Paradigms of Denotational Mathematics for Cognitive Informatics and Cognitive Computing
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
The abstract, rigorous, and expressive needs in cognitive informatics, intelligence science, software science, and knowledge science lead to new forms of mathematics collectively known as denotational mathematics. Denotational mathematics is a category of expressive mathematical structures that deals with high level mathematical entities beyond numbers and sets, such as abstract objects, complex relations, behavioral information, concepts, knowledge, processes, and systems. Denotational mathematics is usually in the form of abstract algebra that is a branch of mathematics in which a system of abstract notations is adopted to denote relations of abstract mathematical entities and their algebraic operations based on given axioms and laws. Four paradigms of denotational mathematics, known as concept algebra, system algebra, Real-Time Process Algebra (RTPA), and Visual Semantic Algebra (VSA), are introduced in this paper. Applications of denotational mathematics in cognitive informatics and computational intelligence are elaborated. Denotational mathematics is widely applicable to model and manipulate complex architectures and behaviors of both humans and intelligent systems, as well as long chains of inference processes.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 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 it