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 #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 #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 #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 #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.

Paper #397590 has the title `Inverting Implication with Small Training Sets  
` and the 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.
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Question: Which category should Paper #397590 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #397590 has the title `Inverting Implication with Small Training Sets  
` and the 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.
`.
Question: Which category should Paper #397590 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