Temporal Causal Models
Definition
Temporal causal models extend structural-equation causal reasoning to systems whose variables evolve over time. Instead of solving one static assignment, a model transforms temporal inputs or previous-step values into a trajectory of endogenous states.
Why It Matters
Many causal claims are temporal: treatment timing, delayed effects, feedback loops, program executions, and agent actions all depend on when events occur. Temporal causal models let interventions and counterfactuals target a specific time step.
Formalism / Key Objects
- A temporal context is a sequence of exogenous assignments, and a computation is a sequence or tree of endogenous assignments.
- In deterministic one-step TSEMs, current endogenous values are generated from previous values:
- In nondeterministic TSEMs, a structural equation can return a set of possible next values:
- Time-indexed interventions such as
do(Y^n <- y)orY(n)<-yfix a variable at a specified step. - Temporal Structural Equation Models collects the CPLTL, equivalence, LBA, and Turing-completeness details.
Connections
- Extends Structural Equation Models beyond static interventions.
- Connects to Linear Temporal Logic through formulas over future and past trajectories.
- Supports Actual Causality claims such as “event A at time t caused event B at time t’“.
- Connects to Formal Methods when TSEMs are used to represent computations and reason about counterfactual program behavior.
Common Confusions
- A temporal SEM tick is a modeling choice, not automatically real-world time.
- Non-recursive dependency graphs are less problematic in one-step temporal semantics than in simultaneous static SEMs.
- TSEM expressivity results do not by themselves make causal inference from data easy; they are representation and reasoning results.