A Dynamic-Epistemic Approach to Conditionals
Talkat Quantum Physics and Statistical Causal Models (Simons Institute workshop, 2022) · 2022-04-27..04-29
summary
Argues for a single dynamic-epistemic framework that represents conditionals as actions on models, using propositional dynamic logic, quantum dynamic logic, relational semantics and model transformers. Shows that public-announcement updates implement Bayesian conditionalization by deleting non-phi worlds, lexicographic upgrades model belief revision, Halpern/Pearl interventions are model-transforming counterfactuals, and projectors as quantum tests turn yes/no measurements into deterministic actions so that Sasaki–Hook = dynamic conditional (a Stalnaker-style selection via projection). Notes work still needed on entanglement and the measurement problem.
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chapters (31)
- 0:00Intro
- 0:29Overview
- 3:16Note on Physical (testable) Properties
- 3:52Two Interpretations for Dynamic Modalities
- 5:28Relational Semantics
- 6:58Generalized Semantics: Model Transformers
- 8:35Existential Modalities
- 9:37"Going backwards in time": converse modalities
- 10:15Regular Operations on Actions
- 12:32PDL terms define "programs"
- 13:18Dynamic semantics for conditionals
- 15:56Refinements of the general idea
- 16:56Dynamic Conditionals: straightforward examples
- 18:01(36) Learning: Updating with 'Hard Information
- 19:50Updating as Elimination of Possibilities
- 23:26(3d) Counterfactuals
- 25:00"Dynamification" of Lewis' semantics
- 27:51The Causal-Intervention Conditionals
- 30:46Notation
- 32:03The Hilbert Space Semantics
- 32:57Deduction theorem fails for the Sasaki Hook
- 33:28What kind of implications are possible?
- 35:04What are the selection functions?
- 35:56Projectors express Measurements
- 36:41Hilbert Spaces as dynamic Kripke models
- 37:27Quantum Conditionals as Dynamic Modalities
- 37:57Quantum Tests as 'interventions
- 38:52Quantum Tests as Learning Actions
- 39:44Conclusion
- 41:47Updating is Probabilistic Conditionalization
- 45:51Quantum Conditional as Stalnaker counterfactual