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 조성식

2. 13-1 Contents 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

3. 13-2 Introduction • 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. 13-3 Inference and Mental Models • 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. 13-4 Inference and Mental Models • 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. 13-5 Meaning and Mental Models Luke B A Matt. Mark • 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

7. 13-6 Images, Propositions, and Mental Models • 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 -> object, “ That dog looks like my dog” -> 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. 13-7 Images, Propositions, and Mental Models • 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 => controversy is neither fundamental nor resolvable.

9. 13-8 Images, Propositions, and Mental Models • Anderson’s 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 => There is no guarantee that a direct method can always be found for two theories. ( indeterminate state -> a single P.R. , many different M.M. ) => 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. 13-9 Images, Propositions, and Mental Models • 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(α,β) , (αKβ) , or (α,β)K • The propositional description of a complicated state of affairs may consist of a large number of propositions. => In a semantic network, propositions about the same entity are gathered together.

11. 13-10 Images, Propositions, and Mental Models • 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?

12. 13-11 Level of Description • 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 -> 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.

13. 13-12 Experiments on M.M. & P. R. 69% correct 42% correct 60% correct • 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 > 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

14. 13-13 Conclusions 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.