The Place of Quasi Topological Structure in the Mathematical Theory of Categorization
Bibliographic record
Abstract
This work is a theoretical one bridging two mathemat- ical models namely the Quasi Topological Structure (QTS) and Soft Sets (SST) theories. We prove that theQuasi Topological Structure (QTS) can be viewed as a complexification of Soft Sets, from the point of view of its capacity of analysis. Our strategy is to compare two mathematical structures, namely the structure of Quasi Topological Structure (QTS) and the structure of Soft Sets from the point of view of their mathematical properties. These properties are expressed by means of mathematical notions that translate conceptual features. The notion of conceptual feature is taken in the com- mon sense outside of any scientific domain. However, the mathematical notions are given inside mathematics by their specific conditions. This paper is a theoretical comparison between two new mathematical structures that can become useful in many approaches of Artificial Intelligence (AI). We propose an epistemological anal- ysis in the frame of mathematical foundations and not a tool or a methodology to solving a particular problem.
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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 | 0.003 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.002 | 0.012 |
| Scholarly communication | 0.005 | 0.011 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".