A QUANTITATIVE ANALYSIS OF THE RESPONDING MAINTAINED BY INTERVAL SCHEDULES OF REINFORCEMENT1

A. Charles Catania, G. S. Reynolds · Journal of the Experimental Analysis of Behavior · 1968 · behaviour-analysis · 10.1901/jeab.1968.11-s327 · record catania1968-a-quantitative-analysis-of-the-res
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How to read this page. The article itself is not reproduced here — this paper is not cleared for redistribution, so what follows is the tag layer alone. The evidence sentences are withheld with the article. The table at the foot lists every tag the record carries; each row names the facet it belongs to, and the whose words column says whether the tag records the paper's own wording or the tagger's sentence about the paper. Every tag links to each other paper in the corpus carrying it. The machine-readable edition of the same thing is the TEI file beside this one, where the tags live in standOff, and the article is at its publisher via the link below. When we have changed our mind. Some entries in the table begin with a word in capitals and the reason for it. EVIDENCE CORRECTED — the finding still stands, but we had quoted the wrong sentence from the paper, and the quotation has been replaced with the right one. RETRACTED — the entry itself was wrong; it stays on the page, marked, with the reason, rather than being deleted. WITHDRAWN AND REPLACED — the entry was wrong, and a corrected version of it appears in the entries below. Each mark carries its own reason, in brackets, because the reasons differ from one entry to the next. An entry we have WITHDRAWN is removed from this page and kept in the record, with its reason. A line reading Audit and a date is a later re-reading of the entry against its whole sentence: DOUBTFUL means it was kept, and the reason says what is loose about it. Quotation marks inside the tagger's sentence. Where a tag is the tagger's own sentence, a phrase in quotation marks inside it is borrowed from the paper — the tagger's wording around it is not. The paper's own sentence is the evidence quote for that row; on this page it is withheld with the article, and the article is at its publisher. Nothing inside quotation marks anywhere on this page is ours: if it is quoted, it is the paper's. Whose words a concept carries. A concept entry records a term the paper itself uses, so the term, the sense given for it, and its evidence are the paper's own words, quoted where the paper fixes them. This is the opposite of a sense entry in the tag table, which is the tagger's sentence about how the paper uses a term. Where a concept entry could not be grounded in the paper's words, the entry says so on its own row.

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Every tag the record carries, each linking to every other paper in the corpus that carries it. A tag appears here whether or not its words occur in the article — the spans below are only the ones a sentence in this paper licenses. Of the 8 concept tags on this paper, all 8 are grounded in a quoted sentence. 4 carry the tagger's gloss of what the term means in this paper, which is not something the article can license.
local rate of reinforcement overall rate of reinforcement rate of responding interval schedule opportunity for reinforcement Reinforcements per opportunity terminal rate of responding The effect of a reinforcement spreads along the continuum of time since reinforcement, so responding at any moment is controlled by reinforcement probability smeared over a surrounding window rather than at that instant alone That temporal spread is interpreted as a gradient of temporal generalization around the moment of reinforcement Overall response rate is produced indirectly: reinforcement rate acts on local response rates at each time after reinforcement, and the overall rate is their weighted average Time since reinforcement acts as a discriminative stimulus dimension, so intervals reliably paired with nonreinforcement come to control low response rates just as other stimulus dimensions do reinforcements per opportunity (rft/op) fixed-interval schedule geometric VI schedule Fibonacci VI schedule overall rate local rate mean interval relative durations probability of reinforcement rate of key-pecking body weight mean arithmetic mean weighted average conditional probability behavioural-experiment

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relation to other workclaim_relationshow this paper stands to another: agrees, contradicts, extends, qualifies
claim typeclaim_typethe shape of the claim: existence, mechanism, method, critique, prediction, null
concept edgeconcept_edgesan asserted relation between two concepts, with the sentence asserting it
conceptconceptsan idea the paper works with, quoted where the paper uses it
content tagcontent_tagsa finding, definition, quantity, statistic or variable named in the paper
controlcontrolsan experiment run to eliminate a rival explanation
limitationlimitationswhat the paper says its evidence cannot support
mechanismmechanismshow the reported effect is said to come about
methodmethodhow the paper produced its evidence
phenomenonphenomenonthe effect or regularity under study
sensesensesa distinct use of a term, quoted where the paper fixes it
unrecordable relationunhoused_relationsa relation the paper asserts that this vocabulary cannot express, with the reason

The paper

The full text is not reproduced here. This article is not cleared for redistribution, so the page carries the tag layer only. Its evidence sentences are withheld; the grounding status remains with each tag, and the article itself is at https://doi.org/10.1901/jeab.1968.11-s327. The reading view exists for the papers whose licence permits it.

Every tag on this page

claim_relations 3 · claim_type 1 · concept_edges 4 · concepts 8 · content_tags 35 · controls 1 · limitations 8 · mechanisms 4 · method 1 · phenomenon 1 · senses 6 · unhoused_relations 1

Relations on this page carry a quotation for the claim. Where a relation was separately evidenced — and so tested against the vocabulary for its type — the row says so; none of 4 relations here carry that mark. The rest are the tagger’s reading of the sentence quoted beside them.

facettagfieldconf.whose words
claim_typemechanism
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claim_typethe paper's words
phenomenonresponding under interval schedules of reinforcement
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phenomenonthe paper's words
methodbehavioural-experiment
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methodthe paper's words
mechanismsmechanisms
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mechanisms[0]the tagger's words
mechanismsmechanisms
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mechanisms[1]the tagger's words
mechanismsmechanisms
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mechanisms[2]the tagger's words
mechanismsmechanisms
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mechanisms[3]the tagger's words
limitationsA function these authors published earlier was fitted to the group average rather than to any animal.
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what this limits: the earlier published power function: the authors state it was fitted
limitations[0]1.0the tagger's words
limitationsThat earlier published function is stated not to fit the data of individual animals.
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what this limits: the earlier power function applied to any individual pigeon: the authors state it does not fit individual data
limitations[1]1.0the tagger's words
limitationsThe choice between two candidate functional forms was made on a priori grounds rather than on which fitted the data better.
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what this limits: the published functional form as an empirical result: the authors state the choice rested on logical considerations rather than superiority of fit
limitations[2]1.0the tagger's words
limitationsIndividual differences between animals are large enough that the authors say a unified quantitative analysis would not survive comparison across them.
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what this limits: pooling or comparing the quantitative results across pigeons: the authors state
limitations[3]1.0the tagger's words
limitationsDeriving a single function across all animals is stated to be complicated by the idiosyncratic character of each animal's data.
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what this limits: a single reinforcement-responding function covering all pigeons: the paper says the derivation is complicated by each pigeon's idiosyncratic data
limitations[4]1.0the tagger's words
limitationsWhether the variable-interval and fixed-interval functions share a form is stated to be undecidable from the data presented.
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what this limits: any claim that the VI and FI functions share a form: the paper states this cannot be decided from the figure presented
limitations[5]1.0the tagger's words
limitationsSeveral quantitative extensions are placed outside the paper's scope.
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what this limits: the quantitative details and their coordination across schedule types: the paper places these beyond its scope
limitations[6]1.0the tagger's words
limitationsAND THE AUTHORS LATER USE THAT ARBITRARINESS AGAINST THEIR OWN RESULT: `Quotation withheld`. A DEFINITIONAL CHOICE DECLARED ARBITRARY WHEN IT IS MADE AND THEN CITED AS A REASON TO DISCOUNT A FINDING THIRTY-FIVE THOUSAND CHARACTERS LATER. The same paper does it a third time near the end - `the computation of local rates of reinforcement is most arbitrary at early and late times after reinforcement` - so the qualification is tracked, not mentioned once and forgotten.
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limitations[7]1.0the tagger's words
controlsarithmetic variable-interval schedules run with and without a 0-second interreinforcement interval, compared directly within the present experiment
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eliminates: the 0-second interval as the source of the local response-rate pattern - the two schedules are the same arithmetic VI otherwise · outcome (stated by the tagger, no quotation): held
controls[0]0.85the tagger's words
conceptslocal rate of reinforcement
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concepts[0]the paper's words
conceptsoverall rate of reinforcement
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concepts[1]the paper's words
conceptsrate of responding
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concepts[2]the paper's words
conceptsinterval schedule
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concepts[3]the paper's words
conceptslocal rate of reinforcement
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about this quote: PAGE FURNITURE IS SPLICED INTO THE QUOTE - the page number and the running head, '342 A. CHARLES CATANIA and G. S. REYNOLDS', between 'successive op-' and the rest of the word. The words on either side of it were never continuous on the page; read the quote with it deleted.
concepts[4]1.0the paper's words
conceptsopportunity for reinforcement
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concepts[5]0.95the paper's words
conceptsReinforcements per opportunity
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concepts[6]0.95the paper's words
conceptsterminal rate of responding
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concepts[7]0.95the paper's words
unhoused_relationstemporal separation → time since reinforcement
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THE TWO CANNOT BE SEPARATED IN THIS STUDY - the DESIGN form / It bounds what the paper's own results can mean, and it lives in a methods paragraph where nothing downstream will find it. A 1968 methods sentence naming its own confound, in a paper nobody would search for it in.
unhoused_relations[0]the tagger's words
sensesrate of reinforcement - the overall rate a schedule provides, which the paper concludes is NOT what determines responding
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senses[0]1.0the tagger's words
sensesrate of reinforcement - the local rate at a particular time within an interval, which the paper concludes is what responding tracks
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senses[1]1.0the tagger's words
sensesrate of responding - a quantity that changes within a single interval, not a single value per schedule
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senses[2]1.0the tagger's words
senses'local rate of reinforcement' - AN OPERATIONAL DEFINITION ITS OWN AUTHORS CALL ARBITRARY, WITH THE REJECTED ALTERNATIVES NAMED: other assignments of time to opportunities are 'possible, SUCH AS BISECTION ... using the geometric rather than the arithmetic mean, or the assignment to a given opportunity of the time since the last opportunity. The present technique, though arbitrary, seems to involve the simplest ad hoc assumptions.' The choice is defended on SIMPLICITY, not on correctness, and the competitors are printed so a reader can substitute one. This record already distinguishes the overall rate of reinforcement from the local one; this is the further fact that the local one is a construct with a dial on it.
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senses[3]1.0the tagger's words
senses`Reinforcements per opportunity` - A NAME SHAPED LIKE A RATE THAT DENOTES A PROBABILITY. `Quotation withheld` The `X per Y` form is how this literature writes rates (`reinforcements per hour` appears in the same paper), so the name invites the reader to expect a count over a denominator and delivers a bounded probability instead. The definition is explicit precisely because the name is misleading.
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senses[4]0.9the tagger's words
senses`opportunity for reinforcement` - THE DEFINITION IS A DISJUNCTION, AND THE TWO LIMBS ARE NOT THE SAME TEST. `a point on the continuum of time since reinforcement at which the probability of reinforcement is greater than zero, or at which at least one interval ends.` The first limb is a property of the schedule; the second is a property of the sample of intervals actually run. They coincide in the limit and can differ in a finite experiment.
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senses[5]0.85the tagger's words
claim_relationsqualifies → Reynolds and Catania (1961); Catania and Reynolds (1963) — the authors' own earlier publication
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differs in: WHETHER THE FUNCTION IS FITTED TO A GROUP OR TO AN ANIMAL, AND WHY THE FORM WAS CHOSEN. Two admissions in one passage: 'The choice between these two functions was based more on logical considerations ... than on the superiority of the fit of the power function to the data', and 'Quotation withheld' The published law was fitted to the group average, chosen on a priori grounds rather than fit, and fails on every individual - said by its own authors
claim_relations[0]0.95the tagger's words
claim_relationsqualifies → Reynolds and Catania (1962); Reynolds (1966); Stubbs (1968)
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differs in: CAPACITY VERSUS CONTROL. 'the performances maintained by FI schedules do not appear to be as well under the control of time since reinforcement as the capacity of the pigeon to discriminate durations would suggest.' What an animal CAN discriminate and what its behaviour IS controlled by come apart, so a discrimination result does not license an inference about what governs performance
claim_relations[1]0.9the tagger's words
claim_relationsbuilds-on → Millenson (1966); Anger (1956)
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differs in: WHAT AN UNEXPECTED DIRECTION OF CHANGE IS TAKEN TO SHOW. Inter-response times shorten 'even in schedules of reinforcement in which long IRTs are differentially reinforced', i.e. against the contingency, and the literature's reading is a property of the reinforcement process itself - 'that short IRTs are more susceptible to reinforcement than long IRTs'. A behaviour that moves opposite to the arranged contingency is explained by postulating an asymmetry in what reinforcement can act on
claim_relations[2]0.9the tagger's words
concept_edgesEVIDENCE CORRECTED (RE-GROUNDED) · local rate of reinforcement —distinct-from→ overall rate of reinforcement
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EVIDENCE CORRECTED: RE-GROUNDED. The old span stated a conclusion without naming either rate. This sentence names both AND DISTINGUISHES THEM BY EXPERIMENT: '…while the overall rate of reinforcement is held constant…' - one is held fixed while the other moves, which is the strongest form a distinction can take: not observed, but constructed. — strength of the relation: 1
concept_edges[0]the tagger's words
concept_edgeslocal rate of reinforcement —causes→ rate of responding
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strength of the relation: 0.9
concept_edges[1]the tagger's words
concept_edgesterminal rate of responding —part-of→ rate of responding
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strength of the relation: 0.9 · note: The terminal rate is the local rate AT A PARTICULAR MOMENT - a restriction of the general measure, which is why 'part-of' and not 'is-a'.
concept_edges[3]0.9the tagger's words
concept_edgesoverall rate of reinforcement —causes→ terminal rate of responding
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strength of the relation: 0.7 · note: DIRECTION CHECKED AGAINST THE SENTENCE, AND MY FIRST VERSION HAD IT BACKWARDS. 'INCREASED AS the overall…' - the reinforcement rate is what the SCHEDULE SETS and the responding is what the animal does, so the schedule variable is the cause. I wrote the edge the other way round while writing a note that said the reinforcement rate was the manipulated side; the dry run is where that was caught. Weight 0.7 records the paper's own hedge - in general, however - stated immediately after 'No systematic relationship…' for the FI rates.
concept_edges[4]0.8the tagger's words
content_tagsmean
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also in: mean
content_tags.statistics[0]the tagger's words
content_tagsweighted average
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content_tags.statistics[1]the tagger's words
content_tagsconditional probability
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content_tags.statistics[2]the tagger's words
content_tagsAcross seven variable-interval schedules the overall rate of pigeons' key-pecking rose monotonically with the overall rate of reinforcement but with diminishing returns, over a span from 8.4 to 300 reinforcements per hour.
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content_tags.findings[0]the tagger's words
content_tagsWithin a single schedule, how fast the bird pecked at a given moment after reinforcement tracked the local rate of reinforcement at that moment, computed from the probability of reinforcement there and the nearness of reinforcement opportunities at other moments.
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content_tags.findings[1]the tagger's words
content_tagsThe paper's overall conclusion is that a schedule's overall response rate is not set by its overall reinforcement rate but is the sum of separate local reinforcement effects distributed across times within the interval.
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content_tags.findings[2]the tagger's words
content_tagsA schedule engineered to hold the probability of reinforcement constant across time since reinforcement flattened the within-interval response gradient, keeping the local pecking rate roughly constant instead of rising.
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content_tags.findings[3]the tagger's words
content_tagsThe local pecking rate at t sec depended on the probability of reinforcement at that time.
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content_tags.findings[4]the tagger's words
content_tagsIncluding a 0-sec interval (first peck after reinforcement is reinforced) raised responding only in the first two or three time bins after reinforcement, not across the whole interval.
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content_tags.findings[5]the tagger's words
content_tagsAn early reinforcement probability of 0.05, unlike 0.50, was less able to maintain responding once the later, higher probability of reinforcement was removed.
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content_tags.findings[6]the tagger's words
content_tagsAt matched overall reinforcement rates, arithmetic variable-interval schedules sustained higher overall response rates than fixed-interval schedules for all but one pigeon.
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content_tags.findings[7]the tagger's words
content_tagsReinforcing a response immediately after a preceding reinforcement affected responding only over a short time since reinforcement.
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content_tags.findings[8]the tagger's words
content_tagsreinforcements per opportunity (rft/op)
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content_tags.definitions[1]the tagger's words
content_tagsopportunity for reinforcement
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content_tags.definitions[2]the tagger's words
content_tagslocal rate of reinforcement
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content_tags.definitions[3]the tagger's words
content_tagsinterval schedule
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content_tags.definitions[4]the tagger's words
content_tagsfixed-interval schedule
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content_tags.definitions[5]the tagger's words
content_tagsgeometric VI schedule
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content_tags.definitions[6]the tagger's words
content_tagsFibonacci VI schedule
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content_tags.definitions[7]the tagger's words
content_tagsoverall rate
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also in: overall rate
content_tags.definitions[8]the tagger's words
content_tagslocal rate
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also in: local rate
content_tags.definitions[9]the tagger's words
content_tagsmean interval
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also in: mean interval
content_tags.variables[0]the tagger's words
content_tagsrelative durations
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content_tags.variables[1]the tagger's words
content_tagsprobability of reinforcement
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content_tags.variables[2]the tagger's words
content_tagsoverall rate of reinforcement
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content_tags.variables[3]the tagger's words
content_tagsrate of key-pecking
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content_tags.variables[4]the tagger's words
content_tagsbody weight
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also in: body weight
content_tags.variables[5]the tagger's words
content_tags8.4 to 300 reinforcements per hour — the span of overall reinforcement rates over which the response-rate function was measured in Experiment 1
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content_tags.quantities[0]the tagger's words
content_tagssix — number of pigeons whose key-pecking was studied in Experiment 1, maintained at 80% of free-feeding weight
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content_tags.quantities[1]the tagger's words
content_tags0.10 + 0.02 — the reinforcement probability held nearly constant in the constant-probability schedule, over a span where the arithmetic schedule's probability rose from 0.07 to 0.33
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content_tags.quantities[2]the tagger's words
content_tagsabout 2 resp/min — the near-flat rise in local response rate across the constant-probability interval, about one-tenth of the rise seen in the arithmetic schedule
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content_tags.quantities[3]the tagger's words
content_tags63.7 and 63.2 resp/min ... 61.1 and 73.7 resp/min — overall response rates on the schedules without and with a 0-sec interval, for Pigeons 278 and 281 respectively
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content_tags.quantities[4]the tagger's words
content_tagsabout 6% ... 50% to 90% — a tiny change in overall reinforcement rate produced a disproportionately large change in overall response rate, showing the distribution of intervals rather than the overall rate was responsible
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content_tags.quantities[5]the tagger's words
content_tagsa factor of almost 40 — the growth of local reinforcement rate from 10 to 140 sec after reinforcement in the arithmetic schedule, far larger than the accompanying growth in local response rate
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content_tags.quantities[6]the tagger's words
content_tagsabout 12 resp/min — the rise in immediate post-reinforcement response rate that a single extra reinforced response would explain, against an observed increment roughly two and a half times larger
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content_tags.quantities[7]the tagger's words

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