Recently there has been an increasing amount of research on learning concepts expressed in subsets of Prolog;the term inductive logic programming (ILP) has been used to describe this growing body of research. This pap...
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Recently there has been an increasing amount of research on learning concepts expressed in subsets of Prolog;the term inductive logic programming (ILP) has been used to describe this growing body of research. This paper seeks to expand the theoretical foundations of ILP by investigating the pac-learnability of logic programs. We focus on programs consisting of a single function-free non-recursive clause, and focus on generalizations of a language known to be pac-learnable: namely, the language of determinate function-free clauses of constant depth. We demonstrate that a number of syntactic generalizations of this language are hard to learn, but that the language can be generalized to clauses of constant locality while still allowing pac-learnability. More specifically, we first show that determinate clauses of log depth are not pac-learnable, regardless of the language used to represent hypotheses. We then investigate the effect of allowing indeterminacy in a clause, and show that clauses with k indeterminate variables are as hard to learn as DNF. We next show that a more restricted language of clauses with bounded indeterminacy is learnable using k-CNF to represent hypotheses, and that restricting the ''locality'' of a clause to a constant allows pac-learnability even if an arbitrary amount of indeterminacy is allowed. This last result is also shown to be a strict generalization of the previous result for determinate function-free clauses of constant depth. Finally, we present some extensions of these results to logic programs with multiple clauses.
In this paper we investigate the learnability of relations in inductive logic programming, by using equality theories as background knowledge. We assume that a hypothesis and an observation are respectively a definite...
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In this paper we investigate the learnability of relations in inductive logic programming, by using equality theories as background knowledge. We assume that a hypothesis and an observation are respectively a definite program and a set of ground literals. The targets of our learning algorithm are relations. By using equality theories as background knowledge we introduce tree structure into definite programs. The structure enable us to narrow the search space of hypothesis. We give pairs of a hypothesis language and a knowledge language in order to discuss the learnability of relations from the view point of inductive inference and PAC learning.
A comparative study is presented of language biases employed in specific-to-general learning systems within the inductive logic programming (ILP) paradigm. More specifically, we focus on the biases employed in three w...
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A comparative study is presented of language biases employed in specific-to-general learning systems within the inductive logic programming (ILP) paradigm. More specifically, we focus on the biases employed in three well known systems: CLINT, GOLEM and ITOU, and evaluate both conceptually and empirically their strengths and weaknesses. The evaluation is carried out within the generic framework of the NINA system, in which bias is a parameter. Two different types of biases are considered: syntactic bias, which defines the set of well-formed clauses, and semantic bias, which imposes restrictions on the behaviour of hypotheses or clauses. NINA is also able to shift its bias (within a predefined series of biases), whenever its current bias is insufficient for finding complete and consistent concept definitions. Furthermore, a new formalism for specifying the syntactic bias of inductive logic programming systems is introduced.
Relative least general generalization, proposed by Plotkin, is widely used for generalizing first-order clauses in inductive logic programming, and this paper describes an extension of Plotkin's work to allow vari...
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Relative least general generalization, proposed by Plotkin, is widely used for generalizing first-order clauses in inductive logic programming, and this paper describes an extension of Plotkin's work to allow various computation domains: Herbrand Universe, sets, numerical data, etc. The theta-subsumption in Plotkin's framework is replaced by a more general constraint-based subsumption. Since this replacement is analogous to that of unification by constraint solving in Constraint logicprogramming, the resultant method can be viewed as a Constraint logicprogramming version of relative least general generalization. Constraint-based subsumption, however, leads to a search on an intractably large hypothesis space. We therefore provide meta-level constraints that are used as semantic bias on the hypothesis language. The constraints functional dependency and monotonicity are introduced by analyzing clausal relationships. Finally, the advantage of the proposed method is demonstrated through a simple layout problem, where geometric constraints used in space planning tasks are produced automatically.
The task of predicate invention in inductive logic programming is to extend the hypothesis language with new predicates if the vocabulary given initially is insufficient for the learning task. However, whether predica...
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The task of predicate invention in inductive logic programming is to extend the hypothesis language with new predicates if the vocabulary given initially is insufficient for the learning task. However, whether predicate invention really helps to make learning succeed in the extended language depends on the language bias currently employed. In this paper, we investigate for which commonly employed language biases predicate invention is an appropriate shift operation. We prove that for some restricted languages predicate invention does not help when the learning task fails and we characterize the languages for which predicate invention is useful. We investigate the decidability of the bias shift problem for these languages and discuss the capabilities of predicate invention as a bias shift operation.
Several applications of inductive logic programming (ILP) are presented. These belong to various areas of engineering, including mechanical, environmental, software, and dynamical systems engineering. The particular a...
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Several applications of inductive logic programming (ILP) are presented. These belong to various areas of engineering, including mechanical, environmental, software, and dynamical systems engineering. The particular applications are finite element mesh design, biological classification of river water quality, data reification, inducing program invariants, learning qualitative models of dynamic systems, and learning control rules for dynamic systems. A number of other applications are briefly mentioned. Finally, a discussion of the advantages and disadvantages of ILP as compared to other approaches to machine learning is given.
FOIL is a first-order learning system that uses information in a collection of relations to construct theories expressed in a dialect of Prolog. This paper provides an overview of the principal ideas and methods used ...
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FOIL is a first-order learning system that uses information in a collection of relations to construct theories expressed in a dialect of Prolog. This paper provides an overview of the principal ideas and methods used in the current version of the system, including two recent additions. We present examples of tasks tackled by FOIL and of systems that adapt and extend its approach.
The finite element method (FEM) is the most successful numerical method, that is used extensively by engineers to analyse stresses and deformations in physical structures. These structures should be represented as a f...
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The finite element method (FEM) is the most successful numerical method, that is used extensively by engineers to analyse stresses and deformations in physical structures. These structures should be represented as a finite element mesh. Defining an appropriate geometric mesh model that ensures low approximation errors and avoids unnecessary computational overheads is a very difficult and time consuming task. It is the major bottleneck in the FEM analysis process. The inductive logic programming system GOLEM has been employed to construct the rules for deciding about the appropriate mesh resolution. Five cylindrical mesh models have been used as a source of training examples. The evaluation of the resulting knowledge base shows that conditions in the domain are well represented by the rules, which specify the required number of the finite elements on the edges of the structures to be analysed using FEM. A comparison between the results obtained by this knowledge base and conventional mesh generation techniques confirms that the application of inductive logic programming is an effective approach to solving the problem of mesh design.
A central problem in inductive logic programming is theory evaluation. Without some sort of preference criterion, any two theories that explain a set of examples are equally acceptable. This paper presents a scheme fo...
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A central problem in inductive logic programming is theory evaluation. Without some sort of preference criterion, any two theories that explain a set of examples are equally acceptable. This paper presents a scheme for evaluating alternative inductive theories based on an objective preference criterion. It strives to extract maximal redundancy from examples, transforming structure into randomness. A major strength of the method is its application to learning problems where negative examples of concepts are scarce or unavailable. A new measure called model complexity is introduced, and its use is illustrated and compared with a proof complexity measure on relational learning tasks. The complementarity of model and proof complexity parallels that of model and proof-theoretic semantics. Model complexity, where applicable, seems to be an appropriate measure for evaluating inductivelogic theories.
Two representation changes are presented: the first one, called flattening, transforms a first-order logic program with function symbols into an equivalent logic program without function symbols;the second one, called...
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Two representation changes are presented: the first one, called flattening, transforms a first-order logic program with function symbols into an equivalent logic program without function symbols;the second one, called saturation, completes an example description with relevant information with respect to both the example and available background knowledge. The properties of these two representation changes are analyzed as well as their influence on a generalization algorithm that takes a single example as input.
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