I'm having difficulty expressing the following thought in first order logic.
I want to say that every agent has an initial position and I'd express it as this (using words):
For All agent of type Agents, There Exists an x of type xCoordinate and an y of type yCoordinate such that I_Position(agent,x,y) AND Tile(x,y)
Or in idp:
!ag[agent]: ? xCo[xCo],yCo[yCo]: I_position(ag, xCo, yCo) & Tile(xCo,yCo).
With tile being an expression for a valid tile, a valid position.
Problem with this expression is that I've been learned that an For All expression is ALWAYS with an implication (=>) and a There Exists expression is always with an And (&).
Obviously, I don't have an implication. Does this sentence do what I think it does?