The need for new frameworks

These case studies illustrate what we need from a framework connecting formal semantics to experimental data:

Maintain Compositionality: Theories must derive complex meanings compositionally, preserving insights from decades of formal semantic research. We cannot abandon compositionality just because judgments are gradient.

Model Uncertainty Explicitly: The framework must represent both types of uncertainty—resolved ambiguities and unresolved gradience—and show how they interact during interpretation.

Make Linking Hypotheses Precise: We need explicit theories of how semantic representations produce behavioral responses. What cognitive processes intervene between computing a meaning and moving a slider?

Enable Quantitative Evaluation: Theories must make testable predictions about response distributions, not just average ratings. Different theories should be comparable using standard statistical metrics.

As we’ll see in the next section, existing computational approaches like Rational Speech Act (RSA) models attempt to bridge formal semantics with probabilistic reasoning (Frank and Goodman 2012; Goodman and Stuhlmüller 2013). While valuable, these approaches face challenges in maintaining the modularity that makes formal semantic theories powerful. This motivates the development of Probabilistic Dynamic Semantics—a framework that preserves semantic insights while adding the probabilistic tools needed to model gradient behavioral data.

References

Frank, Michael C., and Noah D. Goodman. 2012. “Predicting Pragmatic Reasoning in Language Games.” Science 336 (6084): 998–98. https://doi.org/10.1126/science.1218633.

Goodman, Noah D., and Andreas Stuhlmüller. 2013. “Knowledge and Implicature: Modeling Language Understanding as Social Cognition.” Topics in Cognitive Science 5 (1): 173–84. https://doi.org/10.1111/tops.12007.

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These case studies illustrate what we need from a framework connecting formal semantics to experimental data:

**Maintain Compositionality**: Theories must derive complex meanings compositionally, preserving insights from decades of formal semantic research. We cannot abandon compositionality just because judgments are gradient.

**Model Uncertainty Explicitly**: The framework must represent both types of uncertainty—resolved ambiguities and unresolved gradience—and show how they interact during interpretation.

**Make Linking Hypotheses Precise**: We need explicit theories of how semantic representations produce behavioral responses. What cognitive processes intervene between computing a meaning and moving a slider?

**Enable Quantitative Evaluation**: Theories must make testable predictions about response distributions, not just average ratings. Different theories should be comparable using standard statistical metrics.

As we'll see in the next section, existing computational approaches like Rational Speech Act (RSA) models attempt to bridge formal semantics with probabilistic reasoning [@frank_predicting_2012; @goodman_knowledge_2013]. While valuable, these approaches face challenges in maintaining the modularity that makes formal semantic theories powerful. This motivates the development of Probabilistic Dynamic Semantics—a framework that preserves semantic insights while adding the probabilistic tools needed to model gradient behavioral data.