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arxiv: 2604.08604 · v1 · submitted 2026-04-08 · 🧬 q-bio.NC · quant-ph

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Quantum-like Cognition in Process Theories: An Analysis

Sean Tull , Masanao Ozawa
Authors on Pith no claims yet

Pith reviewed 2026-05-10 17:10 UTC · model grok-4.3

classification 🧬 q-bio.NC quant-ph
keywords quantum-like cognitionprocess theoriesclassical instrument modelssequential decisionsBell inequalitiescognitive effectsprobabilistic models
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The pith

Classical instrument models can reproduce every cognitive effect in sequential decision data.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper extends models of cognition to general probabilistic process theories that include both classical and quantum cases. It shows that quantum-like effects such as order effects and conjunction fallacies appear even in simple deterministic classical instruments. The central result is a proof that any set of sequential choice probabilities admits a classical instrument model, so quantum models are not required for sequential decisions. Standard comparisons that restrict classical models to measurement-induced instruments are therefore too narrow. To rule out classical accounts one must instead use parallel composition of decisions and test for Bell inequality violations in real data.

Core claim

In any probabilistic process theory, every sequential decision experiment can be represented by a classical instrument model, and even deterministic classical instruments already produce all the reported cognitive effects; only when joint decisions are modelled with parallel composition do violations of Bell inequalities become possible evidence against classical instruments.

What carries the argument

Instruments in probabilistic process theories, where a classical instrument is any process on a classical system that updates probabilities according to the theory's rules rather than being limited to standard Bayesian measurement updates.

If this is right

  • Sequential decision data alone cannot distinguish classical from quantum accounts of cognition.
  • Deterministic classical models already generate order effects, conjunction fallacies, and similar phenomena.
  • Comparisons that only consider measurement-induced instruments miss the generality of classical models.
  • Bell inequality tests on jointly modelled decisions become the relevant test for non-classicality.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Cognitive experiments should be redesigned to collect parallel rather than only sequential choice data.
  • Real-world data sets claimed to require quantum models can be re-examined for compatibility with general classical instruments.
  • Process-theoretic language supplies a single framework in which both classical and quantum accounts can be compared directly.

Load-bearing premise

That observed cognitive phenomena are accurately captured by instruments acting on systems in probabilistic process theories.

What would settle it

A collection of sequential choice probabilities for which no classical instrument model exists in any probabilistic process theory.

read the original abstract

Various effects in human cognition, often considered `non-classical', have been argued to be most naturally modelled by quantum-like models of decision making. We extend this approach to describe models of cognition and decision-making in general probabilistic process theories, which include both classical probabilistic models and quantum instrument models as special cases. We show how many aspects of quantum-like cognition can be described diagrammatically in process theories, before using our approach to assess the arguments for quantum-like models. While standard Bayesian classical models are insufficient, we prove that any sequential decision data can in fact be given a more general form of classical instrument model, and see that even simple deterministic models can exhibit all cognitive effects. Restricting attention to instruments induced by measurements, such as classical Bayesian and quantum POVM models, rules out such a result, but is challenged by the fact that such instruments cannot account for certain effects. Finally, we argue that to strictly rule out classical instrument models one should make use of parallel composition in the modelling of joint decisions, and find real world cognitive data violating Bell inequalities.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The paper extends quantum-like models of cognition to general probabilistic process theories (encompassing classical probabilistic and quantum instrument models). It presents a diagrammatic approach to modeling cognitive effects, proves that any sequential decision data admits a classical instrument model (with even deterministic models reproducing the effects), shows that restricting to measurement-induced instruments (e.g., Bayesian or POVM) fails to account for certain effects, and argues that parallel composition plus Bell inequality violations in joint decisions are needed to rule out the general classical case.

Significance. If the central proof holds, the work is significant for clarifying the scope of quantum-like models in cognition: it demonstrates that general classical instruments suffice for sequential data, thereby refining (rather than refuting) the motivation for quantum models, while supplying a concrete, falsifiable test via Bell inequalities on joint decisions. The diagrammatic process-theoretic framework and emphasis on reproducible constructions are strengths that could unify disparate modeling approaches in the field.

major comments (2)
  1. [proof section (following the diagrammatic setup)] The central proof that 'any sequential decision data can in fact be given a more general form of classical instrument model' (abstract and the section presenting the result) is load-bearing for the claim that classical models are sufficient; the explicit construction of the instruments, including how they handle parallel composition and avoid implicit non-classical features, must be fully detailed and verified to confirm it remains strictly classical.
  2. [assessment of quantum-like arguments] The argument that restricting to measurement-induced instruments rules out the result but is challenged by effects those instruments cannot account for (abstract) requires a concrete example of an effect that forces general instruments; without it, the distinction between standard Bayesian models and the broader classical construction remains somewhat schematic.
minor comments (3)
  1. [diagrammatic sections] Diagrammatic representations of instruments and sequential composition would benefit from consistent labeling of wires and explicit indication of which maps are classical versus general.
  2. [results on cognitive effects] The paper should include a short table or comparison explicitly listing which cognitive effects (order, conjunction, etc.) are reproduced by deterministic classical instruments versus requiring general instruments.
  3. [preliminaries] Notation for process theories (e.g., the definition of instruments) should be introduced with a brief reminder in the main text even if defined in an appendix.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their insightful comments on our manuscript. The suggestions will help improve the clarity and rigor of our presentation, particularly regarding the central proof and the distinction between instrument types. We address each major comment below and indicate the revisions we plan to make.

read point-by-point responses

  1. Referee: [proof section (following the diagrammatic setup)] The central proof that 'any sequential decision data can in fact be given a more general form of classical instrument model' (abstract and the section presenting the result) is load-bearing for the claim that classical models are sufficient; the explicit construction of the instruments, including how they handle parallel composition and avoid implicit non-classical features, must be fully detailed and verified to confirm it remains strictly classical.

    Authors: We agree that providing the explicit construction is essential to substantiate the claim. In the revised version, we will expand the relevant section to include a detailed, step-by-step construction of the classical instruments for any sequential decision data. This will specify how the instruments are defined within the classical probabilistic process theory, ensuring they are strictly classical (i.e., based on deterministic or probabilistic processes without superposition or entanglement). We will also clarify that the construction applies to sequential composition and does not rely on parallel composition for this result; parallel composition is discussed separately in the context of joint decisions. The verification will be included to show that the model reproduces the data while remaining classical. revision: yes

  2. Referee: [assessment of quantum-like arguments] The argument that restricting to measurement-induced instruments rules out the result but is challenged by effects those instruments cannot account for (abstract) requires a concrete example of an effect that forces general instruments; without it, the distinction between standard Bayesian models and the broader classical construction remains somewhat schematic.

    Authors: We appreciate this point and agree that a concrete example would make the argument more compelling. While the manuscript notes that measurement-induced instruments (such as Bayesian or POVM models) cannot account for certain effects, we will revise the text to include a specific example. For instance, we can reference cognitive phenomena like the 'sure-thing principle' violations or specific order effects in decision making that require instruments not induced by a single measurement. This will illustrate why the broader class of classical instruments is necessary and how it differs from standard models. We will ensure the example is grounded in the process-theoretic framework. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper's central results are mathematical proofs inside the probabilistic process theory framework demonstrating that sequential decision data admits general classical instrument models (distinct from standard Bayesian or measurement-induced ones) and that deterministic models can reproduce cognitive effects. These follow from the explicit definitions and greater generality of instruments versus restricted maps, without any reduction of a claimed prediction to a fitted parameter, self-citation chain, or definitional equivalence. The argument for Bell inequality tests on joint decisions is presented as an independent, falsifiable criterion rather than an internal assumption. No load-bearing step reduces to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper rests on the standard axioms of probabilistic process theories (monoidal categories with probabilistic structure) and the assumption that cognitive data can be represented by instruments. No free parameters are introduced and no new entities are postulated.

axioms (1)
  • domain assumption Probabilistic process theories form a general framework that includes both classical probabilistic models and quantum instrument models as special cases
    Invoked throughout the abstract as the ambient setting for the analysis and proofs.

pith-pipeline@v0.9.0 · 5477 in / 1228 out tokens · 48352 ms · 2026-05-10T17:10:52.224147+00:00 · methodology

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