JOURNAL OF THE EXPERIMFNTAL ANALYSIS OF BEHAVIOR

SELF-INHIBITING EFFECTS OF REINFORCEMENT'

A. CHARLES CATANIA

NEW YORK UNIVERSITY

The reinforcers produced by one response reduce the rate of other, concurrently reinforcedresponses. An analysis of the logical and empirical implications of the relation indicatesthat one reinforcer must have this effect on responses maintained by other reinforcerseven when all reinforcers are produced by the same class of responses. A quantitative ex-pression of the relation leads to a formulation, mathematically equivalent to Herrnstein's(1970), in which the rate of a reinforced response is a joint function of (1) an excitatoryeffect of the reinforcers produced by that class of responses, and (2) an inhibitory effect ofthe total reinforcers produced both by that class and by other classes of responses.

Studies of food-reinforced key-pecking in thepigeon have established two relations betweenresponding and reinforcement. With respectto the reinforcers produced by a particular re-sponse, responding increases as a negativelyaccelerated function of reinforcement (Cataniaand Reynolds, 1968). But when response-pro-duced reinforcers are held constant, respond-ing decreases as a function of reinforcementfrom other sources (Catania, 1963, 1969; Rach-lin and Baum, 1969, 1972). These two relationsseem mutually compatible, and consistent withour preconceptions about how behavior isstrengthened and maintained. Yet on examina-tion, the relations have some paradoxical im-plications.

Let us consider a pigeon pecking on twokeys, Key A and Key B. For one or both of thekeys, a variable-interval (VI) schedule oper-ates: reinforcement is scheduled for the firstpeck that occurs on the key after a variabletime has elapsed since the last reinforced peckon that key. The advantage of studying therelation between responses and reinforcementwith this schedule is that changes in responserate over a substantial range have little effecton reinforcement rate. A hypothetical experi-ment is outlined in Table 1. In the first condi-tion, a VI schedule arranges 30 rft/hr (rein-forcements per hour) for Key A alone, andmaintains Key-A pecking at a rate of 50 resp/

1Research supported by NIH Grant MH-18506. Re-prints may be obtained from the author at the Depart-ment of Psychology, University College of Arts andScience, New York University, New York, N. Y. 10453.

min (responses per minute). When the VIschedule is moved to Key B, in the second con-dition, the pecking, still at 50 resp/min, alsomoves to Key B. Now we examine the two VIsclhedules operating concurrently: 30 rft/hr forKey A, and 30 rft/hr for Key B. In this condi-tion, the pigeon pecks both keys, but each at alower rate than when either operated alone:35 resp/min on Key A, and 35 resp/min onKey B. The Key-A reinforcers reduce Key-Bresponding, and the Key-B reinforcers reduceKey-A responding. The combined VI sched-ules, wlhich provide a total of 60 rft/hr, do notmaintain the sum of the response rates thatthey maintained separately; instead of 100'resp/min, they together maintain only 70resp/min.

Consider now what happens when these con-current VI schedules are combined on a singlekey, so that Key A alone provides the entire60 rft/hr. This time, the concurrent rates ofresponding summate: the Key-A schedulemaintains 70 resp/min. The 35 resp/minmaintained on Key B simply moved to Key A,consistent with the finding that the total re-sponding maintained by a given total rateof reinforcement is independent of the way inwhich reinforcers are distributed among theresponses (Catania, 1963).But here is the paradox: this rate of re-

sponding is the summation of two responserates, each of which was reduced by the other'sreinforcers. Now that all of the reinforcers arescheduled for pecks on the single key, why doesthe reduction remain? Why is the total re-

517

1973, 19, 517-526 NUMBER 3 (MAY)

A. CHARLES CA TANIA

Table 1

Hypothetical data from four procedures with con-current and single-response variable-interval (VI) sched-ules.

VI Schedule in rft/hr Responding in pecks/min

Key A Key B Total Key A Key B Total

30 - 30 50 0 50- 30 30 0 50 5030 30 60 35 35 7060 - 60 70 0 70

sponding on the single key not equal insteadto the summation of the respective rates of re-sponding maintained when each of the compo-nent schedules operated singly? The Key-Areinforcers reduced Key-B responses and theKey-B reinforcers reduced Key-A responses inthe concurrent condition, and these reinforcersapparently continue to produce reductionseven when they are now all scheduled for asingle response.We have already noted that reinforced re-

sponding decreases with increases in reinforce-ment from other sources. The present accountargues that this effect holds for reinforcementfrom any source, including the reinforced re-sponse itself. According to this view, each re-inforcer has an excitatory effect, specific to theresponse that produced it (or, more precisely,to responses in the same operant class as theresponse that produced it; for convenience ofexposition, this qualification will be left im-plicit in the subsequent development). Buteach reinforcer also has an inhibitory effectthat operates on all responses, including theone that produced it; it is in this sense thatwe shall claim that reinforcement is self-in-hibiting. To support the claim, we will firstreview some data on inhibitory effects of re-inforcement; we will then consider some actualand hypothetical findings from an experimentdesigned to illustrate the issues; finally, wewill examine some quantitative and theoreti-cal implications of the analysis.

EFFECTS OF VARIOUSSOURCES OF REINFORCERS

Several experiments involving concurrentVI VI schedules with pigeons have establishedthat the rate of one response decreases withincreases in the reinforcement of other re-sponses. The data are summarized in Figure 1.

In one experiment, the VI schedule for thefirst response was held constant while the VIschedule for the other response was varied(Catania, 1963, Experiment 1). In another, theschedule for the other response was modifiedso that reinforcement was stimulus-correlated,or signalled; the signal was presented onlywhen reinforcement had been scheduled forthe next occurrence of the response (Catania,1963, Experiment 2). Because that responseoccurred rarely in the absence of the signal, itsrate was reduced while its reinforcement wasmaintained. The rate of the first response wasaffected similarly by changes in the other re-sponse's VI schedule in both experiments,even though the rate of the other responsewas reduced to negligible levels in the secondexperiment. Thus, the effect could be attrib-uted directly to reinforcers produced by theother response, rather than to changes in theother response's rate; the reduction was notcaused by some kind of competition betweenthe two responses for available time.

Rachlin and Baum (1969) obtained similarresults when they varied the duration ratherthan the rate of signalled reinforcement for theother response. In later experiments, Rachlinand Baum (1972) examined the effects of differ-ent sources of reinforcement in more detail.In Experiment 1, they added a schedule ofsignalled reinforcement, but moved it fromthe other key to the same key as the first re-sponse. The pigeon now pecked at a singlekey, and its pecking was reinforced accordingto one VI schedule. Occasionally, according toanother VI schedule, the keylight changedcolor and the next peck was reinforced. Thissignalled reinforcement reduced the rate ofresponding on the key in approximately thesame way as had the signalled reinforcementthat was scheduled for pecks on a different keyin the earlier experiments. Rachlin and Baumnext varied both the duration (Experiment 2)and the rate (Experiment 3) of added rein-forcers that were unsignalled and were notproduced by pecks on the key. In one proce-dure, the reinforcers were added, according toan independent VI schedule, for periods dur-ing which a key peck had not occurred for atleast 2 sec (a in Figure 1); in another, the re-inforcers were added according to the inde-pendent VI schedule, but without referenceto key pecks (b in Figure 1). In these pro-cedures, too, the rate of responding on the

518

REINFORCEMENT AS SELF-INHIBITING

80

401

O0C) 160 320 1440E r: TOTAL SEC of RFT/HR, ALL SOURCES

Fig.l. Rate of Key-A pecking as a function of total reinforcement. A 20-rft/hr variable-interval schedule main-tained Key-A pecks; additional reinforcers were provided from other sources. Reinforcement is expressed in sec-

onds of food availability per hour of opportunity for Key-A pecking. Data are means (Catania, 1963) and medians(Rachlin and Baum, 1969, 1972) across data from three or four pigeons in each experiment. A theoretical curve isalso shown. In Experiments 2 and 3 of Rachlin and Baum (1972), added variable-interval reinforcers were sched-uled according to two procedures: in a, reinforcers were delivered after at least 2 sec without a Key-A peck; in b,reinforcers were delivered independently of Key-A pecks. Additional details in text.

key was reduced by the added reinforcers inapproximately the same way as in the earlierexperiments. Rachlin and Baum thus elimi-nated the signalling of the added reinforcersand the difference in the locus of the responses

that produced them, and varied the temporalrelation of the added reinforcers to the re-

sponses on the single key. In each case, re-

sponding decreased as a function of the addedreinforcers, no matter what the source: sched-uled for another response, scheduled for an-

other response and signalled, scheduled for thesame response and signalled, scheduled forperiods of no response, or scheduled indepen-dently of responding. The data strongly sup-

port the conclusion that the source is notcritical; the decrease in one response with

increases in other reinforcers is independentof how these other reinforcers are delivered.But one more case remains to be examined.

What happens when the added reinforcersare added, not from other source, but ratherfor the same response, and unsignalled? Inother words, what happens on a single keywhen we simply increase the rate of reinforce-ment provided by its VI schedule? It is clearwhy this example might be overlooked: weknow that these added reinforcers will producean increase and not a decrease in the rate ofthat response. But perhaps the finding is notproperly interpreted. Maybe the rate of thatresponse does decrease with added reinforcers,but the decrease is overshadowed by the new

responses that are generated by these added re-

ul

z

C,)LUJ

CATANIA (1963) Exp.i: +Exp.2: x

RACHLIN & BAUM(1969):

+\< (1972) Exp.i:a. b.

Zs\ Exp.2: ' o3t\~~~~~~~~Exp.3: *

rA: KEY-A l40 rARFT RA 120+Xr --,-_

l~~~~~ ' / I

*0<

A. CHARLES CATANIA

inforcers. In fact, this is precisely the con-clusion drawn from the example in Table 1:the reduction of Key-A responses by Key-Breinforcers was apparently included in thesummation of the Key-A and Key-B perform-ances.

ANALYSIS OF PERFORMANCE BYTOPOGRAPHICAL TAGGING

Let us elaborate the argument by examingin finer detail a single response maintainedby VI reinforcement. For the sake of the anal-ysis, we will restrict our attention to an arbi-trary sequence of reinforcers arranged by thisschedule. Let us divide a sequence of 10 succes-sive reinforcers into reinforcers 1, 3, 4, 7, and9, which we will call A reinforcers, and rein-forcers 2, 5, 6, 8, and 10, which we will callB reinforcers. We can attribute a certain pro-portion of the total responses to each of thesegroups of reinforcers, and we will call these Aresponses and B responses, respectively. Weare interested in the A responses, those main-tained by the A reinforcers, and the effect onthese responses of the B reinforcers. All ofthe responses, however, occur on the same key;thus, in this single-key case we cannot un-ambiguously identify any particular responseas either an A response or a B response. Butif we move to a two-key procedure, we canseparate the responses by the technique oftopographical tagging (Catania, 1971): we canmove the B reinforcers to another key, andobserve which responses follow the B rein-forcers to the other key and whiclh remain witlhthe A reinforcers at the first key. In thissituation, A responses and B responses can beidentified by their different locations. Thelegitimacy of this technique rests with thefinding, already cited, that the total respond-ing maintained by a given rate of reinforce-ment is constant; it does not vary with the dis-tribution of reinforcers among two or morekeys. The only consequence of moving somereinforcers to another key is to change theirlocation, and the change in location consti-tutes the way in which the responses becometagged so that they can be attributed to aparticular source.When we move the B reinforcers to another

key, we find that half the responses move tothat other key with them. The other half re-main at the original key, where they continue

to be maintained by the A reinforcers. But wenow have, in effect, two concurrent VI sched-ules, and the responding maintained by eachgroup of reinforcers is reduced by the rein-forcers scheduled for the response on the otherkey. The A responding is lower when the Breinforcers are scheduled on the other keythan it would have been if the A reinforcerswere scheduled alone. If this reduction is dem-onstrable in the two-key situation, however,it must have been present in the single-keysituation, when the A and B reinforcers werescheduled on the same key; even in that case,the B reinforcers must have reduced the Aresponding. We did not see the reduction inthe single-key case because B responses weresuperimposed on the reduced A respondingmaintained by the A reinforcers: the added Bresponses masked the decrement in A responsesproduced by the added B reinforcers. In fact,the B responses were similarly reduced by theA reinforcers and, more generally, respondingmaintained by any combination of reinforcerswas reduced by the remaining reinforcers. Re-inforcement is self-inlhibiting: each reinforcergenerates responding, but at the same time italso inhibits responding. The function relatingresponding to reinforcement is the resultant ofthese two opposing effects of reinforcement.These relationships are exhibited in the

illustrative data from a three-key experimentpresented in Table 2. Although the relevantdata already exist in literature previouslycited, the present example is useful becausethe schedules operated in a way that corre-sponds precisely to the design of the precedinghypothetical case. Three separate 20-rft/hrVI schedules operated independently, each de-signed according to the specifications of Cat-ania and Reynolds (1968, Appendix II). Anyschedule could operate alone for a given key,or could operate for that key at the sametime as one or both of the other two VI sched-ules. Thus, each of the VI schedules presum-ably was responsible for different responsesthat could be located at a single key or, as inthe preceding illustration, could be movedfrom one key to another. The procedure didnot incorporate a changeover delay.The experiment was conducted in a stan-

dard pigeon chamber, with three 2-cm (0.75in.) diameter Gerbrands keys mounted 24 cm(9.5 in.) above the floor. The keys, lit white,were 7.5 cm (3 in.) apart, center-to-center,

520

REINFORCEMENT AS SELF-INHIBITING

Table 2

Schedules, and actual and idealized response rates, from four concurrent variable-interval(VI) procedures. Data are based on means over the last five sessions of about two weeks ofdaily sessions on each procedure. Rates for asymmetrical procedures were averaged acrossdifferent permutations of key position (e.g., rates in the last condition are based on averagesacross separate determinations with VI 20-rft/hr assigned to Key 1, Key 2, and Key 3).

VI Schedule in rft/hr Resp/nzin, Pigeon 105 Resp/min, Idealized

Keys: 1 2 3 Total Keys: 1 2 3 Total Keys: 1 2 3 Total

60 - - 60 69 2 4 75 75 0 0 7540 20 - 60 48 23 2 73 50 25 0 7520 20 20 60 24 23 29 76 25 25 25 7520 - - 20 56 7 3 66 65 0 0 65

with the middle key directly above the stan-dard Gerbrands feeder. Each key operated ata minimum force of about 0.14 N. Reinforce-ment consisted of the 4-sec operation of thefeeder, during which the keylights were outand the feeder was illuminated amber. Sessionslasted 1 hr, reinforcement duration excluded.When the three VI schedules all operated

for Key 1, responding occurred predominantlyon that key. When, in the second procedure,one of the schedules was shifted to Key 2,about 25 resp/min moved from Key 1 to Key2. These responses presumably were thoseattributable to the reinforcers that were movedfrom Key 1 to Key 2. In the vocabulary of our

earlier example, we can regard the scheduleshifted to Key 2 and the responses that movedwith it as the B reinforcers and the B re-

sponses; the A reinforcers and the A responsesremained on Key 1. The advantage of thisprocedure, as opposed to shifting from a single60-rft/hr VI schedule to individual 40-rft/hrand 20-rft/hr VI schedules, was that the tem-poral distribution of reinforcers remained ap-proximately the same in the two procedures,whether these reinforcers were produced bypecks on a single key or by pecks on two or

more keys. (For the present purposes, thetime between the scheduling of a reinforcerand its actual delivery is assumed to be neg-

ligible; the difference in temporal distributionbetween the single-key and the two- or three-key cases is necessarily smaller than it would beif different-valued VI schedules were used forthe different conditions.)When, in the third procedure, one of the

two remaining VI schedules was shifted toKey 3, more responding was removed fromKey 1. This time, about 25 resp/min movedfrom Key 1 to Key 3. Throughout these pro-

cedures, the total responding maintained bythe total 60 rft/hr remained roughly constantat about 75 resp/min. (These procedures alsodemonstrate, incidentally, that the rate of agiven response is independent of the way inwhich reinforcers are distributed among otheralternatives; the rate of responding main-tained by 20 rft/hr on Key 2 was about thesame when the remaining 40 rft/hr were sched-uled exclusively for Key 1 as when the re-maining 40 rft/hr were distributed equally toKeys 1 and 3.)We have thus demonstrated how the re-

sponding on Key 1 can be analyzed into itscomponents by topographical tagging. Wecould have proceeded further by adding morekeys to which additional fractions of the re-maining Key-l reinforcers were assigned. Butthe point can be made adequately at the pres-ent level of analysis. We now know that 20rft/hr of the original 60 rft/hr maintainedabout 25 resp/min. When we removed theremaining 40 rft/hr, however, as in the finalprocedure, the rate of responding maintainedby 20 rft/hr more than doubled; the 40 rft/hrscheduled for Keys 2 and 3 had been inhibitingthe responding maintained by 20 rft/hr onKey 1. But we must then conclude that thereduction in responding maintained by these20 rft/hr must have existed when all 60 rft/hrwere scheduled on Key 1 alone. Reinforcersare inhibiting, no matter what their source.

QUANTITATIVE FORMULATIONOF THE EXCITATORY ANDINHIBITORY EFFECTS OF

REINFORCEMENTIt remains to provide a quantitative ex-

pression of these relations. Let us begin by

521

A. CHARLES CA TANIA

assuming that responding on a key (R1 inresp/min) is a joint function of the excitatoryeffects, f, of the reinforcers produced by thatresponse (ri) and the inhibitory effects, g, ofthe total reinforcers (yr) from all sources:

R, = f(r1) g(Ir). (1)

The subscripts on R and r represent the cor-respondence between particular responses andthe reinforcers they produce.

For the excitatory function, the assumptionthat responding is linearly related to rein-forcement is simple and economical:

f(r1) = Kr1. (2)This view, corresponding to the concept ofthe reflex reserve (Skinner, 1938), was dis-carded early in the face of failures to providedirect evidence. Nevertheless, it is consistentwith the plausible view that each reinforceradds an increment to total responding. Laterwe will see that this assumption can be justi-fied by some of its implications.With respect to the inhibitory function,

our conclusion that reinforcers reduce re-sponding regardless of their source suggestsa proportionality that involves :r, the sumof all reinforcers:

g(Y.r) = I E =C+ >' (3)

where C is a constant that depends on the mag-nitude of the inhibitory effect of particular re-inforcers and that can be derived empiricallyfrom data such as those in Figure 1. This ex-pression approaches 1 as total reinforcers ap-proach zero, and zero as total reinforcers in-crease. Since this term will multiply f(rl), itsrange is appropriate: it will neither produceincreases in responding nor generate respond-ing in negative quantities. It represents aninhibitory process that is restricted to themodulation of an excitatory process. Note thatthe summation rather than multiplication off(r1) and g(Ir) is precluded by a dimensionalanalysis (Bridgman, 1931): both R1 and f(r1)are in response-rate units, whereas g(Yr) isdimensionless.

Substituting from Equation 2 and 3 inEquation 1:

R, = Kr, (c +hr) = cKC r* (4)

Setting KC equal to a new constant, k:

R _-- kr1- + Ir

(4A)

This equation is mathematically equivalent toHerrnstein's (1970) formulation, where C cor-responds to Herrnstein's r.. In Herrnstein'saccount, this constant represents unspecifiedreinforcers that are not included above inIr. A comparison of the two accounts is there-fore of interest.

Herrnstein's derivation first assumes that re-inforcement, independent of quantity, gen-erates constant responding: R = k (Herrnstein,1970, Equation 12). But responding is dis-tributed to alternatives in proportion to thedistribution of reinforcers among those alter-natives:

Ri _ ri

(cf. Herrnstein's Equation 10; see also recentcommentaries on the Matching Law: Rachlin,1971; Killeen, 1972). When these equations areapplied to a single-response situation, the roleof unspecified or unidentified reinforcers, ro,is particularly critical. The negatively acceler-ated function relating single-key responding torate of reinforcement is generated because theunspecified reinforcers represent a smaller andsmaller proportion of the total reinforcers asthe rate of reinforcement for the single re-sponse increases. The derivation is schematizedin the left column of Figure 2.

For n sources of reinforcement, Herrnstein'sgeneral account takes the form:

R-_krl - kr1- n 11

I ri rO+ I rii = O i = 1

(5)

This equation (Herrnstein, 1970, Equation 17)includes ro, and is presumably more funda-mental than the equations from which it isderived. In fact, Herrnstein implies that theearlier equations may be more important asheuristic devices in generating Equation 5than as representations of fundamental prop-erties of behavior.The derivation from the present account is

schematized in the right column of Figure 2.As reinforcement of a single response increases,the linear increase in responding is counter-balanced by an inhibitory effect that also in-

522

REINFORCEMENT AS SELF-INHIBITING

HERRNSTEIN (1970)

RA=k

RA

rA

RA r,AER Xr

RA

rAr

R =A+rA

2r

rA

RA

PRESENT ACCOUNT

RA= KrA

rA

R=cR-C+Xr

r (rA constant)

R =.krA

A>rA+C /

/f 1

rAFig. 2. Graphic derivations of the function relating responding on Key A (RA) to the rate of variable-interval

reinforcement for that key (rA) in Herrnstein's (1970) and the present account. The rows show (1) the presumedunderlying function that relates responding to reinforcement, (2) the way a response is affected by the distribu-tion of reinforcers to that and other responses, and (3) how these two relationships combine to produce the func-tion that has been obtained empirically. In Herrnstein's account, constancy of responding (1) combines with theMatching Law (2) via the assumption that unspecified reinforcers (r.) make up a smaller proportion of the totalreinforcement as the rate of Key-A reinforcement increases (3). In the present account, a linear relationship be-tween responding and reinforcement (1) combines with an inhibitory effect of the total reinforcement (2), via theassumption that the inhibitory effect occurs not only when the reinforcers originate from another source but alsowhen they are produced by the response itself (3). Since rA cannot be less than Jr, this condition has been ignoredfor purposes of the graphical presentation of (2) in the present account. ZR-total responses; Jr-total reinforce-ment; K, C, and k-constants.

RA

RA 2

//

-4,

3

523

2

A. CHARLES CA TANIA

creases with reinforcement. (As a corollary,whenever total reinforcement, Jr, is constant,the relation between R1 and r, is linear; thisapplies not only when all reinforcers are re-sponse-produced, in concurrent performanceswith total reinforcement held constant, butalso in situations in which some proportion ofthe total reinforcers originates from a re-sponse-independent source.)Both accounts permit an extension to sched-

ules in wlhich the effect on one response of re-inforcers from anotlher source is attenuated(e.g., multiple schedules: Reynolds, 1961a,1961b; Lander and Irwin, 1968). In Herrn-stein's account, reinforcers from a given source,ri, can be multiplied by an interaction term,m1(O 2 m1 2 1), that proportionately reducesthe effect of these reinforcers in the generalequation:

RI kr1 (6)n

rO + E miri

A similar term is appropriate in the presentaccount, to the extent that inhibitory effectsof reinforcers may diminish as a function ofstimulus control in multiple schedules, tem-poral separation from the response of interest,or other factors related to different sources ofreinforcement:

R= krl (7)11

Note also thiat, in Equation 3, we can rewrite

asrC + C

It follows that, since ro is a constant, it hasthe same status. If k = cro, then:

k cro cri+ro ri+ro ri

rO

In other words, in their formal mathematicalproperties, C and ro are related to ri in thesame way as m (or, strictly, the reciprocal ofm). The only property that distinguishes mfrom these other terms is that mi may have adifferent value for each r1.

EMPIRICAL AND THEORETICALIMPLICATIONS

In all essential respects, Equations 6 and 7are identical; both accounts generate the sameconclusions. How then can we choose betweenthem? Neither the underlying constancy ofreinforced responding in Herrnstein's accountnor the underlying linear relation betweenresponding and reinforcement in the presentaccount (Row 1 in Figure 2) originates fromdirect empirical evidence. On the other hand,both the matching relation of Herrnstein andthe inhibitory effect of the present account(Row 2 of Figure 2) are directly representedby data. On the side of the present account, wemay note that the inhiibitory function (Equa-tion 4) applies comfortably to data for whichthe matching function is inappropriate. Forexample, with signalled reinforcement andother sources of reinforcement that do notprovide substantial increments in measuredresponding, the ratio of one response to totalresponding will not ordinarily match theratio of that response's reinforcement to totalreinforcement. But Herrnstein's account doesnot critically depend on the matching relation;once the more general relation of Equation 6is established, the matching relation merelybecomes a corollary. According to both ac-counts, matching is derivative rather thanfundamental.The relation between C (Equation 4 and

4A) and Herrnstein's r. may provide the basisfor a distinction. The two constants in thepresent account, k and C, each have a simpleempirical interpretation. The first varies withunits of measurement; the second varies withthe magnitude of the inhibitory effect, de-rived from data (e.g., Figure 1). Herrnstein'sro, however, has an additional theoretical in-terpretation: it is regarded as the quantitativeexpression of the effects of unidentified rein-forcers that may operate in any experimentalsetting. As we have just seen, the mathematicalproperties of ro are different from those ofspecified reinforcers, ri. In addition, exceptfor the case of grain spilled from a pigeonfeeder, such reinforcers are likely to differ fromthe reinforcers scheduled for responding. Fewconcurrent-schedule studies of the effects ofone type of reinforcer on the responding main-tained by other types of reinforcers are avail-able (e.g., Catania, Deegan, and Cook, 1966;

524

REINFORCEMENT AS SELF-INHIBITING 525

Hollard and Davison, 1971). In single-responsestudies, varied reinforcers have been shownto maintain higher response rates than con-stant reinforcers (e.g., with rats, an irregularalternation of food-pellet and sucrose rein-forcers maintained higher response rates thanan equal number of either food-pellet rein-forcers or sucrose reinforcers alone: Steinman,1968). Thus, it may be that the present accountholds only when all reinforcers are the same.A given food reinforcer, for example, may re-duce the effectiveness of other food reinforcersof the same type, but may have little or noeffect on water reinforcers. Resolution of thisempirical issue is experimentally difficult, be-cause studies involving two or more types ofreinforcers must examine the independenceof the various reinforcers (e.g., a study of con-current food and water reinforcement mustassess the interactions between food and waterdeprivations). If, however, the present rela-tions hold only when reinforcers are not var-ied, it then becomes difficult to appeal to thepresumably different unspecified reinforcersthat are identified as ro.A further argument, also not yet capable of

resolution, concerns the nature of the under-lying relation between responding and rein-forcement. On the one hand is the assumptionthat reinforced responding is constant, inde-pendent of the quantity of reinforcement. Thisassumption is incompatible with the view thatreinforcement can change the quantity of be-havior as well as the way behavior is distrib-uted among alternatives. The latter view sug-gests some experimental possibilities. There issome evidence that the inhibitory effects ofreinforcement diminish over time (e.g., transi-ent contrast: Catania and Gill, 1964; Nevinand Shettleworth, 1966). Thus, it may be pos-sible to reduce or eliminate inhibitory effectsby allowing only brief and temporally sepa-rated opportunities for reinforced responding.For example, if the function relating respond-ing to reinforcement were examined withinbrief components of a multiple schedule, thenthe function should become more linear withdecreases in the duration of the reinforcementcomponent and increases in the separation ofreinforcement components in time. (Appropri-ate data do not seem to be available in theliterature, but, with respect to such an experi-ment, the finding that response rates in multi-ple schedules vary with component duration

is of special interest: Shimp and Wheatley,1971; Todorov, 1972).

Yet, Equations 6 and 7 remain equivalent.Thus, any data that can be represented interms of one account can be represented interms of the other. Differences in the accountscan have empirical implications only throughdifferent interpretations of the conditions un-der which the equations can be applied. Vari-ous applications and their limits have alreadybeen thoroughly examined by Herrnstein(1970). Perhaps one value of the present al-ternative account is in its suggestion that theeffects of some reinforcers can be separatedfrom the effects of others even when theyoriginate within the same schedule. This kindof analysis, of sub-classes within more broadlydefined classes of responses and reinforcingevents (cf. Schoenfeld, 1950), may provide ameans for reconciling the molar relations ofEquations 6 and 7 with molecular analysesof the relations between particular responsesand particular reinforcers (e.g., Catania, 1971).

In any case, the present inhibitory accountis not new, although it differs in its quantita-tive expression from some earlier formulations(e.g., Hovland, 1936; Hull, 1943). It has theadvantage, common to well-established ex-amples of physiological inhibitory processes(e.g., Ratliff and Hartline, 1959), of specifyingnot only what is inhibited (responding) butalso what is doing the inhibiting (reinforce-ment). As argued elsewhere (Catania, 1969),the disadvantage of the vocabulary of inhibi-tion does not rest with the concept of inhibi-tion, but rather with its application whenthere has been a failure to specify explicitlyboth the inhibited and the inhibiting event.In the present instance, it is clear that rein-forcers, whatever their source, reduce respond-ing: this is precisely and, more important,exclusively the sense in which we speak hereof reinforcement as self-inhibiting.

REFERENCESBridgman, P. W. Dimensional analysis (rev. ed.) New

Haven: Yale, 1931.Catania, A. C. Concurrent performances: reinforce-

ment interaction and response independence. Jour-nal of the Experimental Analysis of Behavior, 1963,6, 253-263.

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526 A. CHARLES CA TANIA

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Received 10 July 1972.(Final Acceptance 14 December 1972.)