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Learning Stochastic Logic Programs
, 2000
"... Stochastic Logic Programs (SLPs) have been shown to be a generalisation of Hidden Markov Models (HMMs), stochastic contextfree grammars, and directed Bayes' nets. A stochastic logic program consists of a set of labelled clauses p:C where p is in the interval [0,1] and C is a firstorder range ..."
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Cited by 1057 (71 self)
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Stochastic Logic Programs (SLPs) have been shown to be a generalisation of Hidden Markov Models (HMMs), stochastic contextfree grammars, and directed Bayes' nets. A stochastic logic program consists of a set of labelled clauses p:C where p is in the interval [0,1] and C is a firstorder rangerestricted definite clause. This paper summarises the syntax, distributional semantics and proof techniques for SLPs and then discusses how a standard Inductive Logic Programming (ILP) system, Progol, has been modied to support learning of SLPs. The resulting system 1) nds an SLP with uniform probability labels on each definition and nearmaximal Bayes posterior probability and then 2) alters the probability labels to further increase the posterior probability. Stage 1) is implemented within CProgol4.5, which differs from previous versions of Progol by allowing userdefined evaluation functions written in Prolog. It is shown that maximising the Bayesian posterior function involves nding SLPs with short derivations of the examples. Search pruning with the Bayesian evaluation function is carried out in the same way as in previous versions of CProgol. The system is demonstrated with worked examples involving the learning of probability distributions over sequences as well as the learning of simple forms of uncertain knowledge.
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.
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...
Predicate Invention and Utilisation
 Journal of Experimental and Theoretical Artificial Intelligence
, 1994
"... Inductive Logic Programming (ILP) involves the synthesis of logic programs from examples. In terms of scientific theory formation ILP systems define observational predicates in terms of a set of theoretical predicates. However, certain basic theorems indicate that with an inadequate theoretical voca ..."
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Cited by 7 (1 self)
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Inductive Logic Programming (ILP) involves the synthesis of logic programs from examples. In terms of scientific theory formation ILP systems define observational predicates in terms of a set of theoretical predicates. However, certain basic theorems indicate that with an inadequate theoretical vocabulary this is not always possible. Predicate invention is the augmentation of a given theoretical vocabulary to allow finite axiomatisation of the observational predicates. New theoretical predicates need to be chosen from a well defined universe of such predicates. In this paper a partial order of utilisation is described over such a universe. This ordering is a special case of a logical translation. The notion of utilisation allows the definition of an equivalence relationship over new predicates. In a manner analogous to Plotkin clause refinement is defined relative to given background knowledge and a universe of new predicates. It is shown that relative least clause refinement is define...
ILP turns 20  Biography and future challenges
 MACH LEARN
, 2011
"... Inductive Logic Programming (ILP) is an area of Machine Learning which has now reached its twentieth year. Using the analogy of a human biography this paper recalls the development of the subject from its infancy through childhood and teenage years. We show how in each phase ILP has been characteri ..."
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Cited by 7 (6 self)
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Inductive Logic Programming (ILP) is an area of Machine Learning which has now reached its twentieth year. Using the analogy of a human biography this paper recalls the development of the subject from its infancy through childhood and teenage years. We show how in each phase ILP has been characterised by an attempt to extend theory and implementations in tandem with the development of novel and challenging realworld applications. Lastly, by projection we suggest directions for research which will help the subject coming of age.
MetaInterpretive Learning of HigherOrder Dyadic Datalog: Predicate Invention revisited ∗
"... In recent years Predicate Invention has been underexplored within Inductive Logic Programming due to difficulties in formulating efficient search mechanisms. However, a recent paper demonstrated that both predicate invention and the learning of recursion can be efficiently implemented for regular an ..."
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Cited by 1 (1 self)
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In recent years Predicate Invention has been underexplored within Inductive Logic Programming due to difficulties in formulating efficient search mechanisms. However, a recent paper demonstrated that both predicate invention and the learning of recursion can be efficiently implemented for regular and contextfree grammars, by way of abduction with respect to a metainterpreter. New predicate symbols are introduced as constants representing existentially quantified higherorder variables. In this paper we generalise the approach of MetaInterpretive Learning (MIL) to that of learning higherorder dyadic datalog programs. We show that with an infinite signature the higherorder dyadic datalog class H 2 2 has universal Turing expressivity though H 2 2 is decidable given a finite signature. Additionally we show that KnuthBendix ordering of the hypothesis space together with logarithmic clause bounding allows our Dyadic MIL implementation Metagol D to PAClearn minimal cardinailty H 2 2 definitions. This result is consistent with our experiments which indicate that MetagolD efficiently learns compact H2 2 definitions involving predicate invention for robotic strategies and higherorder concepts in the NELL language learning domain. 1
Proceedings of the TwentyThird International Joint Conference on Artificial Intelligence MetaInterpretive Learning of HigherOrder Dyadic Datalog: Predicate Invention Revisited ∗
"... In recent years Predicate Invention has been underexplored within Inductive Logic Programming due to difficulties in formulating efficient search mechanisms. However, a recent paper demonstrated that both predicate invention and the learning of recursion can be efficiently implemented for regular an ..."
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In recent years Predicate Invention has been underexplored within Inductive Logic Programming due to difficulties in formulating efficient search mechanisms. However, a recent paper demonstrated that both predicate invention and the learning of recursion can be efficiently implemented for regular and contextfree grammars, by way of abduction with respect to a metainterpreter. New predicate symbols are introduced as constants representing existentially quantified higherorder variables. In this paper we generalise the approach of MetaInterpretive Learning (MIL) to that of learning higherorder dyadic datalog programs. We show that with an infinite signature the higherorder dyadic datalog class H 2 2 has universal Turing expressivity though H 2 2 is decidable given a finite signature. Additionally we show that KnuthBendix ordering of the hypothesis space together with logarithmic clause bounding allows our Dyadic MIL implementation Metagol D to PAClearn minimal cardinailty H 2 2 definitions. This result is consistent with our experiments which indicate that MetagolD efficiently learns compact H2 2 definitions involving predicate invention for robotic strategies and higherorder concepts in the NELL language learning domain. 1