Hazeltine et al. - Timing mechanisms Neural mechanisms of ... · Hazeltine et al.- Timing...

Hazeltine et al. - Timing mechanisms

Neural mechanisms of timing

Eliot Hazeltine, Laura L. Helmuth and Richard B. Ivry

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P recise timing is essential in many of our behaviors.

Reaching for an object requires a specific temporal pattern

of activity across the muscles of the shoulder, arm and wrist.

Similarly, predicting events, such as when a traffic light will

change to red, demands an accurate estimate of relevant

durations, such as how long the light has been yellow.

These examples emphasize that temporal information

underlies both sensory and motoric processes; in everyday

activities, temporal intervals must be perceived and pro-

duced correctly.

Component analysis of temporal variability

For both perception and production there is, of course, vari-

ability in temporal accuracy. The components of a move-

ment differ from trial to trial, and on perception tasks, we

make slight misestimations of elapsed time intervals.

However, errors can also emerge from a variety of sources

that do not necessarily involve timing per se but, instead, re-

sult from variability in other task-related processes. Indeed,

movement commands may be initiated at the correct time,

but delays in implementation may occur downstream, lead-

ing to poor performance. An analogous situation exists for

perception. Returning to the example of the traffic light, an

error in predicting the change to red can be caused by mis-

judging the relevant duration or by failing to detect the

light’s transition from green to yellow rapidly enough. Box 1

describes two approaches used to partition variability in

temporal tasks into component sources.

A common mechanism

Are perception and production subserved by the same

clock? Evidence for a common timing mechanism can be

observed in the tendency for movements to become en-

trained automatically with external stimuli. For instance,

when we enter a nightclub, we immediately find ourselves

moving to the beat.

Along this line, Treisman and colleagues examined how

trains of evenly spaced clicks affected time perception’ and

production task.?. In both cases, the influence of the clicks

was shown to be dependent on their frequency; particular

frequencies systematically increased or decreased perceived

or produced intervals. Moreover, frequencies that shortened

estimates of perceived time, presumably by slowing down

the clock, tended to lengthen movement times, and vice

versa. This significant negative correlation between the biases

observed on the perception and production tasks is consist-

ent with the hypothesis of a common timing mechanism.

Ivry and Hazeltine also found similarities between the

performance of time perception and time production using

the slope method (see Box 1). Subjects produced temporal

intervals by tapping and made temporal judgments across a

range ofdurations (325-550 ms). The increase in the variance

as a function of the duration was comparable for the two

tasks. Assuming that this duration-dependent component of

the variance provides an estimate of variability in an internal

timing mechanism, these results implicate a common timing

process in the two tasks. Studies measuring variation among

individuals’ perceptuomotor skills have also supported this

hypothesis. Keele eta/.* observed significant correlations be-

tween performance in a repetitive tapping task and a duration

discrimination task. Furthermore, acuity on the perception

task was not correlated with performance on a non-temporal

motor task (see also Ref. 5), suggesting that the correlation

reflects an overlap in the neural systems subserving these tasks.

Neural substrates

Given the correlational nature of these studies, it is important

to look for converging evidence supporting the common

Copyright 0 1997, Elsevier Science Ltd. All rights reserved. 1364.6613/97/$17.00 PII: 513646613(97)01058-9

Trends in Cognitive Sciences - Vol. 1, No. 5, August 1997


Box 1. Isolating timing variability

Wing and Krisrofferson’ developed a simple model to analyze

variability on a motor timing task. Initially, subjects matched

their movements to a pacing signal (e.g. 2.5 Hz), and then con-

tinued to make periodic movements after the signals termi-

nated. Variability during the unpaced phase was hypothesized

to arise from two sources: an inrernal clock providing an appro-

p&rely rimed trigger for each movement and a motor imple-

mentation system that rranslared this signal into a movcmenr.

Two assumprions arc important for this model. Firstly, the vari-

ability of the clock and motor implemenration systems must be

independent. Secondly, rhe operation of these processes must

OCCUI in an ‘open-loop’ fashion so chat no attempt is made to

correct errors on previous taps. These assumptions mean that

motor implementation variability causes a negative correlation

between the timing of successive inrervals whereas the effects of

clock variability are restricted co a single interval (see Fig. a).

Thus, implemenrarion variability can be identified by the co-

variance between successive intervals. By subrracting this esti-

mate from rhe total variability, an estimate can be made of clock

variability.

The slope method is an alcernarive approach thar is based on a

well-established phenomenon in the time perception literature:

rhar variance increases linearly as a function of the square of rhe

duration being estimated. In other words, time perception ad-

heres to Weber’s la+. Ivry and Hazeltine’applied this logic in

a time production task in which subjects capped over a range of

time intervals (Fig. b). The function relating the variance to the

target durarion was very nearly linear and had a positive y-inrer-

ccpt. Thus, regression analyses were used to separate duration-

dependent and durarion-independent processes, defined by the

slope and inrercepr rcrms, respectively. It was assumed rhar the

duration-dependent variance reflected the operation ofan internal

clock, as other processes, such as signal detection or motor im-

plementation, should remain constam across different durations.

Close agreement is found for estimates of implementation vari-

ability calculated from the slope method or via the Wing and

Kristofferson model (see also Ref. g).

a Wing, A. and Kristoffenon. A. (1973) Response delays and the

timing of discrete motor responses Percept Psychophys. 14, 512

b Allan. L. (1979) The perception of time Percept. Psychophys. 26.

340-354

c Bizo, L.A. and White, K.G. (1997) Timing with controlled reinforce

density: implications for models of timing J. Exp. Psycho/. Anim.

Behav. Proc. 23,44-55

d Getty, D. (1975) Discrimination of short temporal intervals: a

comparison of two models Percept Psychophys. 18, l-8

e Gibbon, 1. (1991) Origins of scalar timing Learn. MO&. 22,3-38

Time c

Central process C C C C C C+D C C

I I I I I I I I I \ \ \ \ \ \ \ \

Peripheral process

Interval

Overt response

I I+D I-D I I I+D I

Tap Tap Tap Tap Tap Tap Tap Tap

Fig. a The Wing and Kristofferson model. Tapping variability is attributed to two processes. The central process issues tap com-

mands about every C ms. The peripheral process requires on average M ms to implement each command. The two processes proceed

independently; delays in one have no effect on the progression of the other. If implementation is delayed by D ms in the motor process

(see left half of figure), the interval whose termination is defined by the tap will be lengthened and the next interval, whose onset is

defined by that tap, will be shortened. In contrast, the influence of clock variability is limited to a single interval (see right half of fig-

ure). Note that in a typical tapping task, the interval C is much longer than the motor delay M.

clock hypothesis. Neuropsychological research provides just

such an alternative method for investigating the neural

bases of internal timing. The cerebellum has been shown to

be critical for a wide variety of timing tasks. Some of the

cardinal symptoms of cerebellar dysfunction (dysmetria and

intentional tremor) have been attributed to a loss in coordi-

nation of the temporal pattern between antagonist mus-

cle&‘. Cerebellar dysarthria is most evident on sounds that

require precise timing between different sets of ardculator?.

Patients with cerebellar lesions also show increased variabil-

ity on a repetitive tapping rask9, and when these data are

analyzed with the Wing and Kristofferson model (see Box I),

a dissociation is observed as a function of the locus of the

pathology . ” Patients with medial cerebellar lesions suffered

from marked peripheral (motor) variability, while those

with lateral cerebellar lesions showed impaired central

(clock) variability.

Importantly, temporal deficits following cerebellar

damage have been reported in the perceptual domain as

well. Ivry and Keele” observed that such lesions not only in-

creased clock variability during tapping, but also impaired

performance on a duration discrimination cask. The pa-

tients’ performance was comparable to control subjects on a

loudness discrimination task, demonstrating that their

deficits were not related to the perception of the stimuli or

to general factors such as motivation. Cerebellar patients


f Ivry, R. and Hazeltine, RX. (1995) Perception and production of

temporal intervals across a range of durations: evidence for a

common timing mechanism J. Exp. Psycho/. Hum. Percept.

Perform. 21,3-18

p Wing, A. (1980) The long and short of timing in response

sequences, in Tutorials in Motor Behavior (Stelmach, G. and

Requin, 1.. eds). pp. 463-486, North-Holland

A 800

s 600 5 8 400 s ‘C 9 200

0

B 800

$- 600 .c.

I I 1 I

325 400 475 550 Duration (m$)

325 400 475 Duration (ms2)

550

Fig. b Evidence for a common mechanism for time perception and production. The variability functions for both the time

production (0) and perception tasks (0) were best described when

the variance was plotted as a function of the duration squared.

Regression lines show the best linear fit. (A) The target interval

was presented once in both the production and perception tasks.

(6) The target interval was presented four times in both tasks. In

both experiments, the slope was comparable for the production

and perception tasks. Moreover, the magnitude of the slope was

affected by the number of intervals produced or presented. This

suggests that duration-dependent variability is reduced when

there are multiple presentations of the target interval.

have also been found to perform poorly on tests of motion

and velocity perception”,‘*, tasks that may rely on a repre-

sentation of precise temporal information. Furthermore, bi-

lateral increases in regional cerebral blood flow (rCBF) were

observed with positron emission tomography (PET) when

subjects judged the duration of tone inrervals’3. While these

imaging results are in accord with the cerebellar timing

hypothesis, the activation can be attributed to a variety of

sources. Indeed, the timing condition was compared with a

control task in which subjects were not required to make

any sensory judgments. Thus attention, motor selection

and other cognitive demands may have contributed to the

activations observed.

Structures within the basal ganglia have also been im-

plicated in timing functions. Jeuptner etaLL3 reported rCBF

increases in the basal ganglia (as well as cerebellar temporal,

prefrontal and cingulate cortex) during their time percep-

tion task. While Ivry and Keele9 failed to find performance

differences between a group of Parkinson’s patients and

controls on the repetitive tapping task, more recent studies

have found that patients with either Huntington’s or

Parkinson’s disease have more variable inter-tap intervals

than control subjects r4,15. Moreover, the performance of the

patients with Parkinson’s disease was improved by L-dopa

medication, and those with asymmetric symptoms produce

more variable time intervals with the more affected limb.

Decomposition of the time interval variability using the

Wing and Kristofferson”j model (see Box 1) attributed the

increased temporal variability to both the central (clock)

and peripheral (motor) sourcesIs.

Cortical structures seem to contribute different, per-

haps more integrative computations in timing tasks than

those attributed to the cerebellum or the basal ganglia. For

example, premotor or supplementary motor cortical lesions

have been associated with deficits in rhythm production”.

Furthermore, laterality effects have been reported on tests of

temporal reproduction: for intervals ranging from 1 to 5 s,

patients with precentral left hemisphere lesions tend to pro-

duce shorter time intervals than control subjects, whereas

patients with precentral right hemisphere lesions tend to

produce longer time intervals’s.

Component analysis of the neural systems for timing: animal models Reports of timing deficits in many different patient groups

have led some researchers to conclude that temporal pro-

cessing is distributed across a variety of cortical and subcor-

tical systems . I5 However, the plurality of participating brain

regions does not necessarily imply functional homogeneity.

Indeed, theoretical models of neural clocks typically have

discrete components each ofwhich is envisioned to perform

a specific operation2,‘9.

Pharmacological and lesion studies with rats have

helped to differentiate the functions of the cortical and sub-

cortical areas implicated in temporal processing. One widely-

used task measures the frequency of an animal’s response

(bar presses) over time. During training trials, reward is pro-

vided for the first response that is made after a set interval

has expired (e.g. 30s). In this paradigm the rats learn to

withhold responding until after the set interval has expired,

despite the fact that the end of an interval is not cued ex-

plicitly. The response rate typically increases when the rats

judge that the interval has expired. Performance is then

evaluated on trials in which no reward is given. Drugs that

target dopaminergic and cholinergic systems produce a shift

in the time at which the response rate peaks. Importantly,

these drugs appear to change temporal processing via differ-

ent mechanisms. The dopamine-related effects are initially

dramatic but diminish with prolonged drug exposure. This

pattern is consistent with the idea that the drug changes

the speed of an internal clock and over time the animal is

able to modify its memory of the reinforcement time. In

contrast, the acetylcholine-related effects develop slowly but


Fig. 1 A three-component clock-counter system. The substantia nigra sends regularly paced signals through the

striatum to the pallidurn. where the internal segment (GPi) acts as an accumulator. Efference from this accumulator

is sent via the thalamus to the frontal cortex, where it is compared with stored representations of task-relevant du-

rations. This model has been proposed to account for data from animal studies using durations of 20 s or longer”.

It is not clear how such a system could time the activations of different muscle groups in multijoint movements,

are more long lasting, suggesting that they affect the ani-

mal’s stored representation of the target interval (reviewed

in Ref. 20).

Meckz” proposed a multi-component model to account

for these findings (Fig. 1). A dopamine-dependent, basal

ganglia system forms the pacemaker-accumulator mecha-

nism, and an acetylcholine-dependent, frontal cortex sys-

tem is associated with temporal memory and attention.

Moreover, within the basal ganglia system, there is evidence

for further specialization. Lesions to the substantia nigra

(SN) prevent rats from learning temporal discriminations

when the time interval is more than 20 s but less than 60 s,

whereas damage to the dorsal striatum disrupts performance

predominantly on the 60 s intervals. To explain this disso-

ciation, Meek hypothesized that the SN provides a time-

keeping pulse which the dorsal striatum integrates for

longer interval discriminations. Output from this integrator

is compared with stored representations of the target inter-

val via the frontal lobes. This model is also consistent with

the timing behavior observed in patients with Parkinson’s

disease, who tend to underestimate time intervalsa’. To

date, the cerebellum has not been considered within the

framework of this model.

One might hypothesize that the cer-

ebellum is critical for short intervals and

other structures, such as the basal ganglia

and cortex, take over for longer intervals.

However, it remains possible that as the

target interval lengthens, additional pro-

cesses involved in memory and atten-

tional functions come into play. It is im-

portant to note that the majority of the

animal timing studies have not included

non-temporal control tasks. For example,

do dopaminergic agents distort perfor-

mance when the task requires discrimi-

nations along a dimension such as stimu-

lus intensity! Studies along this line

would help develop a component analysis of temporal pro-

cessing tasks, and in particular, help identify if a target

neural system is linked specifically to temporal processing.

This strategy has been explored in a recent study with hu-

mansZ6. Cerebellar and frontal patients were tested on du-

ration discrimination tasks and pitch discrimination tasks

in which the interval between the standard and comparison

interval varied between short and long. Cerebellar patients

were impaired on both duration discrimination tasks (inter-

vals centered on 400 ms and 4 s), while frontal patients were

impaired on both tasks, but only when the stimuli were sep-

arated by 4 s. This result suggests that the frontal contribu-

tion on these tasks may not be specific to timing, but may

manifest whenever the working memory or attentional re-

quirements are increased.

Do distinct mechanisms operate at different temporal

intervals?

With some exceptions’5, research examining the role of the basal ganglia in timing has involved time intervals spanning

several seconds or more2K22, while studies focusing on the

cerebellum have used events of less than 1 s (Refs 7,9). Does

this mean that these two systems mediate timing at two dif-

ferent areas along a temporal spectrum? Some animal research

supports this hypothesis. For example, cerebellar lesions in

the rat led to a selective deficit on a duration discrimination

task when the stimulus range was centered at 500 ms, but

did not affect performance when the range was centered at

30 s (Ref. 23). Human studies also sug-

gest a qualitative change in temporal pro-

cessing for intervals longer than 1.5-2 s

(Ref. 24). When attempting to tap in

synchrony with a series of tones, responses

are anticipatory when the inter-tone inter-

val is less than 1800 ms; for longer inter-

vals, the responses tend to be reactive to

the tones25.

A further problem is that investigations into the role of

the cerebellum and basal ganglia in timing have emphasized

different dependent variables. Timing abnormalities follow-

ing cerebellar lesions are manifest as increased variability,

whereas basal ganglia research has focused on changes in

bias. The former effects have been viewed as evidence of a

noisy timing system, the latter as a change in clock speed.

A multi-component timing mechanism can produce

such deficits in a variety of ways. According to the model

presented by Meckzo, the dorsal striatum acts as an accumu-

lator that stores output from other sources. A related idea

builds upon the hypothesis that the basal ganglia are critical

for shifting cognitive set2 ’ 30. Patients with Parkinson’s dis-

ease take longer to switch from one task to another, particu-

larly when both tasks use the same stimuli. In such tasks, the

internal ‘set’ as well as the external stimuli determine the

correct response. If timing long durations, in the absence of

external cues, requires the accumulation of short intervals

and the updating of internal states, then dopamine depletion

may slow this process, leading to timing problems in

parkinsonian patients. The pacemaker providing the short

Trends in Cognitive Sciences - Vol. 1. No. 5, August 1997

Box 2. How a cerebellar timing system might operate

Cerebellar Purkinje cells are the site of a tremendous conver- gence of information; a single Purkinje cell may receive inputs from as many as 200 000 parallel fibers. This architecture is ideal for pattern recognitior@. These cells might learn to recognize the duration-dependent pattern of activity along rhe parallel fibers to signal when expected events should occur. Input to Purkinje cells could code duration in several ways. For example, granule, stellate and basket may interact to operate much like the networks transducing temporal information to spatial information described by Buonomano and colleagues’,d. According to this explanation, relatively slow pre- and post- synaptic mechanisms allow neurons to create local representations of temporal information. For example, Buonomano and Merzenichd have shown how temporal estimates can be derived from a neural network with random variation in the time course of paired pulse facilitation and slow inhibitory posrsynaptic po- tentials. Because of these properties, the network is in a con- tinuously changing state after firing in response to an initial stimulus. Therefore, responses to subsequent stimulation are contingent on the length of the intervening interval. A second hypothesis proposes that the cerebellum may house populations of interval-based timers, each coding a different duration for a particular effector’. Just as in the visual cortex, in which specific neurons code for orientarion in each region of the visual field, units in the cerebella cortex could code for a

specific time inrerval. These units could then be associated with specific muscle groups, or be linked with perceptual infor-


mation. When more than one effector is used, such as when an in- dividual taps with both the left and right index fingers, output from all the units is averaged, resulting in a decrease in variabil- i$. These two accounrs are not mutually exclusive. Such timing mechanisms are unlikely to be adequate for intervals much greater than 1 s. Longer durations may be timed by the striatal system described above, or by the cerebellum in con- cert with orher neural suuctures. For example, the cerebellum might time srate changes in the frontal cortex with the basal ganglia required to effect these state changes. In this model, the cerebellum could provide the timed initiation signal while the frontal strucmres act as an accumulator.

References

a Albur. J.S. (1971) A theory of cerebellar function Math. Biosci. 10,

25-61

b Marr, D.A. (1969) A theory of cerebellar cortex 1. Physiol. 202,

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c Buonomano, D.V. and Mauk, M.D. (1994) Neural network model

of the cerebellum Neural Computat 6,38-55

d 8uonomano, D.V. and Merzenich, M.M. (1995) Temporal

information transformed into a spatial code by a neural network

with realistic properties Science 267, 1028-1030

8 Ivry, R. (1996) The representation of temporal information in

perception and motor control Curr. Opin. Neurobiol. 6, 851-857

f Helmuth, L.L. and Ivry. R.B. (1996) When two hands are better than

one: reduced timing variability during bimanual movements

1. Exp. Psycho/. Hum. Percept Perform. 22, 278-293

intervals could be instantiated by other structures such as

the cerebellum or substantia nigra, but the critical represen-

tation of time would be related to the updating or changing

of behavioral stateP.

How the cerebellum might perform timing

Beginning with Braitenbere33, many theorists have sug-

gested that the cerebellum’s architecture is well-suited for

calculating the precise temporal relationship between differ-

ent inputs and between input and output patterns (see

Box 2). In a recent review, Raymond etaL3* argued that the

cerebellum plays a critical role in timing based on the com-

putational overlap between two behaviors for which the

structure has been shown to be critical, eyeblink condition-

ing (reviewed in Ref. 35) and the vestibular ocular reflex

(VOR). In both cases, motor outputs (e.g. eyeblinks or eye

movements) must be timed precisely to be effective.

Why should the cerebellum, traditionally labeled as a

motor structure, be involved in the perception of time? In

many cases, the distinction between time production and

time perception is unclear. Consider, for example, when

one attempts to grab a moving object, a task widely consid-

.ered to be the purview of the cerebellum. Here, motor com-

mands must be integrated with dynamic sensory infor-

mation to perform the action properly. Timing is relevant

for both predicting the location of the target object and

scheduling the activation of component muscle groups.

A system that learns to solve such complex problems

might analyze correspondences between the two sets of

events rather than independently compute the requisite

temporal information for the sensory and motoric

processes. Strong evidence for the cerebellum’s ability to as-

sociate inputs from different sensory channels comes from

experiments establishing its critical role in eyeblink condi-

tioninti5, a learning task in which there is a need to encode

the precise temporal relationships between the uncondi-

tioned stimulus and the conditioned stimulus36,37. Perhaps

this system has evolved so that it can continue to operate

when there is only one source of input. For example, when

the duration of a short tone must be judged, the cerebellum

may compare its representation of the tone with some

internal standard instead of .a second stimulus or motor

signal.

In motor control theory, it has been proposed that the

cerebellum coordinates and fine-tunes cortical outputs by

performing complex pattern recognition across a wide range

of inputs 38,39. This sort of computation can be used to inter-

pret time-varying representations of sensorimotor patterns

so as to estimate elapsed durations4”,41. In other words, the

cerebellum may train other brain regions to recognize and

anticipate representational states by identifying activations

across sets of neurons that are associated with particular in-

tervals. This hypothesis has some similarity with that pro-

posed by Courschesne and colleagues42,43, who suggest that

the cerebellum coordinates internal operations with antici-

pated sensory information. Discrete motor actions are gen-

erally less than 1 s in duration, and the hypothesized mecha-

nisms for sustaining local neural activity are also thought to

be limited to relatively short durations*‘. Thus, for longer

durations, such a system is unlikely to be sufficient.


Outstanding questions

l Evidence suggests that perception and production share a common timing mechanism. How is such a system implemented?

l How do ensembles of neurons provide accurate temporal information? l What are the temporal ranges of these ensembles? l How do the basal ganglia, cerebellum and frontal lobes interact to

perform temporal computations?

A pattern recognition approach to timing could help

account for some notable phenomena in the timing litera-

ture. Indeed, despite the hypothesis that the cerebellum is

critical for timing, there is a little evidence that it behaves as

a pacemaker or oscillator44. Moreover, the character of cer-

ebellar timing deficits (an increase in variability without a

bias to shorten or lengthen intervals) is in accord with a

non-oscillatory form of computation. In addition, Helmuth

and Ivry4’ compared unimanual and bimanual finger tap-

ping, and observed that the temporal variability of each fin-

ger was reduced during the bimanual condition. When

Wing and Kristofferson analysis was applied to these data,

the advantage was restricted to the clock component of the

variability. The researchers interpreted this advantage as

evidence that independent clocks subserved the two fingers,

and that the clock signals were averaged to determine move-

ment initiation time. In the present framework, the im-

provement would be attributed to a gain in the information

available. The signal from the two fingers would have richer

dynamic properties than the signal from just one finger.

Conclusion

Temporal error takes many forms, which suggests that mul-

tiple operations are required to compute time. The results

of human and animal studies suggest that different neural

systems are essential for performance in timing tasks. The

question that remains is how do we characterize the func-

tions of these different systems? While it is possible that the

representation of temporal information is distributed across

multiple systems, a more parsimonious view is that each sys-

tem makes a distinct contribution. Therefore, the use of a

range of tasks and temporal intervals is essential for a com-

plete understanding of the relations between these neural

systems in both temporal and non-temporal processes.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Semantic networks: visualizations of knowledge

Roger T. Hartley and John A. Barnden

n conferences and in the literature,

complexity theory in computer science. Many ex

written, and yet it is our belief that none of them

b& between their use as a formal scheme for knowledge

use as an informal tool for thinking. In our

. i.._ . ( ^

T he history of the development of semantic networks is

well known (for an introduction to semantic networks, see

Box 1). Both Sowa’ and Lehmann’ have expounded in ex-

cellent scholarly fashion as to their origins in the study of

language. Their later development as a tool for representing

knowledge is also well knowr?, as is their role in building

computerized inference systemPO. Indeed, the triad of in-

telligent thought, logic and language will never be far from

our discussion. From all these sources we learn that seman-

tic networks have three main attributes:

(1) They originate in the conceptual analysis of language.

(2) They can have an expressiveness equivalent to first-

order logic, at least (although many do not).

(3) They can support inference through an interpreter

that manipulates internal representations.

Many people would go further and say that semantic net-

works are indistinguishable from formal logic representa-

tions”. However, there is something missing here. The visual

aspect of the semantic network idea is clearly important. As

Sowa says: ‘network notations are easy for people to read”

and this pragmatic aspect ofthe formalism cannot be ignored.

According to Sowa: ‘graphs...can keep all the information

about an entity at a single node and show related information

by arcs connected directly to that node”. In contrast, in

symbolic logic notations: ‘the scattering of information not

only destroys the readability of the formula, but also obscures

the semantic structure of the sentence from which the formula

was derived. So the battle is joined! The visual aspects of the

semantic network notation are preferred (at least by Sowa)

over the arcane, but more traditional notation of symbolic

logic. Interestingly, this traditional notion was invented by

C.S. Peirce before he abandoned it in favor of a diagram-

matic form’a.

In this paper, we hope to show that this argument is only

one component of a larger, more complex one involving the

nature of semantics; we will also show how different notations

can lead to different systems with different pragmatic uses.

Meaning

The design and use of a knowledge representation revolves

around the business of meaning. Actually, one spin-off from

studies in natural language provides a good start, namely,

the meaning triangle of Ogden and Richards”. The triangle

relates objects in the real world, concepts that correspond to

Copyright 0 1997, Elsevier Science Ltd. All rights reserved. 1364-6613/97/$17.00 PII: 51364-6613(97)01057-7

Trends in Cognitive Sciences - Vol. 1. No. 5, August 1997

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