MaLeCoP: Machine Learning Connection Prover

Abstract

Probabilistic guidance based on learned knowledge is added to the connection tableau calculus and implemented on top of the lean-CoP theorem prover, linking it to an external advisor system. In the typical mathematical setting of solving many problems in a large complex theory, learning from successful solutions is then used for guiding theorem proving attempts in the spirit of the MaLARea system. While in MaLA Rea learning-based axiom selection is done outside unmodified theorem provers, in MaLeCoP the learning-based selection is done inside the prover, and the interaction between learning of knowledge and its application can be much finer. This brings interesting possibilities for further construction and training of self-learning AI mathematical experts on large mathematical libraries, some of which are discussed. The initial implementation is evaluated on the MPTP Challenge large theory benchmark. © 2011 Springer-Verlag.