@cite{beller-gerstenberg-2025}: Causation, Meaning, and Communication #

@cite{beller-gerstenberg-2025}

Formalizes Beller & Gerstenberg (2025) "Causation, Meaning, and Communication," Psychological Review 133(2), 339–381.

A counterfactual simulation model of causal language combining:

Causal knowledge module: computes whether-causation (W), how-causation (H), and sufficient-causation (S) from counterfactual simulations
Semantics module: defines four causal expressions as logical combinations of W, H, S (Eqs. 4–7)
Pragmatics module: RSA inference selects the most informative true expression

Semantics (Eqs. 4–7) #

affected(A → e) = W ∨ H ∨ S (any causal involvement)
enabled(A → e) = W ∨ S (necessity or sufficiency)
caused(A → e) = H ∧ (W ∨ S) ∧_σ M ∧_σ U (how-cause + counterfactual, softened by movement M and uniqueness U; σ controls softening)
made no difference(A → e) = ¬W ∧ ¬_ν H ∧ ¬S (no causal role, with soft negation ¬_ν of how-cause; ν controls softening)

The expressions form a hierarchy of specificity: caused ⊂ enabled ⊂ affected. This hierarchy drives scalar implicatures via RSA pragmatic reasoning.

Simplification #

This formalization uses Boolean W, H, S (matching Table 1's illustrative scenarios where aspect values are 0 or 1). The full paper computes W and S as graded probabilities from noisy counterfactual simulations (Eqs. 1, 3).

The core Boolean semantics omit M (movement) and U (uniqueness), which only affect "caused" via soft conjunction. These features are process constraints that reduce the probability of "caused" when the candidate cause was stationary (M=false) or not the unique contactor (U=false). For the illustrative Table 1 scenarios, M=true and U=true throughout.

Experiments #

Experiment 1A: Norming study (N=50). 15/20 sentence frames had median acceptability ≥ 4 (scale midpoint) for all three causal expressions.
Experiment 1B: Semantic relations (N=53). Contradictory orderings (e.g., "caused but did not enable") rated less acceptable than consistent orderings (e.g., "affected but did not cause"). Confirms overlapping (not inconsistent) semantics for "caused" and "enabled."
Experiment 1C: Implicature cancellation (N=51). "in fact" cancellations (e.g., "affected, in fact caused") rated more acceptable than redundant specifications (e.g., "caused, in fact affected").
Experiment 2: Speaker task (N=62, 30 billiard scenarios). Full model r=0.87, RMSE=0.13. Fitted: θ=1.0, σ=0.65, ν=0.25, λ=40.18.
Experiment 3: Listener task (N=50, 36 trials). Full model r=0.91, RMSE=0.10.

B&G aspect	Structural definition
W (whether)	`causallyNecessary` — would effect still occur without cause?
H (how)	`hasDirectLaw` — does a causal law directly connect cause to effect?
S (sufficient)	`causallySufficient` — does adding cause guarantee effect?

@cite{beller-gerstenberg-2025}: Causation, Meaning, and Communication #

Semantics (Eqs. 4–7) #

Simplification #

Experiments #

S1 speaker predictions from the full 8-world Boolean model #

L1 listener predictions: scalar implicature effects #

Bridge to Core.StructuralEquationModel #

Structural Model → Causation Type → Expression → S1 #

Overall Acceptance Rates (Figure 2) #

Main Effect Coefficients (Table 8) #

Per-Verb Interaction Reliability (Table 9) #

Acceptability Contrasts #