Above are papers related to the following paper: [Paper_ID] Paper #151430. 	[Title] Pac-Learning Recursive Logic Programs: Efficient Algorithms [Abstract] We present algorithms that learn certain classes of function-free recursive logic programs in polynomial time from equivalence queries. In particular, we show that a single k-ary recursive constant-depth determinate clause is learnable. Two-clause programs consisting of one learnable recursive clause and one constant-depth determinate non-recursive clause are also learnable, if an additional "basecase" oracle is assumed. These results immediately imply the pac-learnability of these classes. Although these classes of learnable recursive programs are very constrained, it is shown in a companion paper that they are maximally general, in that generalizing either class in any natural way leads to a compu-tationally difficult learning problem. Thus, taken together with its companion paper, this paper establishes a boundary of efficient learnability for recursive logic programs. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #6917. 	[Title] Covering vs. Divide-and-Conquer for Top-Down Induction of Logic Programs [Abstract] covering has been formalized and used extensively. In this work, the divide-and-conquer technique is formalized as well and compared to the covering technique in a logic programming framework. Covering works by repeatedly specializing an overly general hypothesis, on each iteration focusing on finding a clause with a high coverage of positive examples. Divide-and-conquer works by specializing an overly general hypothesis once, focusing on discriminating positive from negative examples. Experimental results are presented demonstrating that there are cases when more accurate hypotheses can be found by divide-and-conquer than by covering. Moreover, since covering considers the same alternatives repeatedly it tends to be less efficient than divide-and-conquer, which never considers the same alternative twice. On the other hand, covering searches a larger hypothesis space, which may result in that more compact hypotheses are found by this technique than by divide-and-conquer. Furthermore, divide-and-conquer is, in contrast to covering, not applicable to learn ing recursive definitions. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1061127. 	[Title] Applications of machine learning: a medical follow up study [Abstract] This paper describes preliminary work that aims to apply some learning strategies to a medical follow-up study. An investigation of the application of three machine learning algorithms-1R, FOIL and InductH to identify risk factors that govern the colposuspension cure rate has been made. The goal of this study is to induce a generalised description or explanation of the classification attribute, colposuspension cure rate (completely cured, improved, unchanged and worse) from the 767 examples in the questionnaires. We looked for a set of rules that described which risk factors result in differences of cure rate. The results were encouraging, and indicate that machine learning can play a useful role in large scale medical problem solving. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #2440. 	[Title] Quinlan, 1990 J.R. Quinlan. Learning logical definitions from relations. Machine Learning, First-order theory revision. In [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1120650. 	[Title] Bottom-up induction of logic programs with more than one recursive clause [Abstract] In this paper we present a bottom-up algorithm called MRI to induce logic programs from their examples. This method can induce programs with a base clause and more than one recursive clause from a very small number of examples. MRI is based on the analysis of saturations of examples. It first generates a path structure, which is an expression of a stream of values processed by predicates. The concept of path structure was originally introduced by Identam-Almquist and used in TIM [ Idestam-Almquist, 1996 ] . In this paper, we introduce the concepts of extension and difference of path structure. Recursive clauses can be expressed as a difference between a path structure and its extension. The paper presents the algorithm and shows experimental results obtained by the method. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #6923. 	[Title] Inductive Constraint Logic [Abstract] A novel approach to learning first order logic formulae from positive and negative examples is presented. Whereas present inductive logic programming systems employ examples as true and false ground facts (or clauses), we view examples as interpretations which are true or false for the target theory. This viewpoint allows to reconcile the inductive logic programming paradigm with classical attribute value learning in the sense that the latter is a special case of the former. Because of this property, we are able to adapt AQ and CN2 type algorithms in order to enable learning of full first order formulae. However, whereas classical learning techniques have concentrated on concept representations in disjunctive normal form, we will use a clausal representation, which corresponds to a conjuctive normal form where each conjunct forms a constraint on positive examples. This representation duality reverses also the role of positive and negative examples, both in the heuristics and in the algorithm. The resulting theory is incorporated in a system named ICL (Inductive Constraint Logic). Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1114512. 	[Title] Integrity Constraints in ILP using a Monte Carlo approach [Abstract] Many state-of-the-art ILP systems require large numbers of negative examples to avoid overgeneralization. This is a considerable disadvantage for many ILP applications, namely indu ctive program synthesis where relativelly small and sparse example sets are a more realistic scenario. Integrity constraints are first order clauses that can play the role of negative examples in an inductive process. One integrity constraint can replace a long list of ground negative examples. However, checking the consistency of a program with a set of integrity constraints usually involves heavy the orem-proving. We propose an efficient constraint satisfaction algorithm that applies to a wide variety of useful integrity constraints and uses a Monte Carlo strategy. It looks for inconsistencies by ra ndom generation of queries to the program. This method allows the use of integrity constraints instead of (or together with) negative examples. As a consequence programs to induce can be specified more rapidly by the user and the ILP system tends to obtain more accurate definitions. Average running times are not greatly affected by the use of integrity constraints compared to ground negative examples. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #49811. 	[Title] Estimating the Accuracy of Learned Concepts [Abstract] This paper investigates alternative estimators of the accuracy of concepts learned from examples. In particular, the cross-validation and 632 bootstrap estimators are studied, using synthetic training data and the foil learning algorithm. Our experimental results contradict previous papers in statistics, which advocate the 632 bootstrap method as superior to cross-validation. Nevertheless, our results also suggest that conclusions based on cross-validation in previous machine learning papers are unreliable. Specifically, our observations are that (i) the true error of the concept learned by foil from independently drawn sets of examples of the same concept varies widely, (ii) the estimate of true error provided by cross-validation has high variability but is approximately unbiased, and (iii) the 632 bootstrap estimator has lower variability than cross-validation, but is systematically biased. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1115670. 	[Title] Which Hypotheses Can Be Found with Inverse Entailment? -Extended Abstract [Abstract] In this paper we give a completeness theorem of an inductive inference rule inverse entailment proposed by Muggleton. Our main result is that a hypothesis clause H can be derived from an example E under a background theory B with inverse entailment iff H subsumes E relative to B in Plotkin's sense. The theory B can be any clausal theory, and the example E can be any clause which is neither a tautology nor implied by B. The derived hypothesis H is a clause which is not always definite. In order to prove the result we give declarative semantics for arbitrary consistent clausal theories, and show that SB-resolution, which was originally introduced by Plotkin, is complete procedural semantics. The completeness is shown as an extension of the completeness theorem of SLD-resolution. We also show that every hypothesis H derived with saturant generalization, proposed by Rouveirol, must subsume E w.r.t. B in Buntine's sense. Moreover we show that saturant generalization can be obtained from inverse entailment by giving some restriction to its usage. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #6935. 	[Title] Inverse entailment and Progol [Abstract] This paper firstly provides a re-appraisal of the development of techniques for inverting deduction, secondly introduces Mode-Directed Inverse Entailment (MDIE) as a generalisation and enhancement of previous approaches and thirdly describes an implementation of MDIE in the Progol system. Progol is implemented in C and available by anonymous ftp. The re-assessment of previous techniques in terms of inverse entailment leads to new results for learning from positive data and inverting implication between pairs of clauses. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1107095. 	[Title] ILP with Noise and Fixed Example Size: A Bayesian Approach [Abstract] Current inductive logic programming systems are limited in their handling of noise, as they employ a greedy covering approach to constructing the hypothesis one clause at a time. This approach also causes difficulty in learning recursive predicates. Additionally, many current systems have an implicit expectation that the cardinality of the positive and negative examples reflect the "proportion" of the concept to the instance space. A framework for learning from noisy data and fixed example size is presented. A Bayesian heuristic for finding the most probable hypothesis in this general framework is derived. This approach evaluates a hypothesis as a whole rather than one clause at a time. The heuristic, which has nice theoretical properties, is incorporated in an ILP system, Lime. Experimental results show that Lime handles noise better than FOIL and PROGOL. It is able to learn recursive definitions from noisy data on which other systems do not perform well. Lime is also capable of learning from only positive data and also from only negative data. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1110426. 	[Title] Incremental Reduced Error Pruning [Abstract] This paper outlines some problems that may occur with Reduced Error Pruning in relational learning algorithms, most notably efficiency. Thereafter a new method, Incremental Reduced Error Pruning, is proposed that attempts to address all of these problems. Experiments show that in many noisy domains this method is much more efficient than alternative algorithms, along with a slight gain in accuracy. However, the experiments show as well that the use of the algorithm cannot be recommended for domains which require a very specific concept description. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #101662. 	[Title] Learning from positive data [Abstract] Gold showed in 1967 that not even regular grammars can be exactly identified from positive examples alone. Since it is known that children learn natural grammars almost exclusively from positives examples, Gold's result has been used as a theoretical support for Chomsky's theory of innate human linguistic abilities. In this paper new results are presented which show that within a Bayesian framework not only grammars, but also logic programs are learnable with arbitrarily low expected error from positive examples only. In addition, we show that the upper bound for expected error of a learner which maximises the Bayes' posterior probability when learning from positive examples is within a small additive term of one which does the same from a mixture of positive and negative examples. An Inductive Logic Programming implementation is described which avoids the pitfalls of greedy search by global optimisation of this function during the local construction of individual clauses of the hypothesis. Results of testing this implementation on artificially-generated data-sets are reported. These results are in agreement with the theoretical predictions. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #591016. 	[Title] First Order Regression: Applications in Real-World Domains [Abstract] A first order regression algorithm capable of handling real-valued (continuous) variables is introduced and some of its applications are presented. Regressional learning assumes real-valued class and discrete or real-valued variables. The algorithm combines regressional learning with standard ILP concepts, such as first order concept description and background knowledge. A clause is generated by successively refining the initial clause by adding literals of the form A = v for the discrete attributes, A v and A v for the real-valued attributes, and background knowledge literals to the clause body. The algorithm employs a covering approach (beam search), a heuristic impurity function, and stopping criteria based on local improvement, minimum number of examples, maximum clause length, minimum local improvement, minimum description length, allowed error, and variable depth. An outline of the algorithm and the results of the system's application in some artificial and real-world domains are presented. The real-world domains comprise: modelling of the water behavior in a surge tank, modelling of the workpiece roughness in a steel grinding process and modelling of the operator's behavior during the process of electrical discharge machining. Special emphasis is given to the evaluation of obtained models by domain experts and their comments on the aspects of practical use of the induced knowledge. The results obtained during the knowledge acquisition process show several important guidelines for knowledge acquisition, concerning mainly the process of interaction with domain experts, exposing primarily the importance of comprehensibility of the induced knowledge. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #591017. 	[Title] Producing More Comprehensible Models While Retaining Their Performance [Abstract] Rissanen's Minimum Description Length (MDL) principle is adapted to handle continuous attributes in the Inductive Logic Programming setting. Application of the developed coding as a MDL pruning mechanism is devised. The behavior of the MDL pruning is tested in a synthetic domain with artificially added noise of different levels and in two real life problems | modelling of the surface roughness of a grinding workpiece and modelling of the mutagenicity of nitroaromatic compounds. Results indicate that MDL pruning is a successful parameter-free noise fighting tool in real-life domains since it acts as a safeguard against building too complex models while retaining the accuracy of the model. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #212777. 	[Title] Inductive Learning of Characteristic Concept Descriptions from Small Sets of Classified Examples [Abstract] This paper presents a novel idea to the problem of learning concept descriptions from examples. Whereas most existing approaches rely on a large number of classified examples, the approach presented in the paper is aimed at being applicable when only a few examples are classified as positive (and negative) instances of a concept. The approach tries to take advantage of the information which can be induced from descriptions of unclassified objects using a conceptual clustering algorithm. The system Cola is described and results of applying Cola in two real-world domains are presented. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1153064. 	[Title] Stochastic Logic Programs [Abstract] One way to represent a machine learning algorithm's bias over the hypothesis and instance space is as a pair of probability distributions. This approach has been taken both within Bayesian learning schemes and the framework of U-learnability. However, it is not obvious how an Inductive Logic Programming (ILP) system should best be provided with a probability distribution. This paper extends the results of a previous paper by the author which introduced stochastic logic programs as a means of providing a structured definition of such a probability distribution. Stochastic logic programs are a generalisation of stochastic grammars. A stochastic logic program consists of a set of labelled clauses p : C where p is from the interval [0; 1] and C is a range-restricted definite clause. A stochastic logic program P has a distributional semantics, that is one which assigns a probability distribution to the atoms of each predicate in the Herbrand base of the clauses in P . These probabilities are assigned to atoms according to an SLD-resolution strategy which employs a stochastic selection rule. It is shown that the probabilities can be computed directly for fail-free logic programs and by normalisation for arbitrary logic programs. The stochastic proof strategy can be used to provide three distinct functions: 1) a method of sampling from the Herbrand base which can be used to provide selected targets or example sets for ILP experiments, 2) a measure of the information content of examples or hypotheses; this can be used to guide the search in an ILP system and 3) a simple method for conditioning a given stochastic logic program on samples of data. Functions 1) and 3) are used to measure the generality of hypotheses in the ILP system Progol4.2. This supports an implementation of a Bayesian technique for learning from positive examples only. fl This paper is an extension of a paper with the same title which appeared in [12] Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #49843. 	[Title] Fossil: A Robust Relational Learner [Abstract] The research reported in this paper describes Fossil, an ILP system that uses a search heuristic based on statistical correlation. This algorithm implements a new method for learning useful concepts in the presence of noise. In contrast to Foil's stopping criterion, which allows theories to grow in complexity as the size of the training sets increases, we propose a new stopping criterion that is independent of the number of training examples. Instead, Fossil's stopping criterion depends on a search heuristic that estimates the utility of literals on a uniform scale. In addition we outline how this feature can be used for top-down pruning and present some preliminary results. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #49844. 	[Title] A Comparison of Pruning Methods for Relational Concept Learning [Abstract] Pre-Pruning and Post-Pruning are two standard methods of dealing with noise in concept learning. Pre-Pruning methods are very efficient, while Post-Pruning methods typically are more accurate, but much slower, because they have to generate an overly specific concept description first. We have experimented with a variety of pruning methods, including two new methods that try to combine and integrate pre- and post-pruning in order to achieve both accuracy and efficiency. This is verified with test series in a chess position classification task. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #101811. 	[Title] Programming Research Group A LEARNABILITY MODEL FOR UNIVERSAL REPRESENTATIONS [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #49847. 	[Title] Top-Down Pruning in Relational Learning [Abstract] Pruning is an effective method for dealing with noise in Machine Learning. Recently pruning algorithms, in particular Reduced Error Pruning, have also attracted interest in the field of Inductive Logic Programming. However, it has been shown that these methods can be very inefficient, because most of the time is wasted for generating clauses that explain noisy examples and subsequently pruning these clauses. We introduce a new method which searches for good theories in a top-down fashion to get a better starting point for the pruning algorithm. Experiments show that this approach can significantly lower the complexity of the task without losing predictive accuracy. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #18615. 	[Title] Learning Trees and Rules with Set-valued Features [Abstract] In most learning systems examples are represented as fixed-length "feature vectors", the components of which are either real numbers or nominal values. We propose an extension of the feature-vector representation that allows the value of a feature to be a set of strings; for instance, to represent a small white and black dog with the nominal features size and species and the set-valued feature color, one might use a feature vector with size=small, species=canis-familiaris and color=fwhite,blackg. Since we make no assumptions about the number of possible set elements, this extension of the traditional feature-vector representation is closely connected to Blum's "infinite attribute" representation. We argue that many decision tree and rule learning algorithms can be easily extended to set-valued features. We also show by example that many real-world learning problems can be efficiently and naturally represented with set-valued features; in particular, text categorization problems and problems that arise in propositionalizing first-order representations lend themselves to set-valued features. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #23738. 	[Title] A THEORY OF LEARNING CLASSIFICATION RULES [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #63931. 	[Title] Combining FOIL and EBG to Speed-up Logic Programs [Abstract] This paper presents an algorithm that combines traditional EBL techniques and recent developments in inductive logic programming to learn effective clause selection rules for Prolog programs. When these control rules are incorporated into the original program, significant speed-up may be achieved. The algorithm is shown to be an improvement over competing EBL approaches in several domains. Additionally, the algorithm is capable of automatically transforming some intractable algorithms into ones that run in polynomial time. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #136766. 	[Title] Learning Goal-Decomposition Rules using Exercises [Abstract] Exercises are problems ordered in increasing order of difficulty. Teaching problem-solving through exercises is a widely used pedagogic technique. A computational reason for this is that the knowledge gained by solving simple problems is useful in efficiently solving more difficult problems. We adopt this approach of learning from exercises to acquire search-control knowledge in the form of goal-decomposition rules (d-rules). D-rules are first order, and are learned using a new "generalize-and-test" algorithm which is based on inductive logic programming techniques. We demonstrate the feasibility of the approach by applying it in two planning do mains. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #12350. 	[Title] Cryptographic Limitations on Learning Boolean Formulae and Finite Automata [Abstract] In this paper we prove the intractability of learning several classes of Boolean functions in the distribution-free model (also called the Probably Approximately Correct or PAC model) of learning from examples. These results are representation independent, in that they hold regardless of the syntactic form in which the learner chooses to represent its hypotheses. Our methods reduce the problems of cracking a number of well-known public-key cryptosys- tems to the learning problems. We prove that a polynomial-time learning algorithm for Boolean formulae, deterministic finite automata or constant-depth threshold circuits would have dramatic consequences for cryptography and number theory: in particular, such an algorithm could be used to break the RSA cryptosystem, factor Blum integers (composite numbers equivalent to 3 modulo 4), and detect quadratic residues. The results hold even if the learning algorithm is only required to obtain a slight advantage in prediction over random guessing. The techniques used demonstrate an interesting duality between learning and cryptography. We also apply our results to obtain strong intractability results for approximating a gener - alization of graph coloring. fl This research was conducted while the author was at Harvard University and supported by an A.T.& T. Bell Laboratories scholarship. y Supported by grants ONR-N00014-85-K-0445, NSF-DCR-8606366 and NSF-CCR-89-02500, DAAL03-86-K-0171, DARPA AFOSR 89-0506, and by SERC. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #136768. 	[Title] Theory-guided Empirical Speedup Learning of Goal Decomposition Rules [Abstract] Speedup learning is the study of improving the problem-solving performance with experience and from outside guidance. We describe here a system that successfully combines the best features of Explanation-based learning and empirical learning to learn goal decomposition rules from examples of successful problem solving and membership queries. We demonstrate that our system can efficiently learn effective decomposition rules in three different domains. Our results suggest that theory-guided empirical learning can overcome the problems of purely explanation-based learning and purely empirical learning, and be an effective speedup learning method. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1119295. 	[Title] Distance Induction in First Order Logic used for classification via a k-nearest-neighbor process. Experiments on [Abstract] This paper tackles the supervised induction of a distance from examples described as Horn clauses or constrained clauses. In opposition to syntax-driven approaches, this approach is discrimination-driven: it proceeds by defining a small set of complex discriminant hypotheses. These hypotheses serve as new concepts, used to redescribe the initial examples. Further, this redescription can be embedded into the space of natural integers, and a distance between examples thus naturally follows. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1127619. 	[Title] Cooperation of Data-driven and Model-based Induction Methods for Relational Learning [Abstract] Inductive learning in relational domains has been shown to be intractable in general. Many approaches to this task have been suggested nevertheless; all in some way restrict the hypothesis space searched. They can be roughly divided into two groups: data-driven, where the restriction is encoded into the algorithm, and model-based, where the restrictions are made more or less explicit with some form of declarative bias. This paper describes Incy, an inductive learner that seeks to combine aspects of both approaches. Incy is initially data-driven, using examples and background knowledge to put forth and specialize hypotheses based on the "connectivity" of the data at hand. It is model-driven in that hypotheses are abstracted into rule models, which are used both for control decisions in the data-driven phase and for model-guided induction. Key Words: Inductive learning in relational domains, cooperation of data-driven and model-guided methods, implicit and declarative bias. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #582343. 	[Title] Transferring and Retraining Learned Information Filters [Abstract] Any system that learns how to filter documents will suffer poor performance during an initial training phase. One way of addressing this problem is to exploit filters learned by other users in a collaborative fashion. We investigate "direct transfer" of learned filters in this setting|a limiting case for any collaborative learning system. We evaluate the stability of several different learning methods under direct transfer, and conclude that symbolic learning methods that use negatively correlated features of the data perform poorly in transfer, even when they perform well in more conventional evaluation settings. This effect is robust: it holds for several learning methods, when a diverse set of users is used in training the classifier, and even when the learned classifiers can be adapted to the new user's distribution. Our experiments give rise to several concrete proposals for improving generalization performance in a collaborative setting, including a beneficial variation on a feature selection method that has been widely used in text categorization. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1108551. 	[Title] From: Computational Learning Theory and Natural Systems, Chapter 18, "Cross-validation and Modal Theories", Cross-Validation and [Abstract] Cross-validation is a frequently used, intuitively pleasing technique for estimating the accuracy of theories learned by machine learning algorithms. During testing of a machine learning algorithm (foil) on new databases of prokaryotic RNA transcription promoters which we have developed, cross-validation displayed an interesting phenomenon. One theory is found repeatedly and is responsible for very little of the cross-validation error, whereas other theories are found very infrequently which tend to be responsible for the majority of the cross-validation error. It is tempting to believe that the most frequently found theory (the "modal theory") may be more accurate as a classifier of unseen data than the other theories. However, experiments showed that modal theories are not more accurate on unseen data than the other theories found less frequently during cross-validation. Modal theories may be useful in predicting when cross-validation is a poor estimate of true accuracy. We offer explanations 1 For correspondence: Department of Computer Science and Engineering, University of California, San Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #72908. 	[Title] Applications of a logical discovery engine [Abstract] The clausal discovery engine claudien is presented. claudien discovers regularities in data and is a representative of the inductive logic programming paradigm. As such, it represents data and regularities by means of first order clausal theories. Because the search space of clausal theories is larger than that of attribute value representation, claudien also accepts as input a declarative specification of the language bias, which determines the set of syntactically well-formed regularities. Whereas other papers on claudien focuss on the semantics or logical problem specification of claudien, on the discovery algorithm, or the PAC-learning aspects, this paper wants to illustrate the power of the resulting technique. In order to achieve this aim, we show how claudien can be used to learn 1) integrity constraints in databases, 2) functional dependencies and determinations, 3) properties of sequences, 4) mixed quantitative and qualitative laws, 5) reverse engineering, and 6) classification rules. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1000012. 	[Title] Stochastic Propositionalization of Non-Determinate Background Knowledge [Abstract] It is a well-known fact that propositional learning algorithms require "good" features to perform well in practice. So a major step in data engineering for inductive learning is the construction of good features by domain experts. These features often represent properties of structured objects, where a property typically is the occurrence of a certain substructure having certain properties. To partly automate the process of "feature engineering", we devised an algorithm that searches for features which are defined by such substructures. The algorithm stochastically conducts a top-down search for first-order clauses, where each clause represents a binary feature. It differs from existing algorithms in that its search is not class-blind, and that it is capable of considering clauses ("context") of almost arbitrary length (size). Preliminary experiments are favorable, and support the view that this approach is promising. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1106388. 	[Title] Predicting Ordinal Classes in ILP [Abstract] This paper is devoted to the problem of learning to predict ordinal (i.e., ordered discrete) classes in an ILP setting. We start with a relational regression algorithm named SRT (Structural Regression Trees) and study various ways of transforming it into a first-order learner for ordinal classification tasks. Combinations of these algorithm variants with several data preprocessing methods are compared on two ILP benchmark data sets to verify the relative strengths and weaknesses of the strategies and to study the trade-off between optimal categorical classification accuracy (hit rate) and minimum distance-based error. Preliminary results indicate that this is a promising avenue towards algorithms that combine aspects of classification and regression in relational learning. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1117786. 	[Title] An intelligent search method using Inductive Logic Programming [Abstract] We propose a method to use Inductive Logic Programming to give heuristic functions for searching goals to solve problems. The method takes solutions of a problem or a history of search and a set of background knowledge on the problem. In a large class of problems, a problem is described as a set of states and a set of operators, and is solved by finding a series of operators. A solution, a series of operators that brings an initial state to a final state, is transformed into positive and negative examples of a relation "better-choice", which describes that an operator is better than others in a state. We also give a way to use the "better-choice" relation as a heuristic function. The method can use any logic program as background knowledge to induce heuristics, and induced heuristics has high readability. The paper inspects the method by applying to a puzzle. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #27230. 	[Title] K unstliche Intelligenz Grdt: Enhancing Model-Based Learning for Its Application in Robot Navigation [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1153254. 	[Title]  [Abstract] A Methodology for Evaluating Theory Revision Systems: Results Abstract Theory revision systems are learning systems that have a goal of making small changes to an original theory to account for new data. A measure for the distance between two theories is proposed. This measure corresponds to the minimum number of edit operations at the literal level required to transform one theory into another. By computing the distance between an original theory and a revised theory, the claim that a theory revision system makes few revisions to a theory may be quantitatively evaluated. We present data using both accuracy and the distance metric on Audrey II, with Audrey II fl Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #37483. 	[Title] Learning Approximate Control Rules Of High Utility [Abstract] One of the difficult problems in the area of explanation based learning is the utility problem; learning too many rules of low utility can lead to swamping, or degradation of performance. This paper introduces two new techniques for improving the utility of learned rules. The first technique is to combine EBL with inductive learning techniques to learn a better set of control rules; the second technique is to use these inductive techniques to learn approximate control rules. The two techniques are synthesized in an algorithm called approximating abductive explanation based learning (AxA-EBL). AxA-EBL is shown to improve substantially over standard EBL in several domains. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #23546. 	[Title] Learning Action-oriented Perceptual Features for Robot Navigation [Abstract]  Please summarise all the given information.

Paper #151430 has the title `Pac-Learning Recursive Logic Programs: Efficient Algorithms  
` and the abstract `We present algorithms that learn certain classes of function-free recursive logic programs in polynomial time from equivalence queries. In particular, we show that a single k-ary recursive constant-depth determinate clause is learnable. Two-clause programs consisting of one learnable recursive clause and one constant-depth determinate non-recursive clause are also learnable, if an additional "basecase" oracle is assumed. These results immediately imply the pac-learnability of these classes. Although these classes of learnable recursive programs are very constrained, it is shown in a companion paper that they are maximally general, in that generalizing either class in any natural way leads to a compu-tationally difficult learning problem. Thus, taken together with its companion paper, this paper establishes a boundary of efficient learnability for recursive logic programs.
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Question: Which category should Paper #151430 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #151430 has the title `Pac-Learning Recursive Logic Programs: Efficient Algorithms  
` and the abstract `We present algorithms that learn certain classes of function-free recursive logic programs in polynomial time from equivalence queries. In particular, we show that a single k-ary recursive constant-depth determinate clause is learnable. Two-clause programs consisting of one learnable recursive clause and one constant-depth determinate non-recursive clause are also learnable, if an additional "basecase" oracle is assumed. These results immediately imply the pac-learnability of these classes. Although these classes of learnable recursive programs are very constrained, it is shown in a companion paper that they are maximally general, in that generalizing either class in any natural way leads to a compu-tationally difficult learning problem. Thus, taken together with its companion paper, this paper establishes a boundary of efficient learnability for recursive logic programs.
`.
Question: Which category should Paper #151430 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Rule_Learning