So I been talking about the game being based on logic and involving theorem proving in a limited sense. But how to do this? Well the general idea was to create a simple formal system and then figure out a way to port the system to a graphical logic representation. The methodology I am thinking of following is that laid out in this paper. This would be for spell creation of which there will be two types. General spells and creation of planes. Spells will be first implemented and it will be my first experimentation of this concept. Spells will be based on my simple formal system and there will be a mapping of theorems to spell aspects and will be a way to get my feet wet for the proper hardcore aspect of the project.
The other type, planes, allow one to map theorems and properties to textures, landscape creatures of an area... You may create a mapping for the system yourself or simply use the default one I provide. The logics backend will be implemented in F# and require F# assemblies, so there will be no Domain specific language. Different logics will allow different directions of exploration, for example, with modal logic we explore concepts of existance and possibility.
The premise itself is very simple, if you map the mathematical structures and object to more farmiliar things, drop down a level an abstraction by entering another, you will be able to enter realms of thought once to difficult to penertrate. In my head i have a dream, The plane, based on your mapping could represent a theorem on the reals. By setting off an explosion or jumping and watching the results you can gain insight into what to do...
Ill have to buck up on my graph theory, combinatorics and graphical logic concpets though.
Instead of defining behaviour and maps explicity we create in a world whose final output is not known to us. It would be truly like exploring a mathematical landscape, a step towards mathematical visualization..