Above are papers related to the following paper: [Paper_ID] Paper #1102751. 	[Title] The Challenge of Revising an Impure Theory [Abstract] A pure rule-based program will return a set of answers to each query; and will return the same answer set even if its rules are re-ordered. However, an impure program, which includes the Prolog cut "!" and not() operators, can return different answers if the rules are re-ordered. There are also many reasoning systems that return only the first answer found for each query; these first answers, too, depend on the rule order, even in pure rule-based systems. A theory revision algorithm, seeking a revised rule-base whose expected accuracy, over the distribution of queries, is optimal, should therefore consider modifying the order of the rules. This paper first shows that a polynomial number of training "labeled queries" (each a query coupled with its correct answer) provides the distribution information necessary to identify the optimal ordering. It then proves, however, that the task of determining which ordering is optimal, once given this information, is intractable even in trivial situations; e.g., even if each query is an atomic literal, we are seeking only a "perfect" theory, and the rule base is propositional. We also prove that this task is not even approximable: Unless P = N P , no polynomial time algorithm can produce an ordering of an n-rule theory whose accuracy is within n fl of optimal, for some fl &gt; 0. We also prove similar hardness, and non-approximatability, results for the related tasks of determining, in these impure contexts, (1) the optimal ordering of the antecedents; (2) the optimal set of rules to add or (3) to delete; and (4) the optimal priority values for a set of defaults. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #353541. 	[Title] Building Intelligent Agents for Web-Based Tasks: A Theory-Refinement Approach [Abstract] We present and evaluate an infrastructure with which to rapidly and easily build intelligent software agents for Web-based tasks. Our design is centered around two basic functions: ScoreThis-Link and ScoreThisPage. If given highly accurate such functions, standard heuristic search would lead to efficient retrieval of useful information. Our approach allows users to tailor our system's behavior by providing approximate advice about the above functions. This advice is mapped into neural network implementations of the two functions. Subsequent reinforcements from the Web (e.g., dead links) and any ratings of retrieved pages that the user wishes to provide are, respectively, used to refine the link- and page-scoring functions. Hence, our agent architecture provides an appealing middle ground between nonadaptive "agent" programming languages and systems that solely learn user preferences from the user's ratings of pages. We present a case study where we provide some simple advice and specialize our general-purpose system into a "home-page finder". An empirical study demonstrates that our approach leads to a more effective home-page finder than that of a leading commercial Web search engine. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #308232. 	[Title] Extending Theory Refinement to M-of-N Rules [Abstract] In recent years, machine learning research has started addressing a problem known as theory refinement. The goal of a theory refinement learner is to modify an incomplete or incorrect rule base, representing a domain theory, to make it consistent with a set of input training examples. This paper presents a major revision of the Either propositional theory refinement system. Two issues are discussed. First, we show how run time efficiency can be greatly improved by changing from a exhaustive scheme for computing repairs to an iterative greedy method. Second, we show how to extend Either to refine M-of-N rules. The resulting algorithm, Neither (New Either), is more than an order of magnitude faster and produces significantly more accurate results with theories that fit the M-of-N format. To demonstrate the advantages of Neither, we present experimental results from two real-world domains. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #104840. 	[Title] An Optimized Theory Revision Module [Abstract] Theory revision systems typically use a set of theory-to-theory transformations f k g to hill-climb from a given initial theory to a new theory whose empirical accuracy, over a given set of labeled training instances fc j g, is a local maximum. At the heart of each such process is an "evaluator", which compares the accuracy of the current theory KB with that of each of its "neighbors" f k (KB)g, with the goal of determining which neighbor has the highest accuracy. The obvious "wrapper" evaluator simply evaluates each individual neighbor theory KB k = k (KB) on each instance c j . As it can be very expensive to evaluate a single theory on a single instance, and there can be a great many training instances and a huge number of neighbors, this approach can be prohibitively slow. We present an alternative system which employs a smarter evaluator that quickly computes the accuracy of a transformed theory k (KB) by "looking inside" KB and reasoning about the effects of the k transformation. We compare the performance of with the naive wrapper system on real-world theories obtained from a fielded expert system, and find that runs over 35 times faster than , while attaining the same accuracy. This paper also discusses 's source of power. Keywords: theory revision, efficient algorithm, hill-climbing system Multiple Submissions: We have submited a related version of this paper to AAAI96. fl We gratefully acknowledge the many helpful comments on this report from George Drastal, Chandra Mouleeswaran and Geoff Towell. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #27535. 	[Title] Combining Connectionist and Symbolic Learning to Refine Certainty-Factor Rule Bases [Abstract] This paper describes Rapture | a system for revising probabilistic knowledge bases that combines connectionist and symbolic learning methods. Rapture uses a modified version of backpropagation to refine the certainty factors of a probabilistic rule base and it uses ID3's information-gain heuristic to add new rules. Results on refining three actual expert knowledge bases demonstrate that this combined approach generally performs better than previous methods. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1105428. 	[Title] From Theory Refinement to KB Maintenance: a Position Statement [Abstract] Since we consider theory refinement (TR) as a possible key concept for a methodologically clear view of knowledge-base maintenance, we try to give a structured overview about the actual state-of-the-art in TR. This overview is arranged along the description of TR as a search problem. We explain the basic approach, show the variety of existing systems and try to give some hints about the direction future research should go. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #155158. 	[Title] Learning Singly-Recursive Relations from Small Datasets [Abstract] The inductive logic programming system LOPSTER was created to demonstrate the advantage of basing induction on logical implication rather than -subsumption. LOPSTER's sub-unification procedures allow it to induce recursive relations using a minimum number of examples, whereas inductive logic programming algorithms based on -subsumption require many more examples to solve induction tasks. However, LOPSTER's input examples must be carefully chosen; they must be along the same inverse resolution path. We hypothesize that an extension of LOPSTER can efficiently induce recursive relations without this requirement. We introduce a generalization of LOPSTER named CRUSTACEAN that has this capability and empirically evaluate its ability to induce recursive relations. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #101145. 	[Title] Abduction, Experience, and Goals: A Model of Everyday Abductive Explanation* [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #51866. 	[Title] Bias-Driven Revision of Logical Domain Theories [Abstract] The theory revision problem is the problem of how best to go about revising a deficient domain theory using information contained in examples that expose inaccuracies. In this paper we present our approach to the theory revision problem for propositional domain theories. The approach described here, called PTR, uses probabilities associated with domain theory elements to numerically track the ``ow'' of proof through the theory. This allows us to measure the precise role of a clause or literal in allowing or preventing a (desired or undesired) derivation for a given example. This information is used to efficiently locate and repair awed elements of the theory. PTR is proved to converge to a theory which correctly classifies all examples, and shown experimentally to be fast and accurate even for deep theories. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #3231. 	[Title] Irrelevant Features and the Subset Selection Problem [Abstract] We address the problem of finding a subset of features that allows a supervised induction algorithm to induce small high-accuracy concepts. We examine notions of relevance and irrelevance, and show that the definitions used in the machine learning literature do not adequately partition the features into useful categories of relevance. We present definitions for irrelevance and for two degrees of relevance. These definitions improve our understanding of the behavior of previous subset selection algorithms, and help define the subset of features that should be sought. The features selected should depend not only on the features and the target concept, but also on the induction algorithm. We describe a method for feature subset selection using cross-validation that is applicable to any induction algorithm, and discuss experiments conducted with ID3 and C4.5 on artificial and real datasets. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #4649. 	[Title] Finding Accurate Frontiers: A Knowledge-Intensive Approach to Relational Learning [Abstract] An approach to analytic learning is described that searches for accurate entailments of a Horn Clause domain theory. A hill-climbing search, guided by an information based evaluation function, is performed by applying a set of operators that derive frontiers from domain theories. The analytic learning system is one component of a multi-strategy relational learning system. We compare the accuracy of concepts learned with this analytic strategy to concepts learned with an analytic strategy that operationalizes the domain theory. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #10796. 	[Title] An Improved Algorithm for Incremental Induction of Decision Trees [Abstract] Technical Report 94-07 February 7, 1994 (updated April 25, 1994) This paper will appear in Proceedings of the Eleventh International Conference on Machine Learning. Abstract This paper presents an algorithm for incremental induction of decision trees that is able to handle both numeric and symbolic variables. In order to handle numeric variables, a new tree revision operator called `slewing' is introduced. Finally, a non-incremental method is given for finding a decision tree based on a direct metric of a candidate tree. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #502574. 	[Title] References Automatic student modeling and bug library construction using theory refinement. Ph.D. ml/ Symbolic revision [Abstract] ASSERT demonstrates how theory refinement techniques developed in machine learning can be used to ef fec-tively build student models for intelligent tutoring systems. This application is unique since it inverts the normal goal of theory refinement from correcting errors in a knowledge base to introducing them. A comprehensive experiment involving a lar ge number of students interacting with an automated tutor for teaching concepts in C ++ programming was used to evaluate the approach. This experiment demonstrated the ability of theory refinement to generate more accurate student models than raw induction, as well as the ability of the resulting models to support individualized feedback that actually improves students subsequent performance. Carr, B. and Goldstein, I. (1977). Overlays: a theory of modeling for computer aided instruction. T echnical Report A. I. Memo 406, Cambridge, MA: MIT. Sandberg, J. and Barnard, Y . (1993). Education and technology: What do we know? And where is AI? Artificial Intelligence Communications, 6(1):47-58. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #10798. 	[Title] Learning physical descriptions from functional definitions, examples, Learning from examples: The effect of different conceptual [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #434. 	[Title] Learning Analytically and Inductively [Abstract] Learning is a fundamental component of intelligence, and a key consideration in designing cognitive architectures such as Soar [ Laird et al., 1986 ] . This chapter considers the question of what constitutes an appropriate general-purpose learning mechanism. We are interested in mechanisms that might explain and reproduce the rich variety of learning capabilities of humans, ranging from learning perceptual-motor skills such as how to ride a bicycle, to learning highly cognitive tasks such as how to play chess. Research on learning in fields such as cognitive science, artificial intelligence, neurobiology, and statistics has led to the identification of two distinct classes of learning methods: inductive and analytic. Inductive methods, such as neural network Backpropagation, learn general laws by finding statistical correlations and regularities among a large set of training examples. In contrast, analytical methods, such as Explanation-Based Learning, acquire general laws from many fewer training examples. They rely instead on prior knowledge to analyze individual training examples in detail, then use this analysis to distinguish relevant example features from the irrelevant. The question considered in this chapter is how to best combine inductive and analytical learning in an architecture that seeks to cover the range of learning exhibited by intelligent systems such as humans. We present a specific learning mechanism, Explanation Based Neural Network learning (EBNN), that blends these two types of learning, and present experimental results demonstrating its ability to learn control strategies for a mobile robot using Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #85688. 	[Title] Finding new rules for incomplete theories: Explicit biases for induction with contextual information. In Proceedings [Abstract] addressed in KBANN (which translates a theory into a neural-net, refines it using backpropagation, and then retranslates the result back into rules) by adding extra hidden units and connections to the initial network; however, this would require predetermining the num In this paper, we have presented constructive induction techniques recently added to the EITHER theory refinement system. Intermediate concept utilization employs existing rules in the theory to derive higher-level features for use in induction. Intermediate concept creation employs inverse resolution to introduce new intermediate concepts in order to fill gaps in a theory than span multiple levels. These revisions allow EITHER to make use of imperfect domain theories in the ways typical of previous work in both constructive induction and theory refinement. As a result, EITHER is able to handle a wider range of theory imperfections than any other existing theory refinement system. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #173884. 	[Title] Revising Bayesian Network Parameters Using Backpropagation [Abstract] The problem of learning Bayesian networks with hidden variables is known to be a hard problem. Even the simpler task of learning just the conditional probabilities on a Bayesian network with hidden variables is hard. In this paper, we present an approach that learns the conditional probabilities on a Bayesian network with hidden variables by transforming it into a multi-layer feedforward neural network (ANN). The conditional probabilities are mapped onto weights in the ANN, which are then learned using standard backpropagation techniques. To avoid the problem of exponentially large ANNs, we focus on Bayesian networks with noisy-or and noisy-and nodes. Experiments on real world classification problems demonstrate the effectiveness of our technique. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #10435. 	[Title] Improving accuracy by combining rule-based and case-based reasoning [Abstract] An architecture is presented for combining rule-based and case-based reasoning. The architecture is intended for domains that are understood reasonably well, but still imperfectly. It uses a set of rules, which are taken to be only approximately correct, to obtain a preliminary answer for a given problem; it then draws analogies from cases to handle exceptions to the rules. Having rules together with cases not only increases the architecture's domain coverage, it also allows innovative ways of doing case-based reasoning: the same rules that are used for rule-based reasoning are also used by the case-based component to do case indexing and case adaptation. The architecture was applied to the task of name pronunciation, and, with minimal knowledge engineering, was found to perform almost at the level of the best commercial systems. Moreover, its accuracy was found to exceed what it could have achieved with rules or cases alone, thus demonstrating the accuracy improvement afforded by combining rule-based and case-based reasoning. This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories of Cambridge, Massachusetts; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories. All rights reserved. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #51909. 	[Title] Automated Refinement of First-Order Horn-Clause Domain Theories [Abstract] Knowledge acquisition is a difficult, error-prone, and time-consuming task. The task of automatically improving an existing knowledge base using learning methods is addressed by the class of systems performing theory refinement. This paper presents a system, Forte (First-Order Revision of Theories from Examples), which refines first-order Horn-clause theories by integrating a variety of different revision techniques into a coherent whole. Forte uses these techniques within a hill-climbing framework, guided by a global heuristic. It identifies possible errors in the theory and calls on a library of operators to develop possible revisions. The best revision is implemented, and the process repeats until no further revisions are possible. Operators are drawn from a variety of sources, including propositional theory refinement, first-order induction, and inverse resolution. Forte is demonstrated in several domains, including logic programming and qualitative modelling. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #5966. 	[Title] Cost-Sensitive Classification: Empirical Evaluation of a Hybrid Genetic Decision Tree Induction Algorithm [Abstract] This paper introduces ICET, a new algorithm for costsensitive classification. ICET uses a genetic algorithm to evolve a population of biases for a decision tree induction algorithm. The fitness function of the genetic algorithm is the average cost of classification when using the decision tree, including both the costs of tests (features, measurements) and the costs of classification errors. ICET is compared here with three other algorithms for costsensitive classification EG2, CS-ID3, and IDX and also with C4.5, which classifies without regard to cost. The five algorithms are evaluated empirically on five real-world medical datasets. Three sets of experiments are performed. The first set examines the baseline performance of the five algorithms on the five datasets and establishes that ICET performs significantly better than its competitors. The second set tests the robustness of ICET under a variety of conditions and shows that ICET maintains its advantage. The third set looks at ICETs search in bias space and discovers a way to improve the search. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1119078. 	[Title] Tractability of Theory Patching [Abstract] In this paper we consider the problem of theory patching, in which we are given a domain theory, some of whose components are indicated to be possibly flawed, and a set of labeled training examples for the domain concept. The theory patching problem is to revise only the indicated components of the theory, such that the resulting theory correctly classifies all the training examples. Theory patching is thus a type of theory revision in which revisions are made to individual components of the theory. Our concern in this paper is to determine for which classes of logical domain theories the theory patching problem is tractable. We consider both propositional and first-order domain theories, and show that the theory patching problem is equivalent to that of determining what information contained in a theory is stable regardless of what revisions might be performed to the theory. We show that determining stability is tractable if the input theory satisfies two conditions: that revisions to each theory component have monotonic effects on the classification of examples, and that theory components act independently in the classification of examples in the theory. We also show how the concepts introduced can be used to determine the soundness and completeness of particular theory patching algorithms. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #59244. 	[Title] Explaining Anomalies as a Basis for Knowledge Base Refinement [Abstract] Explanations play a key role in operationalization-based anomaly detection techniques. In this paper we show that their role is not limited to anomaly detection; they can also be used for guiding automated knowledge base refinement. We introduce a refinement procedure which takes: (i) a small number of refinement rules (rather than test cases), and (ii) explanations constructed in an attempt to reveal the cause (or causes) for inconsistencies detected during the verification process, and returns rule revisions aiming to recover the consistency of the KB-theory. Inconsistencies caused by more than one anomaly are handled at the same time, which improves the efficiency of the refinement process. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #8687. 	[Title] The Difficulties of Learning Logic Programs with Cut [Abstract] As real logic programmers normally use cut (!), an effective learning procedure for logic programs should be able to deal with it. Because the cut predicate has only a procedural meaning, clauses containing cut cannot be learned using an extensional evaluation method, as is done in most learning systems. On the other hand, searching a space of possible programs (instead of a space of independent clauses) is unfeasible. An alternative solution is to generate first a candidate base program which covers the positive examples, and then make it consistent by inserting cut where appropriate. The problem of learning programs with cut has not been investigated before and this seems to be a natural and reasonable approach. We generalize this scheme and investigate the difficulties that arise. Some of the major shortcomings are actually caused, in general, by the need for intensional evaluation. As a conclusion, the analysis of this paper suggests, on precise and technical grounds, that learning cut is difficult, and current induction techniques should probably be restricted to purely declarative logic languages. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #38000. 	[Title] on Inductive Logic Programming (ILP-95) Inducing Logic Programs without Explicit Negative Examples [Abstract] This paper presents a method for learning logic programs without explicit negative examples by exploiting an assumption of output completeness. A mode declaration is supplied for the target predicate and each training input is assumed to be accompanied by all of its legal outputs. Any other outputs generated by an incomplete program implicitly represent negative examples; however, large numbers of ground negative examples never need to be generated. This method has been incorporated into two ILP systems, Chillin and IFoil, both of which use intensional background knowledge. Tests on two natural language acquisition tasks, case-role mapping and past-tense learning, illustrate the advantages of the approach. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #89335. 	[Title] Utilising Explanation to Assist the Refinement of Knowledge-Based Systems [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #8696. 	[Title] The Complexity of Theory Revision [Abstract] A knowledge-based system uses its database (a.k.a. its "theory") to produce answers to the queries it receives. Unfortunately, these answers may be incorrect if the underlying theory is faulty. Standard "theory revision" systems use a given set of "labeled queries" (each a query paired with its correct answer) to transform the given theory, by adding and/or deleting either rules and/or antecedents, into a related theory that is as accurate as possible. After formally defining the theory revision task and bounding its sample complexity, this paper addresses the task's computational complexity. It first proves that, unless P = N P , no polynomial time algorithm can identify the optimal theory, even given the exact distribution of queries, except in the most trivial of situations. It also shows that, except in such trivial situations, no polynomial-time algorithm can produce a theory whose inaccuracy is even close (i.e., within a particular polynomial factor) to optimal. These results justify the standard practice of hill-climbing to a locally-optimal theory, based on a given set of labeled sam ples. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #8699. 	[Title] Theory Revision in Fault Hierarchies [Abstract] The fault hierarchy representation is widely used in expert systems for the diagnosis of complex mechanical devices. On the assumption that an appropriate bias for a knowledge representation language is also an appropriate bias for learning in this domain, we have developed a theory revision method that operates directly on a fault hierarchy. This task presents several challenges: A typical training instance is missing most feature values, and the pattern of missing features is significant, rather than merely an effect of noise. Moreover, the accuracy of a candidate theory is measured by considering both the sequence of tests required to arrive at a diagnosis and its agreement with the diagnostic endpoints provided by an expert. This paper first describes the algorithm for theory revision of fault hierarchies that was designed to address these challenges, then discusses its application in knowledge base maintenance and reports on experiments that use to revise a fielded diagnostic system. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #8703. 	[Title] Theory Refinement Combining Analytical and Empirical Methods [Abstract] This article describes a comprehensive approach to automatic theory revision. Given an imperfect theory, the approach combines explanation attempts for incorrectly classified examples in order to identify the failing portions of the theory. For each theory fault, correlated subsets of the examples are used to inductively generate a correction. Because the corrections are focused, they tend to preserve the structure of the original theory. Because the system starts with an approximate domain theory, in general fewer training examples are required to attain a given level of performance (classification accuracy) compared to a purely empirical system. The approach applies to classification systems employing a propositional Horn-clause theory. The system has been tested in a variety of application domains, and results are presented for problems in the domains of molecular biology and plant disease diagnosis. Please summarise all the given information.

Paper #1102751 has the title `The Challenge of Revising an Impure Theory  
` and the abstract `A pure rule-based program will return a set of answers to each query; and will return the same answer set even if its rules are re-ordered. However, an impure program, which includes the Prolog cut "!" and not() operators, can return different answers if the rules are re-ordered. There are also many reasoning systems that return only the first answer found for each query; these first answers, too, depend on the rule order, even in pure rule-based systems. A theory revision algorithm, seeking a revised rule-base whose expected accuracy, over the distribution of queries, is optimal, should therefore consider modifying the order of the rules. This paper first shows that a polynomial number of training "labeled queries" (each a query coupled with its correct answer) provides the distribution information necessary to identify the optimal ordering. It then proves, however, that the task of determining which ordering is optimal, once given this information, is intractable even in trivial situations; e.g., even if each query is an atomic literal, we are seeking only a "perfect" theory, and the rule base is propositional. We also prove that this task is not even approximable: Unless P = N P , no polynomial time algorithm can produce an ordering of an n-rule theory whose accuracy is within n fl of optimal, for some fl &gt; 0. We also prove similar hardness, and non-approximatability, results for the related tasks of determining, in these impure contexts, (1) the optimal ordering of the antecedents; (2) the optimal set of rules to add or (3) to delete; and (4) the optimal priority values for a set of defaults. 
`.
Question: Which category should Paper #1102751 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #1102751 has the title `The Challenge of Revising an Impure Theory  
` and the abstract `A pure rule-based program will return a set of answers to each query; and will return the same answer set even if its rules are re-ordered. However, an impure program, which includes the Prolog cut "!" and not() operators, can return different answers if the rules are re-ordered. There are also many reasoning systems that return only the first answer found for each query; these first answers, too, depend on the rule order, even in pure rule-based systems. A theory revision algorithm, seeking a revised rule-base whose expected accuracy, over the distribution of queries, is optimal, should therefore consider modifying the order of the rules. This paper first shows that a polynomial number of training "labeled queries" (each a query coupled with its correct answer) provides the distribution information necessary to identify the optimal ordering. It then proves, however, that the task of determining which ordering is optimal, once given this information, is intractable even in trivial situations; e.g., even if each query is an atomic literal, we are seeking only a "perfect" theory, and the rule base is propositional. We also prove that this task is not even approximable: Unless P = N P , no polynomial time algorithm can produce an ordering of an n-rule theory whose accuracy is within n fl of optimal, for some fl &gt; 0. We also prove similar hardness, and non-approximatability, results for the related tasks of determining, in these impure contexts, (1) the optimal ordering of the antecedents; (2) the optimal set of rules to add or (3) to delete; and (4) the optimal priority values for a set of defaults. 
`.
Question: Which category should Paper #1102751 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: Theory