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Record W2949892358 · doi:10.1088/1742-6596/67/1/012018

An exercise in "anhomomorphic logic"

2007· article· en· W2949892358 on OpenAlex

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

VenueJournal of Physics Conference Series · 2007
Typearticle
Languageen
FieldComputer Science
TopicLogic, Reasoning, and Knowledge
Canadian institutionsPerimeter Institute
Fundersnot available
KeywordsBoolean algebraHomomorphismAlgebra over a fieldTruth valueSet (abstract data type)Quantum logicMathematicsSpace (punctuation)Simple (philosophy)Pure mathematicsFree Boolean algebraDiscrete mathematicsTwo-element Boolean algebraComputer scienceQuantumEpistemologyPhysicsProgramming languagePhilosophyQuantum computerAlgebra representationQuantum mechanics

Abstract

fetched live from OpenAlex

A classical logic exhibits a threefold inner structure comprising an algebra of propositions A, a space of “truth values ” V, and a distinguished family of mappings φ from propositions to truth values. Classically A is a Boolean algebra, V = Z2, and the admissible maps φ: A → Z2 are homomorphisms. If one admits a larger set of maps, one obtains an anhomomorphic logic that seems better suited to quantal reality (and the needs of quantum gravity). I explain these ideas and illustrate them with three simple examples. From a certain point of view, the phrase “classical logic ” should be used in the plural, not the singular, because the things with which logic deals depend on the “domain of discourse”, and this can vary both with time and with the “system ” one has in mind. To each such domain corresponds its own Boolean algebra, namely the algebra A of all “questions ” one may ask about the system. 1 But there is more to a logic than just a domain of questions together with rules for combining them via and, xor, not, etc. In ⋆ To appear in a special volume of Journal of Physics, edited by L. Diosi, H-T Elze, and G. Vitiello, and devoted to the Proceedings of the DICE2006 meeting, held September

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: none
Teacher disagreement score0.823
Threshold uncertainty score0.487

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 studies0.0000.000
Scholarly communication0.0000.002
Open science0.0010.000
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 head0.029
GPT teacher head0.271
Teacher spread0.242 · 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