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Inductive programming (IP) is a special area of automatic programming, covering research from artificial intelligence and programming, which addresses learning of typically declarative (logic or functional) and often recursive programs from incomplete specifications, such as input/output examples or constraints.
An example is the set of natural numbers N, where 0 is the first element, and the others are produced by adding 1 successively. [ 2 ] Roitman considers the same construction in a more concrete form: the elements are sets, the empty set ∅ {\displaystyle \emptyset } among them, and the successor of every element y {\displaystyle y} is the set y ...
Inductive logic programming (ILP) is an approach to machine learning that induces logic programs as hypothetical generalisations of positive and negative examples. Given a logic program representing background knowledge and positive examples together with constraints representing negative examples, an ILP system induces a logic program that ...
Inductive logic programming has adopted several different learning settings, the most common of which are learning from entailment and learning from interpretations. [16] In both cases, the input is provided in the form of background knowledge B, a logical theory (commonly in the form of clauses used in logic programming), as well as positive and negative examples, denoted + and respectively.
Structural recursion is usually proved correct by structural induction; in particularly easy cases, the inductive step is often left out. The length and ++ functions in the example below are structurally recursive. For example, if the structures are lists, one usually introduces the partial order "<", in which L < M whenever list L is the tail ...
Most recursive definitions have two foundations: a base case (basis) and an inductive clause. The difference between a circular definition and a recursive definition is that a recursive definition must always have base cases, cases that satisfy the definition without being defined in terms of the definition itself, and that all other instances in the inductive clauses must be "smaller" in some ...
Counter-example guided inductive synthesis (CEGIS) is an effective approach to building sound program synthesizers. [ 9 ] [ 10 ] CEGIS involves the interplay of two components: a generator which generates candidate programs, and a verifier which checks whether the candidates satisfy the specification.
The language that Lparse accepts is now commonly called AnsProlog, [9] short for Answer Set Programming in Logic. [10] It is now used in the same way in many other answer set solvers, including assat, clasp, cmodels, gNt, nomore++ and pbmodels. (dlv is an exception; the syntax of ASP programs written for dlv is somewhat different.)