  Domain of mathematical logic in computers is dominated by automated theorem
provers (ATP) and interactive theorem provers (ITP). Both of these are hard to
access by AI from the human-imitation approach: ATPs often use human-unfriendly
logical foundations while ITPs are meant for formalizing existing proofs rather
than problem solving. We aim to create a simple human-friendly logical system
for mathematical problem solving. We picked the case study of Euclidean
geometry as it can be easily visualized, has simple logic, and yet potentially
offers many high-school problems of various difficulty levels. To make the
environment user friendly, we abandoned strict logic required by ITPs, allowing
to infer topological facts from pictures. We present our system for Euclidean
geometry, together with a graphical application GeoLogic, similar to GeoGebra,
which allows users to interactively study and prove properties about the
geometrical setup.
