Logical and relational learning by Luc De Raedt

By Luc De Raedt

This first textbook on multi-relational info mining and inductive common sense programming presents a whole review of the sphere. it really is self-contained and simply obtainable for graduate scholars and practitioners of information mining and computing device studying.

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Only one point changes: the method to prove C |= h ← b1 , · · · , bn by refutation. More specifically, the step where the clause is negated needs to take into account the quantifiers and the variables occurring in the clause. As the negation of a universally quantified formula is an existentially quantified negated formula, the refutation proof uses ← hθ, b1 θ ←, ... , bn θ ←, where θ is a so-called skolem substitution. , bn by distinct constants not appearing anywhere else in the theory or clause.

5 A Generate-and-Test Algorithm Depending on the type and nature of the quality criterion considered, different algorithms can be employed to compute T h(Q, D, Lh ). For a given quality criterion and hypotheses space, one can view mining or learning as a search process. By exploiting this view, a (trivial) algorithm based on the well-known generate-and-test technique in artificial intelligence can be derived. This socalled enumeration algorithm is shown in Algo. 1. 1 The enumeration algorithm for all h ∈ Lh do if Q(h, D) = true then output h end if end for Although the algorithm is naive, it has some interesting properties: whenever a solution exists, the enumeration algorithm will find it.

Another model for this example is {human(john), male(john)}. 19. Reconsider the bibliographic database together with the clause defining the predicate cites/2. Algo. 1 would generate the interpretation consisting of all ground facts for the predicates reference/2, cites/2 and authorOf/2 that were listed in the earlier examples. 20. Reconsider the definition of the natural numbers using the predicate nat/1. For these clauses, the algorithm does not terminate, because it attempts to generate the infinite model I5 defined above.

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