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 #308003. 	[Title] Relational Knowledge Discovery in Databases [Abstract] In this paper, we indicate some possible applications of ILP or similar techniques in the knowledge discovery field, and then discuss several methods for adapting and linking ILP-systems to relational database systems. The proposed methods range from "pure ILP" to "based on techniques originating in ILP". We show that it is both easy and advantageous to adapt ILP-systems in this way. Please summarise all the given information.

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 #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 #63915. 	[Title] Learning the Past Tense of English Verbs: The Symbolic Pattern Associator vs. Connectionist Models [Abstract] Learning the past tense of English verbs | a seemingly minor aspect of language acquisition | has generated heated debates since 1986, and has become a landmark task for testing the adequacy of cognitive modeling. Several artificial neural networks (ANNs) have been implemented, and a challenge for better symbolic models has been posed. In this paper, we present a general-purpose Symbolic Pattern Associator (SPA) based upon the decision-tree learning algorithm ID3. We conduct extensive head-to-head comparisons on the generalization ability between ANN models and the SPA under different representations. We conclude that the SPA generalizes the past tense of unseen verbs better than ANN models by a wide margin, and we offer insights as to why this should be the case. We also discuss a new default strategy for decision-tree learning algorithms. 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 #238099. 	[Title] Mining for Causes of Cancer: Machine Learning Experiments at Various Levels of Detail [Abstract] This paper presents first results of an interdisciplinary project in scientific data mining. We analyze data about the carcinogenicity of chemicals derived from the carcinogenesis bioassay program performed by the US National Institute of Environmental Health Sciences. The database contains detailed descriptions of 6823 tests performed with more than 330 compounds and animals of different species, strains and sexes. The chemical structures are described at the atom and bond level, and in terms of various relevant structural properties. The goal of this paper is to investigate the effects that various levels of detail and amounts of information have on the resulting hypotheses, both quantitatively and qualitatively. We apply relational and propositional machine learning algorithms to learning problems formulated as regression or as classification tasks. In addition, these experiments have been conducted with two learning problems which are at different levels of detail. Quantitatively, our experiments indicate that additional information not necessarily improves accuracy. Qualitatively, a number of potential discoveries have been made by the algorithm for Relational Regression because it can utilize all the information contained in the relations of the database as well as in the numerical dependent variable. 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 #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 #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 #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 #101660. 	[Title] Extraction of Meta-Knowledge to Restrict the Hypothesis Space for ILP Systems incorporating them in FOIL. [Abstract] Many ILP systems, such as GOLEM, FOIL, and MIS, take advantage of user supplied meta-knowledge to restrict the hypothesis space. This meta-knowledge can be in the form of type information about arguments in the predicate being learned, or it can be information about whether a certain argument in the predicate is functionally dependent on the other arguments (supplied as mode information). This meta knowledge is explicitly supplied to an ILP system in addition to the data. The present paper argues that in many cases the meta knowledge can be extracted directly from the raw data. Three algorithms are presented that learn type, mode, and symmetric meta-knowledge from data. These algorithms can be incorporated in existing ILP systems in the form of a preprocessor that obviates the need for a user to explicitly provide this information. In many cases, the algorithms can extract meta- knowledge that the user is either unaware of, but which information can be used by the ILP system to restrict the hypothesis space. Please summarise all the given information.

Paper #1115670 has the title `Which Hypotheses Can Be Found with Inverse Entailment? -Extended Abstract  
` and the 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.
`.
Question: Which category should Paper #1115670 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #1115670 has the title `Which Hypotheses Can Be Found with Inverse Entailment? -Extended Abstract  
` and the 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.
`.
Question: Which category should Paper #1115670 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