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CHAPTER
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LEARNING SETS OF RULES
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One of the most expressive and human readable representations for learned hypotheses is sets of if-then rules This chapter explores several algorithms for learning such sets of rules One important special case involves learning sets of rules containing variables, called first-order Horn clauses Because sets of first-order Horn clauses can be interpreted as programs in the logic programming language PROLOG, learning them is often called inductive logic programming (ILP) This chapter examines several approaches to learning sets of rules, including an approach based on inverting the deductive operators of mechanical theorem provers
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101 INTRODUCTION
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In many cases it is useful to learn the target function represented as a set of if-then rules that jointly define the function As shown in 3, one way to learn sets of rules is to first learn a decision tree, then translate the tree into an equivalent set of rules-one rule for each leaf node in the tree A second method, illustrated in 9, is to use a genetic algorithm that encodes each rule set as a bit string and uses genetic search operators to explore this hypothesis space In this chapter we explore a variety of algorithms that directly learn rule sets and that differ from these algorithms in two key respects First, they are designed to learn sets of first-order rules that contain variables This is significant because first-order rules are much more expressive than propositional rules Second, the algorithms discussed here use sequential covering algorithms that learn one rule at a time to incrementally grow the final set of rules
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As an example of first-order rule sets, consider the following two rules that jointly describe the target concept Ancestor Here we use the predicate Parent(x, y) to indicate that y is the mother or father of x, and the predicate Ancestor(x, y) to indicate that y is an ancestor of x related by an arbitrary number of family generations
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Parent (x,y) Parent(x, z) A Ancestor(z, y )
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Note these two rules compactly describe a recursive function that would be very difficult to represent using a decision tree or other propositional representation One way to see the representational power of first-order rules is to consider the In programs are sets of general purpose programming language PROLOG PROLOG, first-order rules such as the two shown above (rules of this form are also called H r clauses) In fact, when stated in a slightly different syntax the above rules on form a valid PROLOG program for computing the Ancestor relation In this light, a general purpose algorithm capable of learning such rule sets may be viewed as an algorithm for automatically inferring PROLOG programs from examples In this chapter we explore learning algorithms capable of learning such rules, given appropriate sets of training examples In practice, learning systems based on first-order representations have been successfully applied to problems such as learning which chemical bonds fragment in a mass spectrometer (Buchanan 1976; Lindsay 1980), learning which chemical substructures produce mutagenic activity (a property related to carcinogenicity) (Srinivasan et al 1994), and learning to design finite element meshes to analyze stresses in physical structures (Dolsak and Muggleton 1992) In each of these applications, the hypotheses that must be represented involve relational assertions that can be conveniently expressed using first-order representations, while they are very difficult to describe using propositional representations In this chapter we begin by considering algorithms that learn sets of propositional rules; that is, rules without variables Algorithms for searching the hypothesis space to learn disjunctive sets of rules are most easily understood in this setting We then consider extensions of these algorithms to learn first-order rules Two general approaches to inductive logic programming are then considered, and the fundamental relationship between inductive and deductive inference is explored
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