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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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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
Learning in Clausal Logic: A Perspective on Inductive Logic Programming
 Computational Logic: Logic Programming and Beyond, volume 2407 of Lecture Notes in Computer Science
, 2002
"... Abstract. Inductive logic programming is a form of machine learning from examples which employs the representation formalism of clausal logic. One of the earliest inductive logic programming systems was Ehud Shapiro’s Model Inference System [90], which could synthesise simple recursive programs like ..."
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Abstract. Inductive logic programming is a form of machine learning from examples which employs the representation formalism of clausal logic. One of the earliest inductive logic programming systems was Ehud Shapiro’s Model Inference System [90], which could synthesise simple recursive programs like append/3. Many of the techniques devised by Shapiro, such as topdown search of program clauses by refinement operators, the use of intensional background knowledge, and the capability of inducing recursive clauses, are still in use today. On the other hand, significant advances have been made regarding dealing with noisy data, efficient heuristic and stochastic search methods, the use of logical representations going beyond definite clauses, and restricting the search space by means of declarative bias. The latter is a general term denoting any form of restrictions on the syntactic form of possible hypotheses. These include the use of types, input/output mode declarations, and clause schemata. Recently, some researchers have started using alternatives to Prolog featuring strong typing and real functions, which alleviate the need for some of the above adhoc mechanisms. Others have gone beyond Prolog by investigating learning tasks in which the hypotheses are not definite clause programs, but for instance sets of indefinite clauses or denials, constraint logic programs, or clauses representing association rules. The chapter gives an accessible introduction to the above topics. In addition, it outlines the main current research directions which have been strongly influenced by recent developments in data mining and challenging reallife applications. 1
A Class of Rewriting Rules and Reverse Transformation for Rulebased Equivalent Transformation
, 2001
"... In the rulebased equivalent transformation (RBET) paradigm, where computation is based on meaningpreserving transformation of declarative descriptions, a set of rewriting rules is regarded as a program. The syntax for a large class of rewriting rules is determined. The incorporation of metavariab ..."
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In the rulebased equivalent transformation (RBET) paradigm, where computation is based on meaningpreserving transformation of declarative descriptions, a set of rewriting rules is regarded as a program. The syntax for a large class of rewriting rules is determined. The incorporation of metavariables of two different kinds enables precise control of rewritingrule instantiations. As a result, the applicability of rewriting rules and the results of rule applications can be rigorously specified. A theoretical basis for justifying the correctness of rewriting rules is established. Reverse transformation operation in the RBET framework is discussed, and it is shown that a correct rewriting rule is reversible, i.e., a correct rewriting rule can in general be constructed by syntactically reversing another correct rewriting rule.
Theorem Proving for Untyped Constructive λCalculus: Implementation and Application
"... This paper presents a theorem prover for a highly intensional logic, namely a constructive version of property theory [25] (this language essentially provides a combination of constructive firstorder logic and the #calculus). The paper presents the basic theorem prover, which is a higherorder ext ..."
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This paper presents a theorem prover for a highly intensional logic, namely a constructive version of property theory [25] (this language essentially provides a combination of constructive firstorder logic and the #calculus). The paper presents the basic theorem prover, which is a higherorder extension of Manthey and Bry's model generation theorem prover for firstorder logic [14]; considers issues relating to the compiletime optimisations that are often used with firstorder theorem provers; and shows how the resulting system can be used in a natural language understanding system.