Mental Models in Cognitive Science

1
Mental Models in Cognitive Science

• P. N. Johnson-Laird
• Univ. of Sussex
• Cognitive Science 4, pp.71-115., 1980
• ???

2
Contents
13-1

• Introduction
• Inference and Mental Models
• Meaning and Mental Models
• Images, Propositions, and Mental Models
• Levels of Desciption
• Experiments on Mental Models and Propositional
  Representations
• Conclusions

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Introduction
13-2

• Cognitive science needs theories that both cohere
  and correspond to the facts.
• Three questions
• The mental processes that underlie ordinary
  reasoning and the question of what rules of
  inference they embody
• the representation of the meanings of words and
  the question of whether they depend on a
  decompositional dictionary or a set of meaning
  postulates
• the form of mental representations and the
  questions of whether images differ from sets of
  propositions
• ? Their answers all implicate the notion of a
  mental model

4
Inference and Mental Models
13-3

• Syllogism Aristotle
• All A are B, All B are C, then All A are C
• Figure effect
• Atmosphere effect
• negative ? negative or affirmative, particular
  ? particular or universial
• Three theories in the last few years
• Ericson Euler circles
• All A are B ? All B are A ,
• Some A are not B ? Some B are not A
• a1 ? B b1 ? A
• a2 ? B b2 ? -A

5
Inference and Mental Models
13-4

• Criteria for evaluating theories of syllogistic
  inference
• account for the systematic mistakes and many
  valid inferences
• should be readily extendable
• provide an account of how children acquire the
  ability to make inferences
• should be at least compatible with the
  development of formal logic
• ? three theories fare pooly on these criteria ? a
  different approach needed
• Syllogistic inference as the manipulation of
  mental models
• An evaluation of the mental model theory of
  inference
• it provides an account of both the figural effect
  and the systematic errors
• can be generated so as to represent all sorts of
  quantified assertions
• illuminates the way in which children learn to
  make inferences
• entirely compatible with the development of
  formal logic

6
Meaning and Mental Models
13-5

• Meaning postulate
• stipulates the semantic relations between words
• the notion that lexical items (words) can be
  defined in terms of relations with other lexical
  items
• Propositional representation
• we store concepts in a non-language form of
  propositions.
• we can bring the concept into our working memory
  to put it into language.
• Two problems for meaning postulates
• Procedures for manipulating mental models
• FUNCT(0, 1)
• DX, DY

Luke
B A
Mark
Matt.
7
Images, Propositions, and Mental Models
13-6

• Propositional representations
• People store concepts in a non-language form of
  proposition.
• A proposition is a complete statement. It can be
  true or false.
• a dog -gt object, That dog looks like my dog -gt
  proposition
• The boy was having a birthday party, and the
  girl had no present to give him.
• P1 ( HAVE boy birthday party )
• P2 ( POSESS girl present )
• P3 ( NEGATIVE P2)
• P4 ( GIVE girl present boy)
• Image
• A mental image is an experience that resembles
  the experience of perceiving some object, event,
  or scene when the relevant object, event, or
  scene is not actually present to the senses.
• Owing to the fundamentally subjective nature of
  the phenomenon, there is little evidence either
  for or against this view.

8
Images, Propositions, and Mental Models
13-7

• Images versus Propositional representations
• An image is distinct from a mere representation
  of propositions
• Mental processes for images are similar to the
  perception of an object or a picture
• a coherent and integrated representation
• amenable to mental transformations
• Represent objects
• An image is epiphenomenal and propositional in
  form
• Mental processes for P.R. are similar to the
  perception of an object or a picture
• When propositions are represented in the form of
  a semantic network, then the representation is
  coherent and integrated.
• A P.R. is discrete and digital rather than
  continuous, but can represent continuous.
• Propositons are true or false of objects.
• The critics of imagery
• An image does not introduce any new
  information, it merely makes the stored
  desciption more accesible and easier to
  manipulate.
• Image and P.R. differ on the function served by
  representation ( 4th characteristics)
• but share many properties
• They are similar and transformed into one another
• gt controversy is neither fundamental nor
  resolvable.

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Images, Propositions, and Mental Models
13-8

• Andersons theorem on Mimicry
• A propositional theory can mimic an imagery
  theory.
• Imaginal theory A stimulus is encoded as an
  image.
• Propositional theory A stimulus is encoded
  as a set of proposition.
• propositions ? propositional encoding
  inversely ? original stimulus ? imaginal encoding
  ? image ? rotate image ? rotated image ? imaginal
  encoding inversely
• ? (rotated) stimulus ? propositional encoding
  ? the set of propositions(rotated)
• the set of propositions(rotated) ?
  propositional encoding inversely ? rotated image
• (rotated) stimulus ? imaginal encoding ?
  rotated image
• gt There is no guarantee that a direct method can
  always be found for two theories.
• ( indeterminate state -gt a single P.R. ,
  many different M.M. )
• gt A theory of P.R. does not yield the same
  equivalence class of representations as the
  class yielded by the theory of mental models.
  There is difference between them.

10
Images, Propositions, and Mental Models
13-9

• The characteristics of propositional
  representations
• A proposition can be treated as a function from
  the set of possible worlds onto the set of truth
  values.
• Grasping a proposition is analogous to compling a
  function, whereas verifying a proposition is
  analogous to evaluating a function.
• Arbitrary syntactic structure K(a,ß) , (aKß) ,
  or (a,ß)K
• The propositional description of a complicated
  state of affairs may consist of a large number of
  propositions.
• gt In a semantic network, propositions about
  the same entity are gathered together.

11
Images, Propositions, and Mental Models
13-10

• The charateristics of mental models
• Propositional representation is a desciption.
  (true or false w.r.t. the world)
• Human being do not apprehend the world directly
  but possess internal representations of it.
• P. R. is true or false with respect to a mental
  model of the world.
• ( This functional difference could be only
  distinction between P.R. and M.M.)
• A model represents a state of affairs in the
  world. Its structure is not arbitrary.
• A single P.R. will suffice, but many alternative
  models will be needed for the discourse.
• Images correspond to the components of models
  that are directly perceptible in the equivalent
  real-world objects.
• Model may underlie thought processes without
  necessarily emerging into concious-ness in the
  form of images.
• Images and models are not necessarily equivalent
  to sets of propositions?

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Level of Description
13-11

• The reconstruction of a theory at a lower level
  of description
• - A psychological description should be a
  functional one.
• - Whole of the original theory of spatial
  inference can be reconstructed in way of program
  formulae. ( A is on the right of B -gt AT(A,1,6),
  AT(B,1,2) )
• Any psychological theory can be based (vacuously)
  on propositional representations
• - Any plausible theory of any psychological
  phenomenon is propositional.
• How to give the notion of a Propositional
  representations an emperical content
• - A propositional representation is based on
  symbols that correspond in a one-to-
• one fashion with the lexical items of
  natuaral language.
• - The same advantage in programming language
  is obtained from high level
• procedures for manipulating both models
  and propositional representations.

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Experiments on M.M. P. R.
13-12

• Hypothesis
• There appear to be different levels of
  representation (differ in kind)
• superficial understanding propositional
  representation
• profound understanding mental model
• Experiments
• continuous vs discontinuous continuous were
  better recalled
• Determinate vs indeterminate
• determinate premises were better recalled
• If subject remembers the original meaning, they
  can remember it verbatim.
• Assumtional results
• Mental models are constructed from propositional
  representations.
• Amount of processing mental model gt P.R.
• P.R. not easy to recall, but if recalled, it
  can be recalled verbatim
• M.M. easy to recall, but no guarantee to be
  recalled verbatim

69 correct 42 correct
60 correct
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Conclusions
13-13

• First, there are indeed distictions to be drawn
  between P.R. and M.M..
• Second, there are likewise distinctions to be
  drawn between a decompositional semantics and a
  set of meaning postultes.
• Third, it is possible to account for the
  psychological principles underlying deductive
  reasoning.