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Record W4313327955 · doi:10.3765/salt.v1i0.5404

Measurements from "per" without complex dimensions

2022· article· en· W4313327955 on OpenAlex
Alan Bale, Bernhard Schwarz

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.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueProceedings from Semantics and Linguistic Theory · 2022
Typearticle
Languageen
FieldComputer Science
TopicRough Sets and Fuzzy Logic
Canadian institutionsMcGill UniversityConcordia University
Fundersnot available
KeywordsDivision (mathematics)ComputationQuotientSemantics (computer science)MathematicsCalculus (dental)Anaphora (linguistics)Computer scienceComposition (language)Algebra over a fieldPure mathematicsArtificial intelligenceLinguisticsArithmeticAlgorithmProgramming languagePhilosophyResolution (logic)

Abstract

fetched live from OpenAlex

To what extent is the compositional structure of quantity terms in natural language aligned with the structure of the quantity calculus commonly used in scientific practice, a calculus that critically relies on mathematical operations like division and the computation of quotients? In pioneering work, Coppock (2021) addresses this general question through a case study on the English preposition "per", as in "0.9 grams per milliliter". Coppock proposes that "per" expresses the operation of quantity division, an operation that forms quantities like 0.9g/mL by using ratios of measurements from different dimensions. Here we show that this “division theory” of "per" makes the wrong prediction with respect to statements about measures of density and concentration. We argue that these types of expressions call for an “anaphoric theory” ofper. On this analysis, anaphora allows for the composition to invoke multiple measurements in basic dimensions, creating the appearance of reference to complex quantities like 0.9g/mL, even though no such quantities are actually composed nor denoted in the formal semantics.

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.

Full frame distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation 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: Empirical
Teacher disagreement score0.086
Threshold uncertainty score0.789

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0010.000
Scholarly communication0.0000.000
Open science0.0010.001
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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.

Opus teacher head0.042
GPT teacher head0.250
Teacher spread0.208 · 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