Two examples of computational creativity: ILP multiple predicate synthesis and the 'Assets' in theorem proving

Abstract

We provide a precise illustration of what can be the idea of "computational creativity", that is, the whole set of the methods by which a computer may simulate creativity. This paper is restricted to multiple predicate learning in Inductive Logic Programming (ILP) and to Program Synthesis from its Formal Specification (PSFS). These two subfields of Computer Science deal with problems where creativity is of primary importance. They had to add to their basic formalisms, ILP and Beth's tableaux (for PSFS), sets of heuristics enabling the program to solve the problem of Multiple Predicate synthesis. Some of these are what is usually called a heuristic, that is, a method by which the execution speed of the program is supposed to be boosted, at the price of a lost of some solutions. This paper, inversely, shows heuristics the goal of which is to provide the program with some kind of inventiveness. The basic tool for computational creativity is what we call an 'asset generator' a specification of which is given in section 4, followed by a detailed description of our methodology for the generation of assets in PSFS. Since it may seem that our 'asset generation methodology' for PSFS relies essentially on making explicit the logician's good sense while performing a recursion constructive proof, and as an example of its efficiency, we provide in conclusion a result, a kind of challenge for the other theorem provers, namely: 'invent' a form of the Ackerman function which is recursive with respect to the second variable instead of the first variable as the usual definitions are. In ILP multiple predicate synthesis, the assets have been provided by members of the ILP community, while our methodology tries to make explicit a way to discover these assets when they are needed. © 2010 Springer-Verlag Berlin Heidelberg.