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 #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 #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 #397590. 	[Title] Inverting Implication with Small Training Sets [Abstract] We present an algorithm for inducing recursive clauses using inverse implication (rather than inverse resolution) as the underlying generalization method. Our approach applies to a class of logic programs similar to the class of primitive recursive functions. Induction is performed using a small number of positive examples that need not be along the same resolution path. Our algorithm, implemented in a system named CRUSTACEAN, locates matched lists of generating terms that determine the pattern of decomposition exhibited in the (target) recursive clause. Our theoretical analysis defines the class of logic programs for which our approach is complete, described in terms characteristic of other ILP approaches. Our current implementation is considerably faster than previously reported. We present evidence demonstrating that, given randomly selected inputs, increasing the number of positive examples increases accuracy and reduces the number of outputs. We relate our approach to similar recent work on inducing recursive clauses. Please summarise all the given information.

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.

Paper #155158 has the title `Learning Singly-Recursive Relations from Small Datasets  
` and the 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. 
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Question: Which category should Paper #155158 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #155158 has the title `Learning Singly-Recursive Relations from Small Datasets  
` and the 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. 
`.
Question: Which category should Paper #155158 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