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Record W4214602829 · doi:10.1002/0471469882.ch2

Boolean Algebras

2003· other· en· W4214602829 on OpenAlexaff
William J. Gilbert, W. K. Nicholson

Bibliographic record

Venuenot available
Typeother
Languageen
FieldComputer Science
TopicAdvanced Algebra and Logic
Canadian institutionsUniversity of CalgaryUniversity of Waterloo
Fundersnot available
KeywordsFree Boolean algebraStone's representation theorem for Boolean algebrasBoolean algebras canonically definedComplete Boolean algebraBoolean algebraTwo-element Boolean algebraMathematicsInterior algebraAlgebra over a fieldSet (abstract data type)Boolean expressionRepresentation (politics)Discrete mathematicsAlgebra representationPure mathematicsJordan algebraComputer scienceBoolean functionProgramming language

Abstract

fetched live from OpenAlex

Chapter 2 introduces the algebra of sets and then defines boolean algebras. These are applied to the logic of propositions, truth tables, the divisors of a square-free number, and the simplification of switching circuits. It ends with a representation theorem of a finite boolean algebra as the algebra of subsets of a set.

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 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)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesInsufficient payload (model declined to judge)
Consensus categoriesInsufficient payload (model declined to judge)
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Not applicable · Consensus signal: Not applicable
GenreCandidate signal: Other · Consensus signal: Other
Teacher disagreement score0.398
Threshold uncertainty score0.999

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0040.002

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 head0.010
GPT teacher head0.227
Teacher spread0.217 · 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; both teacher heads agree on what is shown here.

Study designNot applicable
Domainnot available
GenreOther

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

Citations0
Published2003
Admission routes1
Has abstractyes

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