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25
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 628 (58 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.
Complexity and Expressive Power of Logic Programming
, 1997
"... This paper surveys various complexity results on different forms of logic programming. The main focus is on decidable forms of logic programming, in particular, propositional logic programming and datalog, but we also mention general logic programming with function symbols. Next to classical results ..."
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Cited by 283 (57 self)
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This paper surveys various complexity results on different forms of logic programming. The main focus is on decidable forms of logic programming, in particular, propositional logic programming and datalog, but we also mention general logic programming with function symbols. Next to classical results on plain logic programming (pure Horn clause programs), more recent results on various important extensions of logic programming are surveyed. These include logic programming with different forms of negation, disjunctive logic programming, logic programming with equality, and constraint logic programming. The complexity of the unification problem is also addressed.
An Efficient Subsumption Algorithm for Inductive Logic Programming
 IN PROCEEDINGS OF THE ELEVENTH INTERNATIONAL CONFERENCE ON MACHINE LEARNING
, 1994
"... In this paper we investigate the efficiency of ` subsumption (` ` ), the basic provability relation in ILP. As D ` ` C is NPcomplete even if we restrict ourselves to linked Horn clauses and fix C to contain only a small constant number of literals, we investigate in several restrictions of D. ..."
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Cited by 30 (3 self)
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In this paper we investigate the efficiency of ` subsumption (` ` ), the basic provability relation in ILP. As D ` ` C is NPcomplete even if we restrict ourselves to linked Horn clauses and fix C to contain only a small constant number of literals, we investigate in several restrictions of D. We first adapt the notion of determinate clauses used in ILP and show that `subsumption is decidable in polynomial time if D is determinate with respect to C. Secondly, we adapt the notion of klocal Horn clauses and show that ` subsumption is efficiently computable for some reasonably small k. We then show how these results can be combined, to give an efficient reasoning procedure for determinate klocal Horn clauses, an ILPproblem recently suggested to be polynomial predictable by Cohen (1993) by a simple counting argument. We finally outline how the `reduction algorithm, an essential part of every lgg ILPlearning algorithm, can be improved by these ideas.
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...
ILP: A Short Look Back and a Longer Look Forward
 Journal of Machine Learning Research
, 2003
"... Inductive logic programming (ILP) is built on a foundation laid by research in other areas of machine learning and computational logic. But in spite of this strong foundation, at just over 10 years of age ILP now faces a number of new challenges brought on by exciting areas of application. Research ..."
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Cited by 19 (0 self)
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Inductive logic programming (ILP) is built on a foundation laid by research in other areas of machine learning and computational logic. But in spite of this strong foundation, at just over 10 years of age ILP now faces a number of new challenges brought on by exciting areas of application. Research in other areas of machine learning and computational logic can contribute much to help ILP meet these challenges. After a brief review, the paper presents ve future research directions for ILP and points to initial approaches or results where they exist. It is hoped that the paper will motivate research workers in machine learning and computational logic to invest some time into ILP.
Least Generalizations and Greatest Specializations of Sets of Clauses
 Journal of Artificial Intelligence Research
, 1996
"... The main operations in Inductive Logic Programming (ILP) are generalization and specialization, which only make sense in a generality order. In ILP, the three most important generality orders are subsumption, implication and implication relative to background knowledge. The two languages used most o ..."
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Cited by 12 (0 self)
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The main operations in Inductive Logic Programming (ILP) are generalization and specialization, which only make sense in a generality order. In ILP, the three most important generality orders are subsumption, implication and implication relative to background knowledge. The two languages used most often are languages of clauses and languages of only Horn clauses. This gives a total of six different ordered languages. In this paper, we give a systematic treatment of the existence or nonexistence of least generalizations and greatest specializations of finite sets of clauses in each of these six ordered sets. We survey results already obtained by others and also contribute some answers of our own. Our main new results are, firstly, the existence of a computable least generalization under implication of every finite set of clauses containing at least one nontautologous functionfree clause (among other, not necessarily functionfree clauses). Secondly, we show that such a least generali...
ILP: Just Do It
, 2000
"... Inductive logic programming (ILP) is built on a foundation laid by research in other areas of computational logic. But in spite of this strong foundation, at 10 years of age ILP now faces a number of new challenges brought on by exciting application opportunities. The purpose of this paper is to int ..."
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Cited by 11 (1 self)
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Inductive logic programming (ILP) is built on a foundation laid by research in other areas of computational logic. But in spite of this strong foundation, at 10 years of age ILP now faces a number of new challenges brought on by exciting application opportunities. The purpose of this paper is to interest researchers from other areas of computational logic in contributing their special skill sets to help ILP meet these challenges. The paper presents five future research directions for ILP and points to initial approaches or results where they exist. It is hoped that the paper will motivate researchers from throughout computational logic to invest some time into "doing" ILP.
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...
On Exact Learning of Unordered Tree Patterns
 Machine Learning
, 2000
"... . Tree patterns are natural candidates for representing rules and hypotheses in many tasks such as information extraction and symbolic mathematics. A tree pattern is a tree with labeled nodes where some of the leaves may be labeled with variables, whereas a tree instance has no variables. A tree pat ..."
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Cited by 9 (0 self)
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. Tree patterns are natural candidates for representing rules and hypotheses in many tasks such as information extraction and symbolic mathematics. A tree pattern is a tree with labeled nodes where some of the leaves may be labeled with variables, whereas a tree instance has no variables. A tree pattern matches an instance if there is a consistent substitution for the variables that allows a mapping of subtrees to matching subtrees of the instance. A finite union of tree patterns is called a forest. In this paper, we study the learnability of tree patterns from queries when the subtrees are unordered. The learnability is determined by the semantics of matching as defined by the types of mappings from the pattern subtrees to the instance subtrees. We first show that unordered tree patterns and forests are not exactly learnable from equivalence and subset queries when the mapping between subtrees is onetoone onto, regardless of the computational power of the learner. Tree and forest pa...
The logic of learning: a brief introduction to Inductive Logic Programming
 University of Manchester
, 1998
"... This paper is intended to provide an introduction to ILP. We will both review some of the established approaches to Horn clause induction (Section 2), and recent work on induction of integrity constraints (Section 3). 2 Horn clause induction ..."
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Cited by 7 (0 self)
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This paper is intended to provide an introduction to ILP. We will both review some of the established approaches to Horn clause induction (Section 2), and recent work on induction of integrity constraints (Section 3). 2 Horn clause induction