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Modeling the RollerSlam Game using Fluent Calculus and FLUX

This document presents a comprehensive guide to modeling the RollerSlam game using FLUX and fluent calculus. The first step involves defining fluents and actions that capture game dynamics, such as player movements and ball interactions. The second step details the precondition and state update axioms necessary for implementing actions like throwing, releasing, and tackling within the game context. Each action is governed by specific conditions to ensure realistic behavior in the game's state updates. This framework enables the construction of logical models for complex scenarios in RollerSlam.

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Modeling the RollerSlam Game using Fluent Calculus and FLUX

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  1. Using FLUX to model The RollerSlam game

  2. Fluent Calculus x FLUX

  3. First Step: Defining the Fluents and the actions

  4. RollerSlam (Fluents)

  5. RollerSlam (Fluents)

  6. RollerSlam (Fluents)

  7. RollerSlam (Actions)

  8. RollerSlam (Actions)

  9. Second Step: Defining the precondition and state update axioms

  10. Programming in FLUX • Precondition Axiom: • Poss(A(x), z)  πA(x,z) or • NotPoss(A(x), z)  ¬πA(x,z) • State Update Axiom • StateUpdate(z1, A(x), z2)  Δ(x, z1), Update(z1, v+, v-, z2) • Do(s, z0, z) • do ([], Z, Z) • do([A|S},Z0, Z) :-poss(A, Z0),sateUpdate (Z0, A, Z1), do (S, Z1, Z2)

  11. Initial State • Init(z0)  Consistent(z0), DuplicateFree(z0)

  12. Defining the ‘poss’ axioms • poss(throwA(Agent,Strength),Z1) :- holds(hasBall(Agent), Z1), not_holds(inGround(Agent),Z1). • poss(release(Agent),Z1) :- holds(hasBall(Agent),Z1). • poss(dash(Agent),Z1):- not_holds(inGround(Agent),Z1). • poss(kick(Agent,Strength),Z1) :- holds(hasBall(Agent), Z1), not_holds(inGround(Agent),Z1). • poss(tackle(Agent,AgentB,vector(Xmax, Ymax), MaxDistance),Z1) :- not_holds(inGround(Agent),Z1), holds(hasBall(AgentB), Z1), not_holds(counterTackle(AgentB),Z1), closer(Sxa, Sya, Sxb, Syb, MaxDistance). • poss(counterTackle(Agent),Z1) :- not_holds(inGround(Agent),Z1). • poss(hit(Agent,Strength, MaxDistance),Z1) :- not_holds(inGround(Agent), Z1), closer(Sxa, Sya, Sxb, Syb, MaxDistance). • poss(catchA(Agent, MaxDistance),Z1) :- not_holds(inGround(Agent),Z1), not_holds(hasBall(Agent), Z1), closer(Sxa, Sya, Sxb, Syb, MaxDistance). • poss(standUp(Agent),Z1) :- holds(inGround(Agent),Z1).

  13. Pre-Conditions For Ramification • poss(ramifySit2, Z1):- holds(isMoving(Ball, Attrition), Z1). • poss(ramifySit3, Z1):- holds(outBoundary(Object), Z1).

  14. ‘State_update’ axioms • state_update(Z1,dash(Agent, vector(X,Y)),Z2,[]) :- holds(acceleration(Agent, vector(X0,Y0)),Z1), update(Z1,[acceleration(Agent,vector(X,Y))],[acceleration(Agent, vector(X0,Y0))],Z2). • state_update(Z1,throwA(Agent,Strength),Z2,[]) :- (poss(throwA(Agent,Strength),Z1), holds(position(Ball, vector(X0, Y0)),Z1), X #= X0 * Strength, Y #= Y0 * Strength, update(Z1,[position(Ball, vector(X,Y))],[hasBall(Agent),position(Ball, vector(X0, Y0))],Z2)) ; (not poss(throwA(Agent,Strength),Z1), Z2=Z1 ). • state_update(Z1,release(Agent),Z2,[]) :- (poss(release(Agent),Z1), update(Z1,[],[hasBall(Agent)],Z2)) ; (not poss(release(Agent),Z1), Z2=Z1).

  15. ‘State_update’ axioms • state_update(Z1,kick(Agent,Strength),Z2,[]) :- (poss(kick(Agent,Strength),Z1), holds(position(Ball, vector(X0, Y0)),Z1), X #= X0 * Strength, Y #= Y0 * Strength, update(Z1,[position(Ball, vector(X,Y))],[hasBall(Agent),position(Ball, vector(X0, Y0))],Z2)) ; (not poss(kick(Agent,Strength),Z1), Z2=Z1). • state_update(Z1,tackle(Agent,AgentB,vector(Xmax, Ymax), MaxDistance),Z2,[]) :- (poss(tackle(Agent,AgentB,vector(Xmax, Ymax), MaxDistance),Z1), holds(position(Agent, vector(Sxa,Sya)),Z1), holds(position(AgentB, vector(Sxb,Syb)),Z1), update(Z1,[inGround(AgentB)],[hasBall(AgentB)],Z2)) ; (not poss(tackle(Agent,AgentB,vector(Xmax, Ymax), MaxDistance),Z1), Z2=Z1).

  16. ‘State_update’ axioms • state_update(Z1,counterTackle(Agent),Z2,[]) :- (poss(counterTackle(Agent),Z1), update(Z1,[counterTackle(Agent)],[],Z2)) ; (not poss(counterTackle(Agent),Z1), Z2=Z1). • state_update(Z1,hit(Agent,Strength, MaxDistance),Z2,[]) :- (poss(hit(Agent,Strength, MaxDistance),Z1), holds(position(Agent, vector(Sxa,Sya)),Z1), holds(position(Ball, vector(Sxb,Syb)),Z1), X #= Sxb * Strength, Y #= Syb * Strength, update(Z1,[position(Ball, vector(X,Y))],[position(Ball, vector(Sxb,Syb))],Z2)) ; (not poss(hit(Agent,Strength, MaxDistance),Z1), Z2=Z1).

  17. ‘State_update’ axioms • state_update(Z1,catchA(Agent, MaxDistance),Z2,[]) :- (poss(catchA(Agent, MaxDistance),Z1), holds(position(Agent, vector(Sxa,Sya)),Z1), holds(position(Ball, vector(Sxb,Syb)),Z1), update(Z1,[hasBall(Agent)],[],Z2)) ; (not poss(catchA(Agent, MaxDistance),Z1), Z2=Z1). • state_update(Z1,standUp(Agent),Z2,[]) :- (poss(standUp(Agent),Z1), update(Z1,[],[inGround(Agent)],Z2)) ; (not poss(standUp(Agent),Z1), Z2=Z1 ).

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