Event Calculus

Structure

• A formalism for reasoning about actions over time
• Time is continuous
• Fluents take on different values in different situations
• Events initiate and terminate changes to fluents
  Events release fluents from the commonsense law of inertia
  
• Discrete event calculus limits time to integer time points

Language

• happens(E,T): Event E occurs at timepoint T.
• holdsAt(F,T): Fluent F is true at T.
• releasedAt(F,T): F is released from the commonsense law of inertia at T.
• initiates(E,F,T): If E occurs at T, then F is true and not released at T+1.
• terminates(E,F,T): If E occurs at T, then F is false and not released at T+1.
• releases(E,F,T): If E occurs at T, then F is released at T+1.
• trajectory(F₁,T₁,F₂,T₂): If F₁ is initiated at T₁, and T₂ > 0, then F₂ is true at T₁+T₂.
• antiTrajectory(F₁,T₁,F₂,T₂): If F₁ is terminated at T₁, and T₂ > 0, then F₂ is true at T₁+T₂.

Examples

• Axiom DEC1

  ∀T1,F,T2 (stoppedIn(T1,F,T2) 
      ⇔ 
  ∃E,T (T1 < T < T2 | happens(E,T) | terminates(E,F,T) ))
  

• ∀T,H1,H2 ((holdsAt(waterLevel(H1),T) & holdsAt(waterLevel(H2),T)) ⇒ H1 = H2)