Heuristic Functions, Primitive Recursion and Recursivity

摘要

When we approach to a problem of Artificial Intelligence, we can distinguish between Classification, Searching and Representation Methods. Within Searching Procedures, we have the Blind Search (without knowledge of the Domain) and the Heuristic Search (with knowledge of the Domain).rnThe Theory of Functions provide us with very useful tools (such as the heuristic function) for the representation and solution of such type of problems. Such function show, for instance, the estimation of distance to the final node, or equivalently, the number of steps to reach the solution.rnAlso, in the problems with Fuzzy Logic and Non-Monotonic reasoning appears a very interesting tool: the membership function, with the information about the degree of completion of the condition defining the respective Fuzzy Set or Fuzzy Relation. Finally, we analyze the interesting Ackermann function, famous counterexample, created to prove that the μ—recursivity does not imply the primitive recursion, with its consequences in Automata Theory.