Evolving Combinators

One of the many abilities that distinguish a mathematician from an automated deduction system is to be able to ooer appropriate expressions based on intuition and experience that are substituted for existentially quantiied variables so as to simplify the problem at hand substantially. We propose to simulate this ability with a technique called genetic programming for use in automated deduction. We apply this approach to problems of combinatory logic. Our experimental results show that the approach is viable and actually produces very promising results. A comparison with the renowned theorem prover Otter underlines the achievements.

[1]  Susanne Biundo-Stephan.  Automated Synthesis of Recursive Algorithms as a Theorem Proving Tool , 1988, ECAI.

[2]  Una-May O'Reilly,et al.  Genetic Programming II: Automatic Discovery of Reusable Programs. , 1994, Artificial Life.

[3]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[4]  Hitoshi Iba,et al.  Distributed genetic programming: empirical study and analysis , 1996 .

[5]  Rick Stevens,et al.  Automated Reasoning Contributed to Mathematics and Logic , 1990, CADE.

[6]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[7]  Kenneth DeJong,et al.  Learning with genetic algorithms: An overview , 1988, Machine Learning.

[8]  Matthias Fuchs,et al.  Goal Oriented Equational Theorem Proving Using Team Work , 1994, KI.

[9]  Raymond M. Smullyan,et al.  To Mock a Mockingbird , 1985 .

[10]  John R. Koza,et al.  Genetic programming - on the programming of computers by means of natural selection , 1993, Complex adaptive systems.

[11]  Michael J. O'Donnell,et al.  Computing in systems described by equations , 1977, Lecture Notes in Computer Science.

[12]  Wolfgang Ertel,et al.  Random competition: a simple, but efficient method for parallelizing inference systems , 1990, Forschungsberichte, TU Munich.

[13]  Larry Wos,et al.  Challenge Problems Focusing on Equality and Combinatory Logic: Evaluating Automated Theorem-Proving Programs , 1988, CADE.

[14]  William McCune,et al.  OTTER 3.0 Reference Manual and Guide , 1994 .

[15]  Dimitris C. Dracopoulos,et al.  Speeding up genetic programming: a parallel BSP implementation , 1996 .

[16]  Henk Barendregt,et al.  The Lambda Calculus: Its Syntax and Semantics , 1985 .

[17]  Larry Wos,et al.  Benchmark Problems in Which Equality Plays the Major Role , 1992, CADE.