Shan-Hwei Nienhuys-Cheng, Ronald de Wolf's Foundations of Inductive Logic Programming PDF

By Shan-Hwei Nienhuys-Cheng, Ronald de Wolf

ISBN-10: 3540629270

ISBN-13: 9783540629276

Inductive common sense Programming is a tender and speedily turning out to be box combining computing device studying and common sense programming. This self-contained educational is the 1st theoretical advent to ILP; it presents the reader with a rigorous and sufficiently large foundation for destiny study within the area.
In the 1st half, an intensive remedy of first-order common sense, resolution-based theorem proving, and common sense programming is given. the second one half introduces the most recommendations of ILP and systematically develops crucial effects on version inference, inverse answer, unfolding, refinement operators, least generalizations, and how you can care for history wisdom. in addition, the authors provide an summary of PAC studying ends up in ILP and of a few of the main proper carried out systems.

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Extra info for Foundations of Inductive Logic Programming

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Hence we may not be able to find out in finite time whether or not D ~ r by checking all possible interpretations. 3. SEMANTICS 31 or E ~: r will be quite prominent in the next chapters. But first we will generalize some other definitions from propositional logic to the first-order case. 33 Two formulas 0 and ~ are said to be (logically) equivalent (denoted by 0 r r if both b ~ ~ and r ~ r (so r and V5 have exactly the same models). Similarly, two sets of formulas E and F are said to be (logically) equivalent, if both E ~ P and r ~ E.

23 Let I be an interpretation, based on the pre-interpretation J with domain D, of the first-order language L, and let V be a variable assignment with respect to L. Let Z be the term assignment with respect to J and V. Then a formula r in L has a truth value under I and V, as follows: 1. , t,~), and di is the domain element assigned to tl by Z (i = 1 , . . ,dn). 22) P(f(a), f(a), f(f(a))) has truth value Ip(1, 1, 2) = T under I and V. P(f(x), a, f(f(y))) has truth value Ip(6, O, 2) = F under I and V.

Which may be subscripted. 2. , which may be subscripted. 3. A set of function symbols: f , g , . . , which may be subscripted. Each function symbol has a natural number (its arity) assigned to it. 4. A non-empty set of predicate symbols: P, Q , . . , which may be subscripted. Each predicate symbol has a natural number (its arity) assigned to it. 5. The following five connectives: -~, A, V, ~ and ~ . 6. Two quantifiers: ~ (called the existential quantifier) and V (called the universal quantifier).

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