Automated Conjecturing II: Chomp and Reasoned Game Play

We demonstrate the use of a program that generates conjectures about positions of the combinatorial game Chomp--explanations of why certain moves are bad. These could be used in the design of a Chomp-playing program that gives reasons for its moves. We prove one of these Chomp conjectures--demonstrating that our conjecturing program can produce genuine Chomp knowledge. The conjectures are generated by a general purpose conjecturing program that was previously and successfully used to generate mathematical conjectures. Our program is initialized with Chomp invariants and example game boards--the conjectures take the form of invariant-relation statements interpreted to be true for all board positions of a certain kind. The conjectures describe a theory of Chomp positions. The program uses limited, natural input and suggests how theories generated on-the-fly might be used in a variety of situations where decisions--based on reasons--are required.