Bibliographic record
Abstract
In the past little work has been done to characterize the models of various mereotopological systems. This thesis focuses on Asher and Vieu's first-order mereotopology which evolved from Clarke's Calculus of Individuals. Its soundness and completeness proofs with respect to a topological translation of the axioms provide only sparse insights into structural properties of the mereotopological models. To overcome this problem, we characterize these models with respect to mathematical structures with well-defined properties - topological spaces, lattices, and graphs. We prove that the models of the subtheory RT− are isomorphic to p-ortholattices (pseudocomplemented, orthocomplemented). Combining the advantages of lattices and graphs, we show how Cartesian products of finite p-ortholattices with one multiplicand being not uniquely complemented (unicomplemented) gives finite models of the full mereotopology. Our analysis enables a comparison to other mereotopologies, in particular to the RCC, of which lattice-theoretic characterizations exist.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| 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".