Projective Unification in Bi-Intuitionistic Logic
Bibliographic record
Abstract
The bi-intuitionistic propositional calculus bi-IPC is the natural symmetric extension of the intuitionistic logic IPC. We provide both an axiomatic and semantic characterization of the consistent axiomatic extensions of bi-IPC which admit projective unification. They are exactly those which contain a theorem of the form (¬ ∼)n p → (¬ ∼)^{n+1} p, for some n ∈ N -or, equivalently, which are valid on Kripke frames of n-bounded zigzag depth, a simple order-theoretic condition. We also prove that bi-IPC does not have a unitary unification type by showing that while the formula ¬ ∼p → (¬ ∼) p is a unifiable formula in bi-IPC, it cannot have a most general unifier.
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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 | 0.005 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.003 | 0.002 |
| 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 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".