Decidable reasoning in a logic of limited belief with introspection and unknown individuals
Bibliographic record
Abstract
There are not very many existing logics of belief which have both a perspicuous semantics and are computationally attractive. An exception is the logic SL, proposed by Liu, Lakemeyer, and Levesque, which allows for a decidable and often even tractable form of reasoning. While the language is first-order and hence quite expressive, it still has a number of shortcomings. For one, beliefs about beliefs are not addressed at all. For another, the names of individuals are rigid, that is, their identity is assumed to be known. In this paper, we show how both shortcomings can be overcome by suitably extending the language and its semantics. Among other things, we show that determining the beliefs of a certain kind of fully introspective knowledge bases is decidable and that unknown individuals in the knowledge base can be accommodated in a decidable manner as well.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.008 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.004 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.006 |
| Scholarly communication | 0.006 | 0.011 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.002 | 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 source (direct Gemma or distilled Codex), 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".