrastructure Engineering 5, no. 1 (2008): 19–28. http://dx.doi.org/10.1111/j.1467-8667.1990.tb00038.x.

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6

Dybjer, Peter. "A general formulation of simultaneous inductive-recursive definitions in type theory." Journal of Symbolic Logic 65, no. 2 (2000): 525–49. http://dx.doi.org/10.2307/2586554.

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AbstractThe first example of a simultaneous inductive-recursive definition in intuitionistic type theory is Martin-Löfs universe à la Tarski. A set U0of codes for small sets is generated inductively at the same time as a function T0, which maps a code to the corresponding small set, is defined by recursion on the way the elements of U0are generated.In this paper we argue that there is an underlyinggeneralnotion of simultaneous inductive-recursive definition which is implicit in Martin-Löf's intuitionistic type theory. We extend previously given schematic formulations of inductive definitions i
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7

Zanger, Daniel Z. "Talagrand’s inductive method and isoperimetric inequalities involving random sets." Statistics & Probability Letters 78, no. 7 (2008): 861–68. http://dx.doi.org/10.1016/j.spl.2007.09.012.

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8

Korobeĭnik, Yu F. "INDUCTIVE AND PROJECTIVE TOPOLOGIES. SUFFICIENT SETS AND REPRESENTING SYSTEMS." Mathematics of the USSR-Izvestiya 28, no. 3 (1987): 529–54. http://dx.doi.org/10.1070/im1987v028n03abeh000896.

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9

Alexandru, Andrei, and Gabriel Ciobanu. "Fuzzy Results for Finitely Supported Structures." Mathematics 9, no. 14 (2021): 1651. http://dx.doi.org/10.3390/math9141651.

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We present a survey of some results published recently by the authors regarding the fuzzy aspects of finitely supported structures. Considering the notion of finite support, we introduce a new degree of membership association between a crisp set and a finitely supported function modelling a degree of membership for each element in the crisp set. We define and study the notions of invariant set, invariant complete lattices, invariant monoids and invariant strong inductive sets. The finitely supported (fuzzy) subgroups of an invariant group, as well as the L-fuzzy sets on an invariant set (with
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10

LUMSDAINE, PETER LEFANU, and MICHAEL SHULMAN. "Semantics of higher inductive types." Mathematical Proceedings of the Cambridge Philosophical Society 169, no. 1 (2019): 159–208. http://dx.doi.org/10.1017/s030500411900015x.

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AbstractHigher inductive typesare a class of type-forming rules, introduced to provide basic (and not-so-basic) homotopy-theoretic constructions in a type-theoretic style. They have proven very fruitful for the “synthetic” development of homotopy theory within type theory, as well as in formalising ordinary set-level mathematics in type theory. In this paper, we construct models of a wide range of higher inductive types in a fairly wide range of settings.We introduce the notion ofcell monad with parameters: a semantically-defined scheme for specifying homotopically well-behaved notions of stru
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11

Pham, D. T., and S. S. Dimov. "An algorithm for incremental inductive learning." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 211, no. 3 (1997): 239–49. http://dx.doi.org/10.1243/0954405971516239.

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This paper describes RULES-4, a new algorithm for incremental inductive learning from the ‘RULES’ family of automatic rule extraction systems. This algorithm is the first incremental learning system in the family. It has a number of advantages over well-known non-incremental schemes. It allows the stored knowledge to be updated and refined rapidly when new examples are available. The induction of rules for a process planning expert system is used to illustrate the operation of RULES-4 and a bench-mark pattern classification problem employed to test the algorithm. The results obtained have show
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12

Taskovic, Milan R. "The Axiom of Choice, Fixed Point Theorems, and Inductive Ordered Sets." Proceedings of the American Mathematical Society 116, no. 4 (1992): 897. http://dx.doi.org/10.2307/2159465.

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13

Takagi, Tomohiro, Atsushi Imura, Hirohide Ushida, and Toru Yamaguchi. "Conceptual fuzzy sets as a meaning representation and their inductive construction." International Journal of Intelligent Systems 10, no. 11 (1995): 929–45. http://dx.doi.org/10.1002/int.4550101102.

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14

Taskovi{ć, Milan R. "The axiom of choice, fixed point theorems, and inductive ordered sets." Proceedings of the American Mathematical Society 116, no. 4 (1992): 897. http://dx.doi.org/10.1090/s0002-9939-1992-1111224-8.

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15

Spreen, Dieter. "Computing with continuous objects: a uniform co-inductive approach." Mathematical Structures in Computer Science 31, no. 2 (2021): 144–92. http://dx.doi.org/10.1017/s0960129521000116.

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AbstractA uniform approach to computing with infinite objects like real numbers, tuples of these, compacts sets and uniformly continuous maps is presented. In the work of Berger, it was shown how to extract certified algorithms working with the signed digit representation from constructive proofs. Berger and the present author generalised this approach to complete metric spaces and showed how to deal with compact sets. Here, we unify this work and lay the foundations for doing a similar thing for the much more comprehensive class of compact Hausdorff spaces occurring in applications. The appro
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Pham, D. T., and A. A. Afify. "Rules-6: A Simple Rule Induction Algorithm for Handling Large Data Sets." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 219, no. 10 (2005): 1119–37. http://dx.doi.org/10.1243/095440605x31931.

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RULES-3 Plus is a member of the RULES family of simple inductive learning algorithms with successful engineering applications. However, it requires modification in order to be a practical tool for problems involving large data sets. In particular, efficient mechanisms are needed for handling continuous attributes and noisy data. This article presents a new rule induction algorithm called RULES-6, which is derived from the RULES-3 Plus algorithm. The algorithm employs a fast and noise-tolerant search method for extracting IF-THEN rules from examples. It also uses simple and effective methods fo
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BRUNI, RICCARDO. "A NOTE ON THEORIES FOR QUASI-INDUCTIVE DEFINITIONS." Review of Symbolic Logic 2, no. 4 (2009): 684–99. http://dx.doi.org/10.1017/s175502030909025x.

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This paper introduces theories for arithmeticalquasi-inductive definitions(Burgess, 1986) as it has been done for first-order monotone and nonmonotone inductive ones. After displaying the basic axiomatic framework, we provide some initial result in the proof theoretic bounds line of research (the upper one being given in terms of a theory of sets extending Kripke–Platek set theory).
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MORRIS, PETER, THORSTEN ALTENKIRCH, and NEIL GHANI. "A UNIVERSE OF STRICTLY POSITIVE FAMILIES." International Journal of Foundations of Computer Science 20, no. 01 (2009): 83–107. http://dx.doi.org/10.1142/s0129054109006462.

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In order to represent, compute and reason with advanced data types like lists with a fixed length, finite sets or well scoped λ-terms one must go beyond the traditional treatment of data types as being inductive types and, instead, consider them as inductive families, or more precisely Strictly Positive Families (SPFs). We have previously shown that the grammar of strictly positive types (SPT) can be given as an inductively defined family. In the present paper we go one step further an show that the universe of SPFs can be encoded as an SPF. We show that SPFs can be used to represent and compu
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19

Cascio, M. Ariel, Eunlye Lee, Nicole Vaudrin, and Darcy A. Freedman. "A Team-based Approach to Open Coding: Considerations for Creating Intercoder Consensus." Field Methods 31, no. 2 (2019): 116–30. http://dx.doi.org/10.1177/1525822x19838237.

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In this article, we discuss methodological opportunities related to using a team-based approach for iterative-inductive analysis of qualitative data involving detailed open coding of semistructured interviews and focus groups. Iterative-inductive methods generate rich thematic analyses useful in sociology, anthropology, public health, and many other applied fields. A team-based approach to analyzing qualitative data increases confidence in dependability and trustworthiness, facilitates analysis of large data sets, and supports collaborative and participatory research by including diverse stake
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20

Charalambous, Michael G., and Vitalij A. Chatyrko. "Some estimates of the inductive dimensions of the union of two sets." Topology and its Applications 146-147 (January 2005): 227–38. http://dx.doi.org/10.1016/j.topol.2003.02.010.

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21

Pham, D. T., S. Bigot, and S. S. Dimov. "A rule merging technique for handling noise in inductive learning." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 218, no. 10 (2004): 1255–68. http://dx.doi.org/10.1243/0954406042369017.

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Inductive learning algorithms are used for extracting IF-THEN rules from examples. The main weakness of most existing algorithms is their poor ability to handle data containing noise. This problem is even more severe when inductive learning techniques are applied to real engineering data. The paper presents a new pruning technique that improves significantly the performance of the RULES family of inductive learning algorithms. The technique is designed for RULES-5, the latest algorithm in the family, but could readily be applied to rule sets created by other algorithms.
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22

GYLTERUD, HÅKON ROBBESTAD. "FROM MULTISETS TO SETS IN HOMOTOPY TYPE THEORY." Journal of Symbolic Logic 83, no. 3 (2018): 1132–46. http://dx.doi.org/10.1017/jsl.2017.84.

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AbstractWe give a model of set theory based on multisets in homotopy type theory. The equality of the model is the identity type. The underlying type of iterative sets can be formulated in Martin-Löf type theory, without Higher Inductive Types (HITs), and is a sub-type of the underlying type of Aczel’s 1978 model of set theory in type theory. The Voevodsky Univalence Axiom and mere set quotients (a mild kind of HITs) are used to prove the axioms of constructive set theory for the model. We give an equivalence to the model provided in Chapter 10 of “Homotopy Type Theory” by the Univalent Founda
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23

LAW, MARK, ALESSANDRA RUSSO, and KRYSIA BRODA. "Learning weak constraints in answer set programming." Theory and Practice of Logic Programming 15, no. 4-5 (2015): 511–25. http://dx.doi.org/10.1017/s1471068415000198.

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AbstractThis paper contributes to the area of inductive logic programming by presenting a new learning framework that allows the learning of weak constraints in Answer Set Programming (ASP). The framework, calledLearning from Ordered Answer Sets, generalises our previous work on learning ASP programs without weak constraints, by considering a new notion of examples asorderedpairs of partial answer sets that exemplify which answer sets of a learned hypothesis (together with a given background knowledge) arepreferredto others. In this new learning task inductive solutions are searched within a h
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24

Branagh, Wayne, Huinan Yu, and Eric D. Salin. "Comparison of Pattern Recognition Techniques for Sample Classification Using Elemental Composition: Applications for ICP-AES." Applied Spectroscopy 49, no. 7 (1995): 964–70. http://dx.doi.org/10.1366/0003702953964688.

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Pattern recognition is very important for many aspects of data analysis and robotic control. Three pattern recognition techniques were examined— k-Nearest Neighbors, Bayesian analysis, and the C4.5 inductive learning algorithm. Their abilities to classify 71 different reference materials were compared. Each training and test example consisted of 79 different elemental concentrations. Different data sets were generated with relative standard deviations of 1, 3, 5, 10, 30, 100, and 500%. Each data set consisted of 2000 examples. These sets were used in both the training stages and in the test st
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25

Erné, Marcel. "Compact generation in partially ordered sets." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 42, no. 1 (1987): 69–83. http://dx.doi.org/10.1017/s1446788700033966.

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AbstractSeveral “classical” results on algebraic complete lattices extend to algebraic posets and, more generally, to so called compactly generated posets; but, of course, there may arise difficulties in the absence of certain joins or meets. For example, the property of weak atomicity turns out to be valid in all Dedekind complete compactly generated posets, but not in arbitrary algebraic posets. The compactly generated posets are, up to isomorphism, the inductive centralized systems, where a system of sets is called centralized if it contains all point closures. A similar representation theo
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Welch, P. D. "Determinacy in strong cardinal models." Journal of Symbolic Logic 76, no. 2 (2011): 719–28. http://dx.doi.org/10.2178/jsl/1305810772.

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AbstractWe give limits defined in terms of abstract pointclasses of the amount of determinacy available in certain canonical inner models involving strong cardinals. We show for example:Theorem A. Det(-IND) ⇒ there exists an inner model with a strong cardinal.Theorem B. Det(AQI) ⇒ there exist type-l mice and hence inner models with proper classes of strong cardinals.where -IND(AQI) is the pointclass of boldface -inductive (respectively arithmetically quasi-inductive) sets of reals.
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TABARES-OSPINA, HÉCTOR A., and MAURICIO OSORIO. "CHARACTERIZATION OF THE RESISTIVE AND INDUCTIVE LOADS OF AN ENERGY DISTRIBUTION SYSTEM WITH JULIA FRACTAL SETS." Fractals 28, no. 05 (2020): 2050082. http://dx.doi.org/10.1142/s0218348x20500826.

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The present paper characterizes the resistive and inductive loads of an electric distribution system by Julia fractal sets, in order to discover other observations enabling the elevation of new theoretical approaches. The result shows that indeed the electrical load reflects a clear graphic pattern in the fractal space of the Julia sets. This result, then, is a new contribution that extends the universal knowledge about fractal geometry.
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Badaev, Serikzhan A., and Steffen Lempp. "A decomposition of the Rogers semilattice of a family of d.c.e. sets." Journal of Symbolic Logic 74, no. 2 (2009): 618–40. http://dx.doi.org/10.2178/jsl/1243948330.

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AbstractKhutoretskii's Theorem states that the Rogers semilattice of any family of c.e. sets has either at most one or infinitely many elements. A lemma in the inductive step of the proof shows that no Rogers semilattice can be partitioned into a principal ideal and a principal filter. We show that such a partitioning is possible for some family of d.c.e. sets. In fact, we construct a family of c.e. sets which, when viewed as a family of d.c.e. sets, has (up to equivalence) exactly two computable Friedberg numberings μ and ν, and μ reduces to any computable numbering not equivalent to ν. The q
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Lian, Renzun, and Jin Pan. "Electromagnetic-Power-Based Modal Classification, Modal Expansion, and Modal Decomposition for Perfect Electric Conductors." International Journal of Antennas and Propagation 2018 (November 25, 2018): 1–17. http://dx.doi.org/10.1155/2018/5313590.

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Traditionally, all working modes of a perfect electric conductor are classified into capacitive modes, resonant modes, and inductive modes, and the resonant modes are further classified into internal resonant modes and external resonant modes. In this paper, the capacitive modes are further classified into intrinsically capacitive modes and nonintrinsically capacitive modes; the resonant modes are alternatively classified into intrinsically resonant modes, which are further classified into nonradiative intrinsically resonant modes and radiative intrinsically resonant modes, and nonintrinsicall
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Baxter, J. "A Model of Inductive Bias Learning." Journal of Artificial Intelligence Research 12 (March 1, 2000): 149–98. http://dx.doi.org/10.1613/jair.731.

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A major problem in machine learning is that of inductive bias: how to choose a learner's hypothesis space so that it is large enough to contain a solution to the problem being learnt, yet small enough to ensure reliable generalization from reasonably-sized training sets. Typically such bias is supplied by hand through the skill and insights of experts. In this paper a model for automatically learning bias is investigated. The central assumption of the model is that the learner is embedded within an environment of related learning tasks. Within such an environment the learner can sample from mu
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31

WU, XINDONG, JOHAN KRISÁR, and PETTER MÅHLÉN. "NOISE HANDLING WITH EXTENSION MATRICES." International Journal on Artificial Intelligence Tools 05, no. 01n02 (1996): 81–97. http://dx.doi.org/10.1142/s0218213096000067.

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HCV is a heuristic attribute-based induction algorithm based on the newly-developed extension matrix approach. By dividing the positive examples (PE) of a specific class in a given example set into intersecting groups and adopting a set of strategies to find a heuristic conjunctive formula in each group which covers all the group’s positive examples and none of the negative examples (NE), it can find a covering formula in the form of variable-valued logic for PE against NE in low-order polynomial time. The original algorithm performs quite well with those data sets where noise and continuous d
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WANG, FARN. "INDUCTIVE COMPOSITION OF NUMBERS WITH MAXIMUM, MINIMUM, AND ADDITION: A New Theory for Program Execution-Time Analysis." International Journal of Foundations of Computer Science 15, no. 06 (2004): 865–92. http://dx.doi.org/10.1142/s0129054104002790.

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We extend the classic work of R.J. Parikh on context-free languages with operators min and max on unary alphabet. The new theory is called CAN (Compositional Algebra of Numbers) and can be used to model software processes that can be concatenated, concurrently executed, and recursively invoked. We propose and analyze an algorithm which constructs the execution time sets of a CAN in semilinear form. Finally, we consider several interesting variations of CAN whose execution time sets can be constructed with algorithms.
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GHANI, NEIL, and PETER HANCOCK. "Containers, monads and induction recursion." Mathematical Structures in Computer Science 26, no. 1 (2014): 89–113. http://dx.doi.org/10.1017/s0960129514000127.

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Induction recursion offers the possibility of a clean, simple and yet powerful meta-language for the type system of a dependently typed programming language. At its crux, induction recursion allows us to define a universe, that is a setUofcodesand a decoding functionT : U → Dwhich assigns to every codeu : U, a valueT, uof some typeD, e.g.the large type Set of small types or sets. The name induction recursion refers to the build-up of codes inUusing inductive clauses, simultaneously with the definition of the functionT, by structural recursion on codes.Our contribution is to (i) bring out expli
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Khokhar, Khalid Mahmud, P. Hadley, and S. Pearson. "Effect of reciprocal transfers of onion sets between inductive and non-inductive temperatures on the incidence of bolting and bulbing and seed yield." Scientia Horticulturae 112, no. 3 (2007): 245–50. http://dx.doi.org/10.1016/j.scienta.2006.12.034.

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Wang, Shitong, and A. Gammermann. "Description of learning space based on interval fuzzy sets and fuzzy inductive learning algorithm ILA." Fuzzy Sets and Systems 103, no. 1 (1999): 83–89. http://dx.doi.org/10.1016/s0165-0114(97)00179-6.

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36

Deptuła, A., and M. A. Partyka. "Inductive Decision Tree Analysis of the Validity Rank of Construction Parameters of Innovative Gear Pump after Tooth Root Undercutting." International Journal of Applied Mechanics and Engineering 22, no. 1 (2017): 25–34. http://dx.doi.org/10.1515/ijame-2017-0002.

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Abstract The article presents an innovative use of inductive algorithm for generating the decision tree for an analysis of the rank validity parameters of construction and maintenance of the gear pump with undercut tooth. It is preventet an alternative way of generating sets of decisions and determining the hierarchy of decision variables to existing the methods of discrete optimization.
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Mohanty, Alok Kumar, and K. B. Yadav. "Performance Characteristics of Six-Phase Induction Generator for Renewable Power Generation." Indonesian Journal of Electrical Engineering and Computer Science 5, no. 2 (2017): 299. http://dx.doi.org/10.11591/ijeecs.v5.i2.pp299-308.

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<p>This paper presents the performance behavior of a multi-phase induction generator operating in six-phase mode. An experimental analysis has been done to determine operating characteristics of the six-phase machine to illustrate the advantageous features of the machine as compared to its three phase counterpart. The machine is configured to operate as a standalone power source in conjunction with a DC prime mover. The multi-phase machine can operate with one three phase capacitor bank which does not lead to complete shutdown of the system during fault conditions across one of its two s
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Nienhuys-Cheng, S. H. "Least Generalizations and Greatest Specializations of Sets of Clauses." Journal of Artificial Intelligence Research 4 (May 1, 1996): 341–63. http://dx.doi.org/10.1613/jair.259.

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The main operations in Inductive Logic Programming (ILP) are generalization and specialization, which only make sense in a generality order. In ILP, the three most important generality orders are subsumption, implication and implication relative to background knowledge. The two languages used most often are languages of clauses and languages of only Horn clauses. This gives a total of six different ordered languages. In this paper, we give a systematic treatment of the existence or non-existence of least generalizations and greatest specializations of finite sets of clauses in each of these si
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DEELEY, ROBIN J., and ALLAN YASHINSKI. "The stable algebra of a Wieler solenoid: inductive limits and -theory." Ergodic Theory and Dynamical Systems 40, no. 10 (2019): 2734–68. http://dx.doi.org/10.1017/etds.2019.17.

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Wieler has shown that every irreducible Smale space with totally disconnected stable sets is a solenoid (i.e., obtained via a stationary inverse limit construction). Using her construction, we show that the associated stable $C^{\ast }$-algebra is the stationary inductive limit of a $C^{\ast }$-stable Fell algebra that has a compact spectrum and trivial Dixmier–Douady invariant. This result applies in particular to Williams solenoids along with other examples. Beyond the structural implications of this inductive limit, one can use this result to, in principle, compute the $K$-theory of the sta
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QIAN, GUOLIANG, DANIEL YEUNG, ERIC C. C. TSANG, and WENHAO SHU. "FEATURE SELECTION FOR CHINESE CHARACTER RECOGNITION BASED ON INDUCTIVE LEARNING." International Journal of Pattern Recognition and Artificial Intelligence 18, no. 08 (2004): 1453–71. http://dx.doi.org/10.1142/s0218001404003836.

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Feature selection is a difficult but important issue in the field of machine learning and pattern recognition. In this paper, features for Chinese character recognition are selected by using inductive learning algorithms. The existing inductive learning method based on extension matrix requires precise consistency between positive example and negative example sets, which is very difficult to maintain in most practical cases. The traditional decision tree algorithm ID3 considers only the performance of the discriminating power while selecting features. However, in actual practice the considerat
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Pytela, Oldřich, and Aleš Halama. "Chemometric Analysis of Substituent Effects. VII. Inductive Effect as a Basic Substituent Effect. Isoeffect Substituent Constant." Collection of Czechoslovak Chemical Communications 60, no. 8 (1995): 1316–32. http://dx.doi.org/10.1135/cccc19951316.

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The paper deals with chemometric analysis of the inductive effect. The notion of inductive effect is discussed, and unambiguous definitions are given for the notions of triad: reaction centre-basic skeleton-substituent, and the therewith connected definitions of inductive effect. For a quantitative description of inductive effect 7 types of chemical models were selected including noncyclic compounds, cyclic, and bicyclic compounds, derivatives of quinuclidine, 3-substituted benzoic acids, sulfonamides and pyridines. Altogether 139 sets of experimental data from literature have been used includ
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Cropper, Andrew, and Sophie Tourret. "Logical reduction of metarules." Machine Learning 109, no. 7 (2019): 1323–69. http://dx.doi.org/10.1007/s10994-019-05834-x.

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AbstractMany forms of inductive logic programming (ILP) use metarules, second-order Horn clauses, to define the structure of learnable programs and thus the hypothesis space. Deciding which metarules to use for a given learning task is a major open problem and is a trade-off between efficiency and expressivity: the hypothesis space grows given more metarules, so we wish to use fewer metarules, but if we use too few metarules then we lose expressivity. In this paper, we study whether fragments of metarules can be logically reduced to minimal finite subsets. We consider two traditional forms of
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Binyamini, Gal, and Dmitry Novikov. "The Pila–Wilkie theorem for subanalytic families: a complex analytic approach." Compositio Mathematica 153, no. 10 (2017): 2171–94. http://dx.doi.org/10.1112/s0010437x17007333.

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We present a complex analytic proof of the Pila–Wilkie theorem for subanalytic sets. In particular, we replace the use of $C^{r}$-smooth parametrizations by a variant of Weierstrass division. As a consequence we are able to apply the Bombieri–Pila determinant method directly to analytic families without limiting the order of smoothness by a $C^{r}$ parametrization. This technique provides the key inductive step for our recent proof (in a closely related preprint) of the Wilkie conjecture for sets definable using restricted elementary functions. As an illustration of our approach we prove that
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Sun, Yu Di. "Region Analogy-Based Quantization Method for Numerical Data." Advanced Materials Research 989-994 (July 2014): 1743–46. http://dx.doi.org/10.4028/www.scientific.net/amr.989-994.1743.

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Data quantization methods for numerical attributes play an extremely important role in handy talents statistics assessment and technology learning because discrete values of attributes are required in most classification methods. In this paper, we present an region analogy-based quantization method for numerical data. It expresses an inner coherence criterion which is thought to be as a new criterion in the ways of quantization. In addition, a heuristic quantization algorithm is proposed to achieve a satisfying quantization result with the aim to improve the performance of inductive learning a
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45

Blockeel, H., L. Dehaspe, B. Demoen, G. Janssens, J. Ramon, and H. Vandecasteele. "Improving the Efficiency of Inductive Logic Programming Through the Use of Query Packs." Journal of Artificial Intelligence Research 16 (February 1, 2002): 135–66. http://dx.doi.org/10.1613/jair.924.

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Inductive logic programming, or relational learning, is a powerful paradigm for machine learning or data mining. However, in order for ILP to become practically useful, the efficiency of ILP systems must improve substantially. To this end, the notion of a query pack is introduced: it structures sets of similar queries. Furthermore, a mechanism is described for executing such query packs. A complexity analysis shows that considerable efficiency improvements can be achieved through the use of this query pack execution mechanism. This claim is supported by empirical results obtained by incorporat
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Tabares-Ospina, Hector A., John E. Candelo-Becerra, and Fredy E. Hoyos Velasco. "Fractal representation of the power demand based on topological properties of julia sets." International Journal of Electrical and Computer Engineering (IJECE) 9, no. 4 (2019): 2831. http://dx.doi.org/10.11591/ijece.v9i4.pp2831-2839.

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In a power system, the load demand considers two components such as the real power (P) because of resistive elements, and the reactive power (Q) because inductive or capacitive elements. This paper presents a graphical representation of the electric power demand based on the topological properties of the Julia Sets, with the purpose of observing the different graphic patterns and relationship with the hourly load consumptions. An algorithm that iterates complex numbers related to power is used to represent each fractal diagram of the load demand. The results show some representative patterns r
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MORDESON, JOHN N., TERRY D. CLARK, ADAM D. GRIESER, and MARK J. WIERMAN. "AN INDUCTIVE APPROACH TO DETERMINING CAUSALITY IN COMPARATIVE POLITICS: A FUZZY SET ALTERNATIVE." New Mathematics and Natural Computation 03, no. 02 (2007): 191–202. http://dx.doi.org/10.1142/s1793005707000719.

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Political science typically tests hypotheses by demonstrating correlations between variables. The most commonly employed method for doing so is regression analysis. The approach is essentially crisp, which carries with it a number of questionable assumptions about the data. Political phenomena such as democracy or stability often involve measuring the degree to which a particular observation demonstrates the qualities of the category. A fuzzy set approach better captures the inherent ambiguity in classifying our observations relative to such categories. However, the attempt to establish correl
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Vermeulen, J. J. C. "A note on iterative arguments in a topos." Mathematical Proceedings of the Cambridge Philosophical Society 111, no. 1 (1992): 57–62. http://dx.doi.org/10.1017/s0305004100075150.

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Intuitively, transfinite iteration is a repetitive process, which eventually reaches completion, but might need to progress through an infinite chain of steps before finally doing so. But whereas such a chain is always readily at hand in classical set theory in the form of ordinals, iterative arguments involving sets (i.e. objects) in a general topos have to depend on some intrinsic or naturally available inductive structure, say algebraic, which might not be associated with a (well-ordered) chain.
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De Groote, Anne, Manuel Paiva, and Yves Verbandt. "Mathematical assessment of qualitative diagnostic calibration for respiratory inductive plethysmography." Journal of Applied Physiology 90, no. 3 (2001): 1025–30. http://dx.doi.org/10.1152/jappl.2001.90.3.1025.

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We present a critical assessment of qualitative diagnostic calibration (QDC), which claims to provide a relative calibration of respiratory inductive plethysmography during natural breathing (Sackner MA, Watson H, Belsito AS, Feinerman D, Suarez M, Gonzalez G, Bizousky F, and Krieger B. J Appl Physiol 66: 410–420, 1989). QDC computes the calibration factor ( K) by considering breaths of constant tidal volume (Vt) and provides a criterion to select breaths when Vt is unknown. We applied QDC on uncalibrated data constructed from simulated sets of thoracic and abdominal volumes, with a predefined
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HASSANIEN, ABOUL ELLA. "INTELLIGENT DATA ANALYSIS OF BREAST CANCER BASED ON ROUGH SET THEORY." International Journal on Artificial Intelligence Tools 12, no. 04 (2003): 465–79. http://dx.doi.org/10.1142/s0218213003001319.

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Extensive amounts of knowledge and data stored in medical databases require the development of specialized tools for storing, accessing, analysis, and effectiveness usage of stored knowledge and data. Intelligent methods such as neural networks, fuzzy sets, decision trees, and expert systems are, slowly but steadily, applied in the medical fields. Recently, rough set theory is a new intelligent technique was used for the discovery of data dependencies, data reduction, approximate set classification, and rule induction from databases.In this paper, we present a rough set method for generating c
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