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23
Inverse entailment and Progol
, 1995
"... This paper firstly provides a reappraisal of the development of techniques for inverting deduction, secondly introduces ModeDirected Inverse Entailment (MDIE) as a generalisation and enhancement of previous approaches and thirdly describes an implementation of MDIE in the Progol system. Progol ..."
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Cited by 631 (59 self)
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This paper firstly provides a reappraisal of the development of techniques for inverting deduction, secondly introduces ModeDirected 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 reassessment of previous techniques in terms of inverse entailment leads to new results for learning from positive data and inverting implication between pairs of clauses.
Automated Refinement of FirstOrder HornClause Domain Theories
 MACHINE LEARNING
, 1995
"... Knowledge acquisition is a difficult, errorprone, and timeconsuming 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 (FirstOrder Revision of Theories f ..."
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Cited by 81 (7 self)
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Knowledge acquisition is a difficult, errorprone, and timeconsuming 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 (FirstOrder Revision of Theories from Examples), which refines firstorder Hornclause theories by integrating a variety of different revision techniques into a coherent whole. Forte uses these techniques within a hillclimbing 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, firstorder induction, and inverse resolution. Forte is demonstrated in several domains, including logic programming and qualitative modelling.
Inductive Synthesis of Recursive Logic Programs
, 1997
"... The inductive synthesis of recursive logic programs from incomplete information, such as input/output examples, is a challenging subfield both of ILP (Inductive Logic Programming) and of the synthesis (in general) of logic programs from formal specifications. We first overview past and present achie ..."
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Cited by 34 (8 self)
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The inductive synthesis of recursive logic programs from incomplete information, such as input/output examples, is a challenging subfield both of ILP (Inductive Logic Programming) and of the synthesis (in general) of logic programs from formal specifications. We first overview past and present achievements, focusing on the techniques that were designed specifically for the inductive synthesis of recursive logic programs, but also discussing a few general ILP techniques that can also induce nonrecursive hypotheses. Then we analyse the prospects of these techniques in this task, investigating their applicability to software engineering as well as to knowledge acquisition and discovery.
Inductive Logic Programming: derivations, successes and shortcomings
 SIGART Bulletin
, 1993
"... Inductive Logic Programming (ILP) is a research area which investigates the construction of firstorder definite clause theories from examples and background knowledge. ILP systems have been applied successfully in a number of realworld domains. These include the learning of structureactivity rules ..."
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Cited by 31 (3 self)
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Inductive Logic Programming (ILP) is a research area which investigates the construction of firstorder definite clause theories from examples and background knowledge. ILP systems have been applied successfully in a number of realworld domains. These include the learning of structureactivity rules for drug design, finiteelement mesh design rules, rules for primarysecondary prediction of protein structure and fault diagnosis rules for satellites. There is a well established tradition of learninginthelimit results in ILP. Recently some results within Valiant's PAClearning framework have also been demonstrated for ILP systems. In this paper it is argued that algorithms can be directly derived from the formal specifications of ILP. This provides a common basis for Inverse Resolution, ExplanationBased Learning, Abduction and Relative Least General Generalisation. A new generalpurpose, efficient approach to predicate invention is demonstrated. ILP is underconstrained by its logical ...
Inverting Implication
 Artificial Intelligence Journal
, 1992
"... All generalisations within logic involve inverting implication. Yet, ever since Plotkin's work in the early 1970's methods of generalising firstorder clauses have involved inverting the clausal subsumption relationship. However, even Plotkin realised that this approach was incomplete. Since inversi ..."
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Cited by 26 (2 self)
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All generalisations within logic involve inverting implication. Yet, ever since Plotkin's work in the early 1970's methods of generalising firstorder clauses have involved inverting the clausal subsumption relationship. However, even Plotkin realised that this approach was incomplete. Since inversion of subsumption is central to many Inductive Logic Programming approaches, this form of incompleteness has been propagated to techniques such as Inverse Resolution and Relative Least General Generalisation. A more complete approach to inverting implication has been attempted with some success recently by Lapointe and Matwin. In the present paper the author derives general solutions to this problem from first principles. It is shown that clausal subsumption is only incomplete for selfrecursive clauses. Avoiding this incompleteness involves algorithms which find "nth roots" of clauses. Completeness and correctness results are proved for a nondeterministic algorithms which constructs nth ro...
Inverting Implication with Small Training Sets
, 1994
"... . 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 n ..."
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Cited by 13 (0 self)
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. 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 re...
Learning Recursive Theories in the Normal ILP Setting
, 2003
"... Induction of recursive theories in the normal ILP setting is a difficult learning task whose complexity is equivalent to multiple predicate learning. In this paper we propose computational solutions to some relevant issues raised by the multiple predicate learning problem. A separateandparallel ..."
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Cited by 13 (9 self)
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Induction of recursive theories in the normal ILP setting is a difficult learning task whose complexity is equivalent to multiple predicate learning. In this paper we propose computational solutions to some relevant issues raised by the multiple predicate learning problem. A separateandparallel conquer search strategy is adopted to interleave the learning of clauses supplying predicates with mutually recursive definitions. A novel generality order to be imposed on the search space of clauses is investigated, in order to cope with recursion in a more suitable way. The consistency recovery is performed by reformulating the current theory and by applying a layering technique, based on the collapsed dependency graph. The proposed approach has been implemented in the ILP system ATRE and tested on some laboratorysized and realworld data sets. Experimental results demonstrate that ATRE is able to learn correct theories autonomously and to discover concept dependencies. Finally, related works and their main differences with our approach are discussed.
Learning Recursive Relations with Randomly Selected Small Training Sets
 In W.W. Cohen and H. Hirsh (eds), Proc. of ICML'94
, 1994
"... We evaluate CRUSTACEAN, an inductive logic programming algorithm that uses inverse implication to induce recursive clauses from examples. This approach is well suited for learning a class of selfrecursive clauses, which commonly appear in logic programs, because it searches for common substructures ..."
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Cited by 9 (0 self)
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We evaluate CRUSTACEAN, an inductive logic programming algorithm that uses inverse implication to induce recursive clauses from examples. This approach is well suited for learning a class of selfrecursive clauses, which commonly appear in logic programs, because it searches for common substructures among the examples. However, little evidence exists that inverse implication approaches perform well when given only randomly selected positive and negative examples. We show that CRUSTACEAN learns recursive relations with higher accuracies than GOLEM, yet with reasonable efficiency. We also demonstrate that increasing the number of randomly selected positive and negative examples increases its accuracy on randomly selected test examples, increases the frequency in which it outputs the target relation, and reduces its number of outputs. We also prove a theorem that defines the class of logic programs for which our approach is complete. 1 MOTIVATION This paper extends our previous work (Ah...
Generalization of Clauses under Implication
 Journal of Artificial Intelligence Research
, 1995
"... In the area of inductive learning, generalization is a main operation, and the usual definition of induction is based on logical implication. Recently there has been a rising interest in clausal representation of knowledge in machine learning. Almost all inductive learning systems that perform gener ..."
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Cited by 9 (0 self)
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In the area of inductive learning, generalization is a main operation, and the usual definition of induction is based on logical implication. Recently there has been a rising interest in clausal representation of knowledge in machine learning. Almost all inductive learning systems that perform generalization of clauses use the relation `subsumption instead of implication. The main reason is that there is a wellknown and simple technique to compute least general generalizations under `subsumption, but not under implication. However generalization under `subsumption is inappropriate for learning recursive clauses, which is a crucial problem since recursion is the basic program structure of logic programs. We note that implication between clauses is undecidable, and we therefore introduce a stronger form of implication, called Timplication, which is decidable between clauses. We show that for every finite set of clauses there exists a least general generalization under Timplic...
Induction in first order logic from noisy training examples and fixed example set size
 In PhD Thesis
, 1999
"... Abstract This dissertation investigates the field of inductive logic programming (ILP) and in so doing an ILP system, Lime, is designed and developed. Lime addresses the problem of noisy training examples; learning from only positive, only negative, or both positive and negative examples; efficientl ..."
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Cited by 6 (0 self)
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Abstract This dissertation investigates the field of inductive logic programming (ILP) and in so doing an ILP system, Lime, is designed and developed. Lime addresses the problem of noisy training examples; learning from only positive, only negative, or both positive and negative examples; efficiently biasing and searching the hypothesis space; and handling recursion efficiently and effectively. The Qheuristic is introduced to address the problem of learning with both noisy training examples and fixed numbers of positive and negative training examples. This heuristics is based on Bayes rule. Both a justification of its derivation and a description of the context in which it is appropriately applied are given. Because of the general nature of this heuristic its application is not restricted to ILP. Instead of employing a greedy covering approach to constructing clauses, Lime employs the Qheuristic to evaluate entire logic programs as hypotheses. To tame the inevitable explosion in the search space, the notion of a simple clause is introduced. These sets of literals may be viewed as subparts of clauses that are effectively independent in terms of variables used. Instead of growing a clause one literal at a time, Lime efficiently combines simple clauses to construct a set of gainful candidate clauses. Subsets of these candidate clauses are evaluated using the Qheuristic to find the final hypothesis. Details of the algorithms and data structures of Lime are discussed. Lime's handling of recursive logic programs is also described. Experimental results are provided to illustrate how Lime achieves its design goals of better noise handling, learning from a fixed set of examples (e.g., from only positive data), and of learning recursive logic programs. These results compare the performance of Lime with other leading ILP systems like Foil and Progol in a variety of domains. Empirical results with a boosted version of Lime are also reported.