Situation Calculus Causal Models
Context
The situation-calculus causality papers use action histories rather than flat variable assignments to reason about actual causes and counterfactuals. Hopkins2005 - Causality and Counterfactuals in the Situation Calculus introduces SCCMs; Liu2026 - A Counterfactual Cause in Situation Calculus gives counterfactual achievement causes in a modal situation-calculus setting.
Formal Statement
Hopkins-Pearl define a situation calculus causal model as
where D is a situation-calculus specification and P=(S,F) is a potential situation. S=[a_1,...,a_n] is a not-necessarily-executable action sequence and F:{a|a in S}->{0,1} flags actions that should be forced despite failed preconditions.
The natural executable subsituation is computed by:
whenever Poss(a_i,NES(M)) holds or F(a_i)=1; otherwise a_i is skipped.
Liu-Belle define a minimal counterfactual cause for a static goal phi by requiring
with z minimal under a chosen ordering.
For a narrative C=<Sigma,z,phi>, a prefix z' is an achievement cause when all extensions from z' through z keep phi true, the filtered counterfactual remainder Filter(z\z') makes not phi true, and no smaller subsequence satisfies those conditions.
Derivation / Construction
- SCCM counterfactuals remove actions from the potential situation or force actions into it before recomputing
NES. - Initial database axioms play the role of exogenous variables; fluents are enduring endogenous conditions; actions are transitional events.
- Successor-state axioms describe fluent mechanisms, while precondition axioms describe action mechanisms.
- Filtering in Liu-Belle removes impossible remnants of a narrative after the candidate causal prefix is deleted.
- The two approaches share the same modeling instinct: counterfactual causal queries should respect action executability and the distinction between actions and fluents.
Implications
- Situation calculus can express object-indexed and temporally ordered causal stories that are awkward in propositional structural models.
- Counterfactual causality over actions requires care: deleting an action can make later actions impossible.
- The formalism is useful for explanation and diagnosis in agent histories, but minimality choices affect the returned cause.