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Record W2063169574 · doi:10.2307/2694928

An intensional type theory: motivation and cut-elimination

2001· article· en· W2063169574 on OpenAlexaff
Paul C. Gilmore

Bibliographic record

VenueJournal of Symbolic Logic · 2001
Typearticle
Languageen
FieldComputer Science
TopicLogic, Reasoning, and Knowledge
Canadian institutionsUniversity of British Columbia
Fundersnot available
KeywordsAxiomType theoryType (biology)MathematicsCompleteness (order theory)Interpretation (philosophy)SyntaxDiscrete mathematicsComputer scienceProgramming languageArtificial intelligence

Abstract

fetched live from OpenAlex

Abstract By the theory TT is meant the higher order predicate logic with the following recursively defined types: (1) 1 is the type of individuals and [] is the type of the truth values: (2) [ τ 1 ….. τ n ] is the type of the predicates with arguments of the types τ 1 ….. τ n . The theory ITT described in this paper is an intensional version of TT. The types of ITT are the same as the types of TT, but the membership of the type 1 of individuals in ITT is an extension of the membership in TT. The extension consists of allowing any higher order term, in which only variables of type 1 have a free occurrence, to be a term of type 1. This feature of ITT is motivated by a nominalist interpretation of higher order predication. In ITT both well-founded and non-well-founded recursive predicates can be defined as abstraction terms from which all the properties of the predicates can be derived without the use of non-logical axioms. The elementary syntax, semantics, and proof theory for ITT are defined. A semantic consistency proof for ITT is provided and the completeness proof of Takahashi and Prawitz for a version of TT without cut is adapted for ITT: a consequence is the redundancy of cut.

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)0.007
metaresearch head score (Gemma)0.009
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 score0.007
Threshold uncertainty score0.035

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0070.009
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0010.002
Bibliometrics0.0030.004
Science and technology studies0.0020.010
Scholarly communication0.0040.013
Open science0.0030.004
Research integrity0.0020.006
Insufficient payload (model declined to judge)0.0060.001

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 head0.028
GPT teacher head0.272
Teacher spread0.244 · 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

Citations14
Published2001
Admission routes1
Has abstractyes

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