Non-deterministic Semantics in Polynomial Format
Why this work is in the frame
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Bibliographic record
Abstract
The method for automatic theorem proving proposed in [Carnielli, W. A., Polynomial ring calculus for many-valued logics, Proceedings of the 35th International Symposium on Multiple-Valued Logic, IEEE Computer Society. Calgary, Canada (2005), 20–25], called Polynomial Ring Calculus , is an algebraic proof mechanism based on handling polynomials over finite fields. Although useful in general domains, as in first-order logic, certain non-truth-functional logics and even in modal logics (see [Agudelo, J. C., Carnielli, W. A., Polynomial Ring Calculus for Modal Logics: a new semantics and proof method for modalities, The Review of Symbolic Logic. 4 (2011), 150–170, URL: doi:10.1017/S1755020310000213 ]), the method is particularly apt for deterministic and non-deterministic many-valued logics, as shown here. The aim of the present paper is to show how the method can be extended to any finite-valued non-deterministic semantics, and also to explore the computational character of the method through the development of a software capable of translating provability in deterministic and non-deterministic finite-valued logical systems into operations on polynomial rings.
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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 | 0.003 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| 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