Take a deterministic, perfect information, abstract strategy, finite game , with absurdly large state space, say chess

Q1 Is the game translatable to an axiomatic system?

Q2 Can all statements in the game be proven or dis proven, are they decidable? Do we have an 'Incompleteness" at play here? (Assuming that the game has not/cannot be solved given our compute resources.)

**Examples**: 
          
 *"There is a set of moves (starting from initial position) which lead white to win regardless                  
  of black's moves" (Perfect strategy)
          
 "There is a set of moves which lead white not  to loose regardless of black's moves" (Perfect 
  strategy)
          
  "All games are decidable (White wins looses or stalemates)after  n-moves into the game" (Forcing a 
    win)
           
  "Given a position, exists a function which tells if a game is decidable from that point on"* 

Q3 Is there an 'intuitive' truth in statements of chess, say as seen by grandmasters which can not be proven?

Aim of the questions is to check behavior for infinitely large state spaces with rule based transitions.