Selected publications - Graeme
Halford
Research
reports
Halford, G.S., Andrews, G., Dalton,
C., Boag, C,
Zielinski, T. (2002) Young childrens performance on the
balance scale: The
influence of relational complexity. Journal of
Experimental Child Psychology, 81, 417-445.
Birney, D.P. & Halford, G.S.
(2002) Cognitive
complexity of suppositional reasoning: An application of
the relational
complexity metric to the knight-knave task. Thinking and
reasoning,
8(2),
109-134.
Halford, G.S., Andrews, G., &
Jensen, I. (2002)
Integration of category induction and hierarchical
classification: One paradigm
at two levels of complexity, Journal of
Cognition and Development, 3(2), 143-177.
Andrews, G. & Halford, G.S. (2002)
A cognitive
complexity metric applied to cognitive development.
Cognitive Psychology, 45, 153-219.
Chalmers, K.A. &
Halford,
G.S.
(2003) Young childrens understanding of oddity: Reducing
complexity by
simple oddity and most differentstrategies. Cognitive
Development, 18(1),
1-23.
Andrews, G., Halford. G.S., Bunch,
K.M, Bowden, D
Jones, T. (2003) Concept of mind and relational complexity.
Child
Development, 74(5), 1476-1499.
Andrews,
G.
&
Halford, G.S. (in press) A complexity metric applied to cognitive
development. Cognitive
Psychology,
Abstract
Two experiments tested
predictions
from a theory in which
processing load depends on relational complexity
(RC), the number of variables
related in a single decision. Tasks from 6
domains (transitivity, hierarchical
classification, class inclusion,
cardinality, relative-clause sentence
comprehension, hypothesis testing)
were administered to children aged 3 to 8
years. Complexity analyses
indicated the domains entailed ternary relations (3
variables). Simpler
binary-relation (2 variables) items were included for each
domain. Thus RC
was manipulated with other factors tightly controlled. Results
indicated
that (i) ternary-relation items were more difficult than
comparable
binary-relation items (ii) the RC manipulation was sensitive to
age-related
changes (iii) ternary relations were processed at a median age
of 5 years (iv)
cross-task correlations were positive, tasks loaded on a
single factor (RC) (v)
RC factor scores accounted for 80% (88%) of
age-related variance in fluid
intelligence (vi) binary- and
ternary-relation items formed separate complexity
classes and (vii) the RC
approach to defining cognitive complexity is
applicable to different
content domains.
Halford, G.S., Andrews, G.,
Dalton,
C., Boag, C,
Zielinski, T. (in press) Young children's performance on the
balance scale: The
influence of relational complexity. Journal of
Experimental Child Psychology,
Abstract
Three experiments investigated
the
effect of complexity on children's understanding of a beam balance.
In
non-conflict problems, weights or distances varied while the other was
held
constant. In conflict items, both weight and distance varied, and
items were of
three kinds: weight dominant, distance dominant, or balance,
in which neither
was dominant. In Experiment 1, 2-year-old children
succeeded on non-conflict
weight and distance problems. This result was
replicated in Experiment 2, but
performance on conflict items did not
exceed chance. In Experiment 3, 3- to
4-year-olds succeeded on all except
conflict balance problems, while 5- to
6-year-olds succeeded on all
problem types. The results were interpreted in
terms of relational
complexity theory. Children aged 2- to 4-years succeeded on
problems that
entailed binary relations, but 5- to 6-year olds also succeeded
on
problems that entailed ternary relations. Ternary relations tasks from
other
domains - transitivity and class inclusion - accounted for 93
percent of the
age-related variance in balance scale
scores.
Halford,
G.S.,
Andrews, G., & Jensen, I. (in press) Integration of category
induction and
hierarchical classification: One paradigm at two levels of
complexity, Journal
of Cognition and Development,
Abstract
Hierarchical
classification and category induction were tested by a
common property
inference procedure to facilitate comparison, and to enable
relative
complexities to be assessed. Relational complexity theory predicts
that
hierarchical classification is more complex because it entails a
ternary
relation between categories, B, A and A' such that A and A' are
included in B,
whereas category induction entails a simpler binary
relation between a category
and its complement. Experiment 1 tested
inferences about familiar categories
with plausible but unfamiliar
attributes, while Experiment 2 assessed
inferences about fictitious
categories with familiar attributes. As predicted,
hierarchical
classification was more difficult than category induction.
Children over 5
years succeeded on both, but 3-year olds succeeded on category
induction
only. Tasks of the same level of complexity predicted 68% (Experiment
1)
and 80% (Experiment 2) of age-related variance. The results suggest
that
hierarchical classification and category induction may be regarded as
one
paradigm with two levels of structural complexity.
Birney,
D.P. &
Halford, G.S. (in press)
Cognitive complexity of suppositional reasoning: An
application of the
relational complexity metric to the knight-knave task. Thinking
and
reasoning,
Halford, G.S., Phillips, S.
&
Wilson, W.H. (in
press) Processing capacity limits are not explained by
storage limits. Comment
on paper by Nelson Cowan, Behavioral Brain
Sciences,
24(1),
Wilson, W. H., Marcus, N. and
Halford,
G. S. (2001)
Access to relational knowledge: a comparison of two models,
pp. 1142-1147 in Johanna
D. Moore and Keith Stenning (eds) Proceedings of
the 23rd Annual Conference of
the Cognitive Science Society, Edinburgh,
Scotland, 1-4 August. Mahwah,
NJ:
Lawrence Erlbaum Associates,
ISBN 0-8058-4152-0, ISSN
1047-1316
Andrews,
G.,
&
Halford, G. S. (1999). Complexity effects are found in all
relative-clause
sentence forms.
Behavioral and
Brain Sciences,
22(1),
95.
Halford, G.S., Wilson, W.H.
&
Phillips, W. (1998)
Processing capacity defined by relational complexity:
Implications for
comparative, developmental and cognitive psychology.
Behavioral Brain
Sciences, 21(6), 803-831.
Abstract
It is argued that working
memory
limitations are best defined in terms of the complexity of
relations that can
be processed in parallel. Relational complexity is
related to processing loads
in problem solving, and discriminates between
higher animal species, as well as
between children of different ages.
Complexity is defined by the number of
dimensions, or sources of
variation, that are related. A unary relation has one
argument and one
source of variation, because its argument can be instantiated
in only one
way at a time. A binary relation has two arguments, and two sources
of
variation, because two argument instantiations are possible at
once.
Similarly, a ternary relation is three dimensional, a quaternary
relation is
four dimensional, and so on. Dimensionality is related to
number of chunks,
because both attributes on dimensions and chunks are
independent units of
information of arbitrary size. Empirical studies of
working memory limitations
indicate a soft limit which corresponds to
processing one quaternary relation
in parallel. More complex concepts are
processed by segmentation or conceptual
chunking. Segmentation entails
breaking tasks into components which do not
exceed processing capacity,
and which are processed serially. Conceptual
chunking entails
"collapsing" representations to reduce their
dimensionality and
consequently their processing load, but at the cost of
making some
relational information inaccessible. Parallel distributed
processing
implementations of relational representations show that relations
with
more arguments entail a higher computational cost, which corresponds
to
empirical observations of higher processing loads in humans. Empirical
evidence
is presented that relational complexity discriminates between
higher species,
is related to processing load in reasoning and in sentence
comprehension, and
that the complexity of relations processed by children
increases with age.
Implications are considered for neural net models, and
for theories of
cognition and cognitive development.
Halford, G.S., Wilson, W.H.
&
Phillips, W. (1998)
Relational complexity metric is effective when
assessments are based on actual
cognitive processes. Reply to commentary
on target article entitled Processing
capacity defined by relational
complexity: Implications for comparative,
developmental and cognitive
psychology.
Behavioral
Brain Sciences,
21(6),
803-864.
Halford, G.S., Bain, J.D. &
Maybery, M.T. &
Andrews, G. (1998). Induction of Relational schemas:
Common processes in
reasoning and complex learning. Cognitive
Psychology,
35, 201-245.
Andrews, G & Halford, GS.
(1998)
Children's
ability to make transitive inferences: The importance of
premise integration and
structural complexity. Cognitive Development,
13(4), 479-513.
Halford, G.S., Wilson, W.H.
&
McDonald, M. (1995)
Complexity of structure mapping in human analogical
reasoning: a PDP model. pp.
597-601.
In J.D. Moore and J.F.
Lehman (Eds). Proceedings of
the Annual Conference of the Cognitive
Science Society, Pittsburgh, Pennsylvania, July 22-25, 1995. Malwah,
New
Jersey: Erlbaum.
Phillips,
S., Halford, G.S. & Wilson, W.H. (1995). The
processing of associations
versus the processing of relations and symbols:
A systematic comparison. In
J.D. Moore and J.F. Lehman (Eds). Proceedings
of the Annual
Conference of the Cognitive Science Society, Pittsburgh,
Pennsylvania,
July
22-25.
Halford, G.S., Maybery M.T.,
O'Hare,
A.W. & Grant,
P. (1994) The Development of
Memory and Processing Capacity. Child
Development,
65(5),
1338-1356.
Halford, G.S. (1992) Analogical
reasoning and
conceptual complexity in cognitive development. Human
Development,
35, (4),
193-217.
Halford, G.S. & Sheehan,
P.W.
(1991) Human Response
to Environmental Changes. International Journal
of Psychology,
26(5),
599-611.
Halford, G.S. (1990) Is
Children's
Reasoning Logical
or Analogical? Further comments on Piagetian Cognitive
Developmental
Psychology. Human Development, 33, 356-361.
Halford, G.S. (1989).
Reflections on
25 years of
Piagetian cognitive developmental psychology, 1963-1988.
Human Development,
32,
325-357.
Halford, G.S., Maybery, M.T.
&
Bain, J.D. (1988)
Set-size effects in primary memory:
An age-related capacity
limitation? Memory and Cognition, 16, 480-487.
Halford, G. S., Maybery, M. T.,
&
Bain, J. D.
(l986) Capacity limitations in children's reasoning: A dual
task approach. Child
Development,
57,
616-627.
Halford, G.S. (1984) Can young
children integrate
premises in transitivity and serial order tasks? Cognitive
Psychology,
16,
65-93.
Halford, G.S.,
& Wilson,
W.H. (1980) A Category Theory
Approach to Cognitive Development. Cognitive
Psychology, 12, 356-411.
Halford, G.S.
(1970) A theory of
the acquisition of conservation.
Psychological Review, 77, 302-316.
Simon, T. & Halford, G.S.
(Eds)
(1995) Developing
Cognitive Competence: New Approaches to Process
Modelling.
Hillsdale,
N.J.: Erlbaum. ISBN
0-8058-1289-X and
0-8058-1998-3.
English, L.D. & Halford,
G.S.
(1995). Mathematics
Education: Models and Processes.
Erlbaum.
This will
be part of a series entitled Studies
in Mathematical Thinking and Learning,
Edited by AlanSchoenfeld.
Hillsdale, N.J.: Erlbaum. ISBN
0-8058-1457-4 0-8058-1458-2. Reprinted.
Halford, G.S. (1993) Children's
understanding: The
development of Mental Models.
Hillsdale, N.J.: Erlbaum. ISBN 0-89859-970-9
and 0-8058-1233-4, pp. 521 +
xiii.
Reviewed in Contemporary
Psychology, 1995, 40(8), 797-799, and
Merrill-Palmer Quarterly, 1995, 41(3),
402-407.
Halford, G.S.
The development of
thought.
Hillsdale, N.J.: Erlbaum,
1982.
Halford, G S (In press)
Information
Processing Models
of Cognitive Development. In U. Goswami (Ed.)
Blackwell Handook of Childhood
Cognitive Development.
Oxford, UK. Blackwell.
Hartel,
C.,
Neal,
A., Halford, G.S. Hartel, G. (in press) Cognitive determinants of
expert
decision making in Air Traffic Control. In A.R. Lowe & B.J.
Hayward (Eds.),
Aviation Resource Management, Volume 2. Aldershot, UK: Ashgate.
.
Halford, G.S., Wilson, W.H.
&
Phillips, S. (1998)
Relational processing in higher cognition:
Implications for analogy, capacity
and cognitive development. In K.
Holyoak, D. Gentner, & B. Kokinov, (Eds.) Advances
in analogy
research: Integration of Theory and Data from the
Cognitive,
Computational, and Neural Sciences, pp. 57-73. Sofia, Bulgaria,
New Bulgarian
University. NBU Series in
Cognitive Science. ISBN: 954-535-200-0.
Halford, G.S. (1997) Capacity
Limitations in
Processing Relations: Implications and Causes.
Proceedings of ILAS 3rd Brain
and Mind International Symposium on
Concept Formation, Thinking and Their
Development,
International
Institute for Advanced
Studies, Kyoto, Japan, May 30-June1, 1996.
Graeme S. Halford, Susan B.
Smith, J.
Campbell
Dickson, Murray T. Maybery,
Mavis
E. Kelly, John D. Bain, and J.E.M. Stewart. (1995) Modelling
the development of
reasoning strategies: The roles of analogy, knowledge,
and capacity. Ch 3 in
Tony Simon and Graeme Halford Eds. Developing
Cognitive Competence: New
Approaches to Process Modelling. pp. 77-156. Hillsdale, N.J.:
Erlbaum, 77-156.
Halford, G.S., Wilson, W.H.,
Guo, J.,
Gayler, R.
W., Wiles, J. and
J.E.M. Stewart
(1994).
Connectionist implications
for processing capacity limitations in
analogies. Chapter 7 in K. J.
Holyoak & J. Barnden (Eds.), Advances
in Connnectionist and Neural
Computation Theory,
Vol. 2: Analogical Connections, pp. 363-415.
Norwood, NJ:
Ablex
Wiles, J., Halford, G.S.,
Stewart,
J.E.M., Humphreys,
M.S., Bain, J.D., & Wilson, W.H. (1994) Tensor
models: A creative basis for
memory retrieval and analogical reasoning. In
T. Dartnall (Ed).
Artificial Intelligence and
Creativity.
Dordrecht:
Kluwer Academic, pp.
145-159.
Halford,
G.S. (1990) Human decision-making about Environmental
Change. Ch 5 in H.
Brookfield and L. Doube (Eds.) Global Change: The
Human Dimension. Canberra, Australia: Academy
of the Social Sciences in
Australia. pp. 35-42.
Boag,
C. C., Hartel, C. E. J., & Halford, G. S. (in press). An
integrated model
of situation awareness and decision making in air traffic
control to explain
performance errors. Paper presented at the European
Association for Aviation
Psychology Conference, Crieff,
Scotland.
Halford, G.S.
& Andrews, G (2000) Human capacity limits:
Theoretical basis and
methods of estimation. Paper in invited symposium
convened by G Halford,
titled Processing capacity limits can be defined by
relational complexity
at the International Congress of Psychology, Stockholm,
July
23-28.
Halford,
G. S. (2000)
Analysis of Complexity in Cognitive Tasks. Keynote address
given to 35th
Annual Conference of the Australian Psychological
Society, Canberra, October
3-7.
Boag, C. C., Neal, A., Halford,
G. S.,
& Goodwin,
G. P. (2000). Comparing measures of cognitive complexity:
Cognitive psychology
applied to air traffic control. Poster presented at
the XVI British
Psychological Society Cognitive Science Section
Conference. The University of
Essex, Essex,
England.
HŠrtel, C.
E. J., Neal, A. F. Halford, G.
S., HŠrtel, G. F. (1998) A New Approach to
Mental Workload Measurement in Air
Traffic Control Based on Advances in
Information Processing and Decision Making
Training Research. Proceedings
of the fourth Australian Aviation Psychology
Conference, Sydney, March
16-20.
Halford,
G.S., Andrews, G. & Jensen,
I. (1998). Category induction and
hierarchical classification assessed by
property inference: The influence
of complexity. Paper presented at Xvth
Biennial Conference of the
International Society for the Study of Behavioral
Development, Berne,
Switzerland, July 1-4. ERIC document Accession number ED
421
674.
Andrews, G.,
Halford, G.S. & Prasad,
A. (1998). Processing Load and ChildrenÕs
Comprehension of Relative Clause
Sentences. Paper presented at Xvth
Biennial Conference of the International
Society for the Study of
Behavioral Development, Berne, Switzerland, July 1-4.
ERIC document
Accession number ED 420 091.
Halford,
G.S., Andrews, G. & Bowden,
D. (1998). Complexity as a Factor in
ChildrenÕs Theory of Mind. Paper presented
at Xvth Biennial Conference of
the International Society for the Study of
Behavioral Development, Berne,
Switzerland, July 1-4. ERIC document Accession
number ED 421
673.