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REVIEW 5 major objections 4 minor 9 references

Arbitrarily Applicable Same/Opposite Relational Responding with NARS

T0 review · 5 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

Pith's one-line read The paper claims that NARS, with its acquired-relations extension, combines mutual and combinatorial entailment to answer never-trained same/opposite matching-to-sample trials at perfect accuracy, thereby exhibiting arbitrarily applicable…

desk verdict The 100% BC accuracy is built into the hand-coded schema, so the emergence claim fails; the paper is a useful NARS implementation but not a demonstration of AARR. read the letter →

arxiv 2505.07079 v2 pith:OAILWSPT submitted 2025-05-11 cs.AI

classification cs.AI
keywords same/oppositerelationalrespondingarbitrarilyapplicableNon-AxiomaticReasoningSystemframetheorymutualentailmentcombinatorialmatching-to-sampleacquiredrelations
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper aims to show that a reasoning system called NARS can learn same/opposite relations from a few reinforced examples and then respond correctly to stimulus pairs it has never seen. To do this, the authors add an 'acquired relations' mechanism that abstracts trained pairings into higher-order rules linking stimulus identities to screen locations. In a context-controlled matching-to-sample design, after explicit pretraining of symmetric and transitive relations, the system scores 100% on the critical test phase, including deriving a same-relation from two trained opposite-relations. If the claim holds, it provides a computational demonstration of relational generalization of the kind psychologists attribute to human symbolic cognition, and a path toward more flexible reasoning in artificial intelligence.

What carries the argument

The load-bearing component is the acquired relation, a higher-order NARS implication that abstracts a trained relation between two stimulus identities together with a spatial relation between two locations into a rule for choosing a match action. In its generalized form it uses variables ($v_1,v_2,v_3,v_4$) and states: if $v_1$ and $v_2$ stand in a learned relation and $v_3$ and $v_4$ stand in a location-pair relation, then matching $v_3$'s stimulus to $v_4$'s stimulus leads to the goal. Paired with explicit relational naming (e.g., `<(X1 * Y1) --> SAME>`), this lets one trained rule apply to arbitrary novel stimuli and locations. Phase 1 pretraining supplies the symmetrical and transitive inference patterns, and Phase 2 maps them onto the AB/AC stimulus network, so the Phase 3 BC test can be passed without any direct BC feedback.

What would settle it

Run the BC test with Phase 1 pretraining omitted while keeping the acquired-relations machinery; if accuracy drops to chance, the symmetric/transitive pretraining carried the generalization. Alternatively, train only A opposite B and A opposite C and test B same C without any prior symmetry or transitivity training; a chance result would show the generalization is not learned from minimal experience alone.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that NARS can generalize explicitly trained same/opposite relations to entirely new stimulus pairs by combining mutual entailment (symmetry) and combinatorial entailment (transitivity). In the critical BC phase, pairs such as B and C had never been reinforced together, yet NARS selected the correct SAME or OPPOSITE match on 100% of trials, using internal relational hypotheses that connect acquired relations between stimulus identities to matching actions between locations. The system's internal confidence for both mutual and combinatorial entailment rises with training and stays high during novel testing, which the authors read as evidence that the relational principles have been internalized rather than applied as isolated memorized pairings.

Load-bearing premise

The result rests on the assumption that the hand-written generalized schema and the Phase 1 symmetric/transitive pretraining do not already encode the same/opposite generalization; if they do, the perfect BC score shows only that the programmed rule executes, not that the relational response emerged from experience.

Editorial extensions

If this is right

  • NARS achieves 100% accuracy on BC trials without feedback, which is above the 50% chance baseline and therefore demonstrates generalized rather than random responding.
  • Because the same acquired-relations mechanism is domain-general over stimulus identities and locations, it can be applied to new stimulus sets without retraining the relational rules.
  • The internal confidence measures for mutual and combinatorial entailment rise with training and stay high in the derived test phase, supporting the authors' claim that the relational principles are internalized.
  • The approach extends prior NARS stimulus-equivalence work by handling two relational frames (SAME and OPPOSITE) and their combination, not just equivalence.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: The experiment does not isolate emergence from execution, because Phase 1 explicitly trains symmetry and transitivity and Section 3.2 provides a hand-written generalized schema; a stronger test would run BC with both removed to see whether the system can learn the rule from the AB/AC reinforcement alone.
  • Editorial inference: If the hand-authored schema is considered part of the model rather than an experimental prompt, the contribution is better described as showing that NARS can execute relational-logic rules in a matching task, not that relational frames emerge from experience.
  • Editorial inference: A natural extension would be to train only OPPOSITE pairs (A opposite B, A opposite C) and test B same C with no preceding symmetric/transitive pretraining; the paper's design already includes this logic, but an ablation would make the derivation path visible.
  • Editorial inference: The perfect deterministic accuracy suggests that a more demanding test, such as noisy or conflicting context cues, or novel relational frames like 'larger/smaller,' would better discriminate learned relational abstraction from rule-following.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 4 minor

Summary. The paper extends the Non-Axiomatic Reasoning System (NARS) with an 'acquired relations' mechanism and applies it to a same/opposite matching-to-sample (MTS) task inspired by Relational Frame Theory (RFT). The experiment has three phases: Phase 1 explicitly pre-trains mutual entailment (symmetry) and combinatorial entailment (transitivity) for SAME and OPPOSITE relations; Phase 2 trains relational networks on novel stimulus sets AB and AC; Phase 3 tests untrained BC stimulus pairs. The reported results are perfect accuracy (100%) in all phases, including the critical BC phase, along with internal confidence metrics. The authors interpret this as demonstrating the emergence of arbitrarily applicable relational responding within NARS.

Significance. If the central claim were supported, the paper would offer a useful computational bridge between RFT and NARS and a concrete implementation of same/opposite relational responding. The formalization in Narsese and the explicit MTS design are clear, and the target phenomenon is genuinely interesting. However, the paper does not currently support the emergence claim: the generalized variable schema and the pretrained entailment rules appear to encode the tested generalization in advance, and no code, data, or learning trace is provided. As a result, the reported 100% BC accuracy is better described as execution of hand-authored rules than as evidence of learned, arbitrary applicable relational responding.

major comments (5)
  1. [§3.2] The generalized variable schema with $1, $2, $3, $4 is introduced as an implementation construct, not as something NARS learns from experience. The schema already states that if two stimuli are related and two locations are related, then the corresponding match action leads to the goal. Because this exactly covers the logic needed for the BC test in Section 5.3, the perfect BC accuracy is evidence that the hand-authored rule executes, not that arbitrarily applicable relational responding emerged.
  2. [§4, Phase 1] Phase 1 explicitly trains both symmetric (mutual entailment) and transitive (combinatorial entailment) relational frames before the BC test. Since the paper itself identifies mutual and combinatorial entailment as the components required for BC responding, the design cannot support the claim that BC responses emerge from untrained combination; the required component inferences were installed by explicit pretraining.
  3. [§5.4] The example combinatorial entailment hypothesis, written as <(<($1 * #1) --> SAME> && <(#1 * $2) --> OPPOSITE>) ==> <($1 * $2) --> OPPOSITE>>, is a hand-formulated Narsese rule that encodes the target SAME/OPPOSITE composition. The paper provides no learning trace or induction procedure showing that this rule was derived from the Phase 1–2 trials, so the internal-representation example does not establish the acquisition claim.
  4. [§3.3] The 'explicit relational naming' step is described as something NARS 'explicitly abstracted and internally represented' after learning explicit contingencies, but no mechanism is given for how the named relational statements are acquired from sensorimotor experience. This is a load-bearing gap because the named relational representations are the basis for the novel derivations reported in the BC phase.
  5. [§5.3 and Figure 3] The reported 100% accuracy in the BC phase is presented without code, data, number of independent runs, or error bars. With four blocks of 16 trials, the result cannot be statistically assessed, and the 'internal confidence' metrics are not precisely defined, so the claim of 'strong internalization' is not independently verifiable from the supplied artifacts.
minor comments (4)
  1. [§4] The text says 'All phases included four blocks of 16 trials each,' but Section 5 reports accuracy per block without giving total trial counts or numbers of runs; please state these explicitly.
  2. [Abstract and §4] The phrase 'minimal explicit training' should be qualified, because Phase 1 explicitly trains both mutual and combinatorial entailment, which are the very capabilities tested in the BC phase.
  3. [Figure 3] The figure caption says 'Average confidence' but does not define how the confidence values are computed from NARS; please add a precise definition and clarify the axis labels.
  4. [§5.4] The term 'combinational' appears where 'combinatorial' is intended; please correct this for consistency with the rest of the paper.

Circularity Check

3 steps flagged · score 8.0 of 10

BC result is pre-structured: Section 3.2's hand-authored variable schema and Phase 1's explicit symmetric/transitive pretraining already contain the target generalization, so 100% BC accuracy does not by itself demonstrate emergent AARR.

  1. self definitional [Section 3.2, 'Acquired Relations and Generalization']
    "Further generalization involves abstracting to variable placeholders (1,2, 3,4): (<($1 * $2) --> (ocr * ocr)> && <($3 * $4) --> (loc * loc)>) ==> (<($3 * $1) --> (loc * ocr)> &/ <($4 * $2) --> (loc * ocr)> &/ <({SELF} * ($3 * $4)) --> ^match>) =/> G>."

    This generalized schema directly supplies the matching rule used in every BC trial: if the system has any stimulus relation and any location relation, it can fire the higher-order implication to choose the matched comparison. Because the variable abstraction is presented as part of the implementation ('abstracting to variable placeholders'), not as an output of Phase 1/2 learning, the perfect BC performance is a direct execution of the authored schema. The schema is, in effect, the matching generalization that the paper claims to demonstrate.

  2. fitted input called prediction [Section 4, 'Phase 1: Explicit Pretraining of Relational Frames (Mutual and Combinatorial Entailment)']
    "Foundational relational responding capabilities were explicitly trained prior to evaluating emergent relational responding. Specifically, NARS was trained explicitly on symmetric (mutual entailment) and transitive (combinatorial entailment) relational frames using SAME and OPPOSITE contexts. Mutual entailment involved explicit training of symmetrical relations (if X → Y, explicitly train Y → X), ensuring NARS derived symmetrical relations spontaneously."

    Phase 1 explicitly trains the mutual and combinatorial entailment operations that the BC test is claimed to derive. The critical test phase requires exactly this symmetric/transitive combination (e.g., deriving same from two opposite relations), so the reported 100% accuracy is the execution of a directly trained competence, not an emergent capability from minimal experience. The pretraining is the fitted input; the BC 'prediction' is forced by that input by construction.

1 more flagged steps
  1. other [Section 5.4, 'Example of Internal Relational Representation']
    "To explicitly illustrate NARS’ internal representation of relational rules, we present an exemplar combinatorial entailment hypothesis derived during explicit pretraining: <(<($1 * #1) –> SAME> && <(#1 * $2) –> OPPOSITE>) ==> <($1 * $2) –> OPPOSITE>>"

    This 'internal representation' is already a variable rule that performs SAME/OPPOSITE combinatorial entailment. The paper labels it as 'derived during explicit pretraining' but provides no acquisition trace showing that the rule was induced from experience; within the paper it functions as a supplied rule. The BC answers are instantiations of this supplied rule, making the reported relational generalization a consequence of the rule's presence rather than emergent behavior.

full rationale

The central derivation chain is: the acquired-relations extension abstracts sensorimotor contingencies into a variable schema (Section 3.2); Phase 1 explicitly trains mutual and combinatorial entailment (Section 4); and Phase 3 tests untrained BC pairs, reporting 100% accuracy (Section 5.3). Reading the paper's own implementation description, the target generalization is present before the BC test: Section 3.2 supplies the generalized relational schema, Section 5.4 displays a combinatorial-entailment rule already in variable form as an 'internal representation', and Phase 1 explicitly trains the symmetric and transitive operations that the test requires. The 100% BC accuracy is therefore execution of supplied components, not evidence that same/opposite AARR emerged from minimal experience. This is a construction-level circularity rather than a self-citation problem. The paper's own Discussion concedes 'the reliance on empirical validation rather than formal proofs of completeness or consistency of the acquired-relations mechanism', and no acquisition trace is provided to show the schema was induced rather than authored. No external benchmark supports the result; the only comparison is 50% chance, which the supplied rules already exceed by construction. Score 8 reflects a central result forced by definition/construction, though not literally Eq. X = Eq. Y.

Assumptions & free parameters 1 free parameters · 4 assumptions · 2 invented entities

This ledger reflects that the central result is carried by the architecture's pretraining and hand-authored rules rather than by fitted parameters. The free-parameter entry captures unspecified NARS thresholds. The two ad hoc axioms are the load-bearing parts: the variable-based schema in Section 3.2 and the Phase 1 pretraining of mutual and combinatorial entailment. The invented entities are the mechanisms introduced to make the demonstration work.

free parameters (1)
  • NARS truth-value and confidence thresholds = not reported
    NARS belief formation, confidence updates, and goal selection depend on internal parameters that the paper never lists; these thresholds determine whether derived relations reach the response criterion in Phase BC.
assumptions (4)
  • domain assumption RFT's mutual and combinatorial entailment are the correct operationalization of relational generalization
    The paper measures success as accuracy and NARS confidence on these RFT-defined constructs, without testing alternative accounts.
  • domain assumption NARS inference rules provide sound-enough approximate reasoning for this task
    The paper states in Section 6 that formal completeness and consistency of the acquired-relations mechanism were not proven; it relies on empirical performance.
  • ad hoc to paper The generalized relational schema with variables ($1,$2,$3,$4) is a legitimate NARS internal representation rather than an external oracle
    Section 3.2 introduces this schema to directly turn relation and location patterns into match actions, and the BC test can be satisfied by executing this authored rule.
  • ad hoc to paper Phase 1 explicit pretraining of symmetric and transitive relations does not constitute training of the tested BC relations
    Section 4 Phase 1 trains the general mutual and combinatorial entailment patterns; the paper treats later BC performance as derived despite this pretraining of the very inference forms.
invented entities (2)
  • Acquired relations
    purpose: Abstract trained stimulus-location contingencies into variable-based relational schemas that directly yield matching actions
    Introduced in Section 3.2 without independent validation; it is the mechanism that makes the reported BC generalization possible, so it provides no out-of-sample falsifiable handle.
  • Explicit relational naming
    purpose: Represent learned contingencies as named statements such as <(X1*Y1)->SAME>
    Introduced in Section 3.3 to make relational knowledge explicit; its equivalence to the expanded Narsese form is assumed, not demonstrated.

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Cite this review

Pith. "Pith review of Arbitrarily Applicable Same/Opposite Relational Responding with NARS." pith.science (2026). https://pith.science/paper/OAILWSPT

@misc{pith2026250507079,
  author       = {Pith},
  title        = {Pith review of: Arbitrarily Applicable Same/Opposite Relational Responding with NARS},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OAILWSPT}},
  note         = {Machine review of arXiv:2505.07079}
}
read the original abstract

Same/opposite relational responding, a fundamental aspect of human symbolic cognition, allows the flexible generalization of stimulus relationships based on minimal experience. In this study, we demonstrate the emergence of \textit{arbitrarily applicable} same/opposite relational responding within the Non-Axiomatic Reasoning System (NARS), a computational cognitive architecture designed for adaptive reasoning under uncertainty. Specifically, we extend NARS with an implementation of \textit{acquired relations}, enabling the system to explicitly derive both symmetric (mutual entailment) and novel relational combinations (combinatorial entailment) from minimal explicit training in a contextually controlled matching-to-sample (MTS) procedure. Experimental results show that NARS rapidly internalizes explicitly trained relational rules and robustly demonstrates derived relational generalizations based on arbitrary contextual cues. Importantly, derived relational responding in critical test phases inherently combines both mutual and combinatorial entailments, such as deriving same-relations from multiple explicitly trained opposite-relations. Internal confidence metrics illustrate strong internalization of these relational principles, closely paralleling phenomena observed in human relational learning experiments. Our findings underscore the potential for integrating nuanced relational learning mechanisms inspired by learning psychology into artificial general intelligence frameworks, explicitly highlighting the arbitrary and context-sensitive relational capabilities modeled within NARS.

Figures

Figures reproduced from arXiv: 2505.07079 by the authors.

Figure 1
Figure 1. The Matching-to-Sample task used in the present study. Pre-training phases are excluded from this figure. The figure illustrates experimental phases 2–3, with underlined options indicating correct responses [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Explicitly trained (left panel) and derived (right panel) relational networks from the present study. S and O denote SAME and OPPOSITE, respectively. Phase 1: Explicit Pretraining of Relational Frames (Mutual and Combinato￾rial Entailment). Foundational relational responding capabilities were explicitly trained prior to evaluating emergent relational responding. Specifically, NARS was trained explicitly on symmetric… view at source ↗
Figure 3
Figure 3. Accuracy (% correct) and internal confidence (mutual entailment and combi￾natorial entailment) across three experimental phases. Phase 1: Explicit pretraining (XY, YX, YZ, XZ). Phase 2: Relational network training (AB, AC). Phase 3: Derived relational testing (BC). Accuracy is reported per block of 16 trials. 5.4 Example of Internal Relational Representation To explicitly illustrate NARS’ internal representation of … view at source ↗

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Works this paper leans on

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    ENTRY address author booktitle chapter doi edition editor eid howpublished institution journal key month note number organization pages publisher school series title type url volume year label INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all := #1 'mid.sentence := #2 'after.sentence := #3 '...

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    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

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