By Luc De Raedt

This first textbook on multi-relational information mining and inductive good judgment programming offers an entire review of the sector. it's self-contained and simply obtainable for graduate scholars and practitioners of information mining and laptop studying.

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The entry authorOf(lloyd, logic for learning) ← for the relation authorOf/2 represents the fact that lloyd is the author of the publication logic for learning. Similarly, reference(logic for learning, foundations of lp) ← is a fact stating that foundations of lp is in the bibliography of logic for learning. 18 2 An Introduction to Logic reference(logic for learning, foundations of lp) ← reference(logic for learning, learning logical definitions from relations) ← reference(logic for learning, ai a modern approach) ← reference(ai a modern approach, foundations of lp) ← reference(ai a modern approach, ilp theory and methods) ← reference(ilp theory and methods, learning logical definitions from relations) ← reference(ilp theory and methods, foundations of lp) ← authorOf(quinlan, learning logical definitions from relations) ← authorOf(lloyd, foundations of lp) ← authorOf(lloyd, logic for learning) ← authorOf(russell, ai a modern approach) ← authorOf(norvig, ai a modern approach) ← authorOf(muggleton, ilp theory and methods) ← authorOf(deraedt, ilp theory and methods) ← Even though the database contains only a small extract of a real database, it will be used to introduce some of the key concepts of the knowledge representation formalism employed in this book.

Second, a large variety of different quality criteria are in use. These can be distinguished on the basis of their global, local or heuristic nature. Local quality criteria are predicates whose truth-value is a function of the hypothesis h, the covers relation c and the data set D only. On the other hand, a global quality criterion is not only a function of the hypothesis h, the covers relation c and the data set D, but also of the other hypotheses in Lh . One function that is commonly used in data mining is that of frequency.

As another example consider the atoms plus(0, X, X) and plus(Y, succ(Y), Z). One possible unifier is {Y/0, X/succ(0), Z/succ(0)}, which illustrates how bindings over one occurrence of a variable are propagated to other occurrences. 4 Inference with Clausal Logic — Proof Theory 33 Notice also that unifiers do not always exist; for instance, the atoms father(john, frank) and father(X, paul) do not unify. In addition, as Ex. 32 illustrates, unifiers are not necessarily unique. To guarantee the refutation completeness of resolution when working with definite clauses in first-order logic it is necessary to work with a special type of unifier, which one calls most general unifiers.

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