Reasoning about “reasoning about reasoning”: semantics and contextual equivalence for probabilistic programs with nested queries and recursion
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Metareasoning can be achieved in probabilistic programming languages (PPLs) using agent models that recursively nest inference queries inside inference queries. However, the semantics of this powerful, reflection-like language feature has defied an operational treatment, much less reasoning principles for contextual equivalence. We give formal semantics to a core PPL with continuous distributions, scoring, general recursion, and nested queries. Unlike prior work, the presence of nested queries and general recursion makes it impossible to stratify the definition of a sampling-based operational semantics and that of a measure-theoretic semantics—the two semantics must be defined mutually recursively. A key yet challenging property we establish is that probabilistic programs have well-defined meanings: limits exist for the step-indexed measures they induce. Beyond a semantics, we offer relational reasoning principles for probabilistic programs making nested queries. We construct a step-indexed, biorthogonal logical-relations model. A soundness theorem establishes that logical relatedness implies contextual equivalence. We demonstrate the usefulness of the reasoning principles by proving novel equivalences of practical relevance—in particular, game-playing and decisionmaking agents. We mechanize our technical developments leading to the soundness proof using the Coq proof assistant. Nested queries are an important yet theoretically underdeveloped linguistic feature in PPLs; we are first to give them semantics in the presence of general recursion and to provide them with sound reasoning principles for contextual equivalence.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it