Reasoning about Probabilities in Unbounded First-Order Dynamical Domains
Bibliographic record
Abstract
When it comes to robotic agents operating in an uncertain world, a major concern in knowledge representation is to better relate high-level logical accounts of belief and action to the low-level probabilistic sensorimotor data. Perhaps the most general formalism for dealing with degrees of belief and, in particular, how such beliefs should evolve in the presence of noisy sensing and acting is the account by Bacchus, Halpern, and Levesque. In this paper, we reconsider that model of belief, and propose a new logical variant that has much of the expressive power of the original, but goes beyond it in novel ways. In particular, by moving to a semantical account of a modal variant of the situation calculus based on possible worlds with unbounded domains and probabilistic distributions over them, we are able to capture the beliefs of a fully introspective knowledge base with uncertainty by way of an only-believing operator. The paper introduces the new logic and discusses key properties as well as examples that demonstrate how the beliefs of a knowledge base change as a result of noisy actions.
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How this classification was reachedexpand
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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".