Diederik Aerts (2009), Journal of Mathematical Psychology 53(5), 314–348.
Key takeaways
From the reading, NOTE-808.
- Exact classical criteria. An item’s weights µ(A), µ(B), µ(A and B) come from one Kolmogorovian space, with “A and B” the intersection event, iff µ(A and B) ≤ min(µ(A), µ(B)) and 1 − µ(A) − µ(B) + µ(A and B) ≥ 0 (Theorems 1–3); dually for “or” (Theorems 4–6).
- Two kinds of failure. Over- or underextension (∆-type, the guppy effect: Cuckoo is 0.575 a Pet and 0.842 a “Bird and Pet”), and a negative Kolmogorovian factor (k-type: Almond is 0.2 a Fruit, 0.1 a Vegetable and 0.425 a “Fruit or Vegetable”).
- The lattice fits only the k-type. Tilted subspaces, whose lattice is not Boolean, fit k-type items (§2.2). Theorem 9 proves that no subspace model with conjunction as meet and disjunction as join can fit a ∆-type item, because projection weights are monotone.
- An emergent concept carries the guppy effect. The model adds a second sector with a fixed 2-dimensional subspace per pair, read as “A or B” (or “A and B”) formed as a new concept. With one free parameter per item it fits all of Hampton’s items (Tables 3–4).
- Negation is a device. The conjunction model is obtained from the disjunction model of hypothetical complements A′, B′ with weight 1 − µ, through the orthocomplement (§3.3). No negated concept is measured.
- Interpretation, not test. Two superposed layers of thought, classical logical and quantum conceptual, and a link to the disjunction effect (one ℂ³ fit of the Hawaii problem).
Standing in the record
Filed on 2026-10-12 from the owner’s papers-feed for QUESTION-055, and read on 2026-10-14 in NOTE-808. It does not supply the orthocomplemented negation the filing expected: the subspace lattice it uses cannot hold its main data, and its orthocomplement only derives one model from another. What it gives QUESTION-055 is a constraint, filed as THEORY-255: guppy-type blends cannot be the lattice meet, whatever the negation. It is the later Aerts paper that NOTE-294 names as where a non-distributive concept lattice is put to the test, and it is the first reading in the record that uses non-commuting subspaces on concept data.