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Record W2091708223 · doi:10.1017/s0305004106009352

All realizability is relative

2006· article· en· W2091708223 on OpenAlexaff
Pieter Hofstra

Bibliographic record

VenueMathematical Proceedings of the Cambridge Philosophical Society · 2006
Typearticle
Languageen
FieldComputer Science
TopicComputability, Logic, AI Algorithms
Canadian institutionsUniversity of Ottawa
Fundersnot available
KeywordsRealizabilityMorphismObject (grammar)Filter (signal processing)MathematicsPreorderVariety (cybernetics)Extensional definitionSubcategoryCharacterization (materials science)Algebra over a fieldComputer sciencePure mathematicsDiscrete mathematicsAlgorithmArtificial intelligence

Abstract

fetched live from OpenAlex

We introduce a category of basic combinatorial objects, encompassing PCAs and locales. Such a basic combinatorial object is to be thought of as a pre-realizability notion. To each such object we can associate an indexed preorder, generalizing the construction of triposes for various notions of realizability. There are two main results: first, the characterization of triposes which arise in this way, in terms of ordered PCAs equipped with a filter. This will include “Effective Topos-like” triposes, but also the triposes for relative, modified and extensional realizability and the dialectica tripos. Localic triposes can be identified as those arising from ordered PCAs with a trivial filter. Second, we give a classification of geometric morphisms between such triposes in terms of maps of the underlying combinatorial objects. Altogether, this shows that the category of ordered PCAs with non-trivial filters serves as a framework for studying a wide variety of realizability notions.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

How this classification was reachedexpand

Full frame machine prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.003
Version: metacan-v3-hybrid-931329e0061cValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.015
Threshold uncertainty score0.050

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0010.003
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0020.001
Science and technology studies0.0020.006
Scholarly communication0.0050.010
Open science0.0010.003
Research integrity0.0010.003
Insufficient payload (model declined to judge)0.0150.002

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.

Opus teacher head0.023
GPT teacher head0.247
Teacher spread0.224 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Classification

machine, unvalidated

Machine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designTheoretical or conceptual
Domainnot available
GenreEmpirical

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".

Quick stats

Citations37
Published2006
Admission routes1
Has abstractyes

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Same venueMathematical Proceedings of the Cambridge Philosophical SocietySame topicComputability, Logic, AI AlgorithmsFrench-language works237,207