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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.
Inductive logic programming (ILP) is a subfield of symbolic artificial intelligence which uses logic programming as a uniform representation for examples, background knowledge and hypotheses. The term " inductive " here refers to philosophical (i.e. suggesting a theory to explain observed facts) rather than mathematical (i.e. proving a property ...
Before covering Inductive-Recursive types, the simpler case is Inductive Types. Constructors for Inductive types can be self-referential, but in a limited way. The constructor's parameters must be "positive": not refer to the type being defined; be exactly the type being defined, or; be a function that returns the type being defined.
Aleph searches for clauses in a top-down manner, using the bottom clause constructed in the preceding step to bound the search from below. It searches the refinement graph in a breadth-first manner, with tunable parameters to bound the maximal clause size and proof depth.
A structurally recursive function uses the same idea to define a recursive function: "base cases" handle each minimal structure and a rule for recursion. Structural recursion is usually proved correct by structural induction; in particularly easy cases, the inductive step is often left out.
System 2 is slower, step-by-step, and explicit. System 1 is the kind used for pattern recognition while System 2 is far better suited for planning, deduction, and deliberative thinking. In this view, deep learning best models the first kind of thinking while symbolic reasoning best models the second kind and both are needed.
In type theory, a system has inductive types if it has facilities for creating a new type from constants and functions that create terms of that type. The feature serves a role similar to data structures in a programming language and allows a type theory to add concepts like numbers , relations , and trees .
Decision Tree. Rule induction is an area of machine learning in which formal rules are extracted from a set of observations. The rules extracted may represent a full scientific model of the data, or merely represent local patterns in the data.