Results 1  10
of
30
Thetasubsumption for structural matching
, 1996
"... Structural matching, originally introduced by Steven Vere in the midseventies, was a popular subfield of inductive conceptlearning in the late seventies and early eighties. Despite various attempts to formalize and implement the notion of "most specific generalisation" of two productions ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
Structural matching, originally introduced by Steven Vere in the midseventies, was a popular subfield of inductive conceptlearning in the late seventies and early eighties. Despite various attempts to formalize and implement the notion of "most specific generalisation" of two productions, several problems remained. These include using background knowledge, the nonuniqueness of most specific generalisations, and handling inequalities. We show how Gordon Plotkin's notions of "least general generalisation" and "relative least general generalisation" defined on clauses can be adapted for use in structural matching such that the remaining problems disappear. De ning clauses as universally quanti ed disjunctions of literals and productions as existentially quanti ed conjunctions of literals, it is shown that the lattice on clauses imposed bysubsumption is orderisomorphic to the lattice on productions needed for structural matching. The mapping also shows the relation between the older work on structural matching and the fashionable inductive logic programming paradigm.
Covering vs. DivideandConquer for TopDown Induction of Logic Programs
 Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence
, 1995
"... Covering and divideandconquer are two wellestablished search techniques for topdown induction of propositional theories. However, for topdown induction of logic programs, only covering has been formalized and used extensively. In this work, the divideandconquer technique is formalized as ..."
Abstract

Cited by 16 (5 self)
 Add to MetaCart
Covering and divideandconquer are two wellestablished search techniques for topdown induction of propositional theories. However, for topdown induction of logic programs, only covering has been formalized and used extensively. In this work, the divideandconquer technique is formalized as well and compared to the covering technique in a logic programming framework. Covering works by repeatedly specializing an overly general hypothesis, on each iteration focusing on finding a clause with a high coverage of positive examples. Divideandconquer works by specializing an overly general hypothesis once, focusing on discriminating positive from negative examples. Experimental results are presented demonstrating that there are cases when more accurate hypotheses can be found by divideand conquer than by covering. Moreover, since covering considers the same alternatives repeatedly it tends to be less efficient than divideand conquer, which never considers the same ...
Specialization of Logic Programs by Pruning SLDTrees
 Proc. of the Fourth International Workshop on Inductive Logic Programming (ILP94) Bad Honnef/Bonn Germany September
, 1994
"... The problem of finding an inductive hypothesis by specializing a logic program w.r.t. positive and negative examples can be viewed as the problem of pruning an SLDtree such that all refutations of negative examples and no refutations of positive examples are excluded. It is shown that the actua ..."
Abstract

Cited by 18 (2 self)
 Add to MetaCart
The problem of finding an inductive hypothesis by specializing a logic program w.r.t. positive and negative examples can be viewed as the problem of pruning an SLDtree such that all refutations of negative examples and no refutations of positive examples are excluded. It is shown that the actual pruning can be performed by applying unfolding and clause removal. The algorithm spectre is presented, which is based on this idea. The input to the algorithm is, besides a logic program and positive and negative examples, a computation rule, which determines the shape of the SLDtree that is to be pruned. It is shown that the generality of the resulting specialization is dependent on the computation rule, and experimental results are presented from using three different computation rules. The experiments indicate that the computation rule should be formulated so that the number of applications of unfolding is kept as low as possible. The algorithm, which uses a divideandconquer...
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 ..."
Abstract

Cited by 10 (0 self)
 Add to MetaCart
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...
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 ..."
Abstract

Cited by 13 (0 self)
 Add to MetaCart
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...
TheoryGuided Induction of Logic Programs by Inference of Regular Languages
 Proc. of the 13th International Conference on Machine Learning
, 1996
"... Previous resolutionbased approaches to theoryguided induction of logic programs produce hypotheses in the form of a set of resolvents of a theory, where the resolvents represent allowed sequences of resolution steps for the initial theory. There are, however, many characterizations of allowe ..."
Abstract

Cited by 9 (2 self)
 Add to MetaCart
Previous resolutionbased approaches to theoryguided induction of logic programs produce hypotheses in the form of a set of resolvents of a theory, where the resolvents represent allowed sequences of resolution steps for the initial theory. There are, however, many characterizations of allowed sequences of resolution steps that cannot be expressed by a set of resolvents. One approach to this problem is presented, the system merlin, which is based on an earlier technique for learning finitestate automata that represent allowed sequences of resolution steps. merlin extends the previous technique in three ways: i) negative examples are considered in addition to positive examples, ii) a new strategy for performing generalization is used, and iii) a technique for converting the learned automaton to a logic program is included. Results from experiments are presented in which merlin outperforms both a system using the old strategy for performing generalization, and a t...
Improving Accuracy of Incorrect Domain Theories
, 1994
"... An approach to improve accuracy of incorrect domain theories is presented that learns concept descriptions from positive and negative examples of the concept. The method uses the available domain theory, that might be both overly general and overly specific, to group training examples before a ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
An approach to improve accuracy of incorrect domain theories is presented that learns concept descriptions from positive and negative examples of the concept. The method uses the available domain theory, that might be both overly general and overly specific, to group training examples before attempting concept induction. gentre is a system that has been implemented to test the performance of the method. gentre is not limited to variablefree, functionfree or nonrecursive domains as many other approaches. In the paper we present results from experiments in three different domains and compare the performance of gentre with that of ID3 and IOU. The learned concept descriptions are consistent with training examples and have an improved classification accuracy relative to the original domain theory. 1 INTRODUCTION Many knowledge intensive techniques require that the application domain is well understood and can be expressed in the form of correct rules of a domain theor...
Covering vs DivideandConquer for TopDown Induction of Logic Programs
"... Covering and divideandconquer are two wellestablished search techniques for topdown induction of propositional theories However, for topdown induction of logic programs, only covering has been formalized and used extensively In this work, the divideandconquer technique is formalized as well an ..."
Abstract
 Add to MetaCart
Covering and divideandconquer are two wellestablished search techniques for topdown induction of propositional theories However, for topdown induction of logic programs, only covering has been formalized and used extensively In this work, the divideandconquer technique is formalized as well and compared to the covering technique in a logic programming framework Covering works by repeatedly specializing an overly general hypothesis, on each iteration focusing on finding a clause with a high coverage of positive examples Divideandconquer works by specializing an overly general hypothesis once, focusing on discriminating positive from negative examples Experimental results are presented demonstrating that there are cases when more accurate hypotheses can be found by divideandconquer than by covering Moreover, since covering considers the same alternatives repeatedly it tends to be less efficient than divideandconquer, which never considers the same alternative twice On the other hand, covering searches a larger hypothesis space, which may result in that more compact hypotheses are found by this technique than by dmdeandconquer Furthermore, divideandconquer is, in contrast to covering, not applicable to learning recursive definitions, 1
The Subsumption Theorem in Inductive Logic Programming: Facts and Fallacies
 Advances in Inductive Logic Programming. IOS
, 1995
"... . The subsumption theorem is an important theorem concerning resolution. Essentially, it says that if a set of clauses \Sigma logically implies a clause C, then either C is a tautology, or a clause D which subsumes C can be derived from \Sigma with resolution. It was originally proved in 1967 by Lee ..."
Abstract

Cited by 9 (2 self)
 Add to MetaCart
. The subsumption theorem is an important theorem concerning resolution. Essentially, it says that if a set of clauses \Sigma logically implies a clause C, then either C is a tautology, or a clause D which subsumes C can be derived from \Sigma with resolution. It was originally proved in 1967 by Lee. In Inductive Logic Programming, interest in this theorem is increasing since its independent rediscovery by Bain and Muggleton. It provides a quite natural "bridge" between subsumption and logical implication. Unfortunately, a correct formulation and proof of the subsumption theorem are not available. It is not clear which forms of resolution are allowed. In fact, at least one of the current forms of this theorem is false. This causes a lot of confusion. In this paper we give a careful proof of the subsumption theorem for unconstrained resolution, and show that the wellknown refutationcompleteness of resolution is just a special case of this theorem. We also show that the subsumption theo...
Induction of Logic Programs by Exampleguided Unfolding
 Journal of Logic Programming
, 1999
"... Resolution has been used as a specialisation operator in several approaches to topdown induction of logic programs. This operator allows the overly general hypothesis to be used as a declarative bias that restricts not only what predicate symbols can be used in produced hypotheses, but also how the ..."
Abstract

Cited by 8 (3 self)
 Add to MetaCart
Resolution has been used as a specialisation operator in several approaches to topdown induction of logic programs. This operator allows the overly general hypothesis to be used as a declarative bias that restricts not only what predicate symbols can be used in produced hypotheses, but also how the predicates can be invoked. The two main strategies for topdown induction of logic programs, Covering and DivideandConquer, are formalised using resolution as a specialisation operator, resulting in two strategies for performing exampleguided unfolding. These strategies are compared both theoretically and experimentally. It is shown that the computational cost grows quadratically in the size of the example set for Covering, while it grows linearly for DivideandConquer. This is also demonstrated by experiments, in which the amount ofwork performed by Covering is up to 30 times the amount ofwork performed by DivideandConquer. The theoretical analysis shows that the hypothesis space is larger for Covering, and thus more compact hypotheses may be found by this technique than by DivideandConquer. However, it is shown that for each nonrecursive hypothesis that can be produced by Covering, there is an equivalent hypothesis (w.r.t. the background predicates) that can be produced by DivideandConquer. A major drawback of DivideandConquer, in contrast to Covering, is that it is not applicable to learning recursive de nitions. 1 1
Results 1  10
of
30