This is Lecture Six


Mental Models as Basis of Meaning and Representation

description from the Syllabus
metaphor in cognitive linguistics; developmental psychology and origin of concepts in action;
mental models as material complexes; mental objects experienced as pictures and animations
derivation of linguistic meaning from models; abstract entities and mathematics as material models

Part of this we have done already so I don't repeat it.
In this lecture I proceed from the action-based perspective obtained so far to the characterization of
    mental structure that can support the episodic and narrative structure of cognition.

A more detailed train of thought is this.
The (evol.) purpose of the mind is motor control, the rest is secondary use.
To achieve the purpose, there is a need for compex sensorimotor integration.
The unit here is not instananeous action (and perception) but an episode - with actors, objects, purpose
    (embodied action is usually understood in this broad sense but not structured, cf food search, exploration, mating etc)
The notion of episode and mechanism puts structuring on embodied action.
We as humans (animals) can reason about epizodes and mechanisms.


1. Mental Models and the Mind
Here is the beggining of the current lecture -
The comprehensive representation of an episode is by means of a mental model.
As causality has a distinguished role in active embodiment, mental models (must) refer to causal actors.
    The mental model of an episode is a mechanism (orinternal narrative - acts of agents) generated from
        the mental model of the causal actors.
    animated not animistic     - intentional agents "simulated"
    cf simulation thery A. Goldman (visited JAIST recently)
mental models are organized around a few fundamental schemes
    a connection to metaphors as the basis of basic pool of mental models.

a "mental representation" is an animated story based not on "raw input: but on the ective control of a situation (episode)
not the external narrative is "stored" but the actors and the constraints of the mechanism which generates the narrative
in other words, the representation of an episode or narrative is itself active, or functionally constructed
        (as if an internal "play" button existed)

[function of dream - rehearsal of replay --> HTM]
[how dream happens - the same actors arrive again - not a movie of the subjective self, but a puppet show of
    mental models, always a live show, not canned]


2. The Mental Model Theory of Thinking and Reasoning
(After W. Sellars, P.N. Johnson-Laird et al)
Here I use introductory material from http://www.tcd.ie/Psychology/Ruth_Byrne/mental_models/index.html
    where a detailed bibliography etc can also be found.

Mental functions are based on theoretical entitites called mental models .
Mental models are representations in the mind of real or imaginary situations.
Scientists sometimes use the term "mental model" as a synonym for "mental representation", but it has a narrower referent in the case
    of the theory of thinking and reasoning.



 Kenneth Craik
(1914 - 1945)

"The idea that people rely on mental models can be traced back to Kenneth Craik’s suggestion in 1943 that the mind constructs "small-scale models" of reality that it uses to anticipate events. Mental models can be constructed from perception, imagination, or the comprehension of discourse. They underlie visual images, but they can also be abstract, representing situations that cannot be visualised. Each mental model represents a possibility. Mental models are akin to architects' models or to physicists' diagrams in that their structure is analogous to the structure of the situation that they represent, unlike, say, the structure of logical forms used in formal rule theories. In this respect they are a little like pictures in the "picture" theory of language described by Ludwig Wittgenstein in 1922."

The mental model theory has been extensively tested and the experiments have corroborated several tell-tale signs of the use of mental models:

"A mental model represents one possibility, capturing what is common to all the different ways in which the possibility may occur."
                                                                                                                         [ ----> "case-based"]
Mental models represent explicitly what is true, but not what is false. "                 [ ---> remember of mechanisms!!!!]
"These characteristics lead naive reasoners into systematic errors."

"The greater the number of models that a task elicits, and the greater the complexity of individual models, the poorer performance is.
Reasoners focus on a subset of the possible models of multiple-model problems - often just a single model - and are led to
erroneous conclusions and irrational decisions."

[a comment on "irrational" - maybe (1) illogical (2) inconsequential, but not (3) "against the rules of thought"]

"Procedures for reasoning with mental models rely on counterexamples to refute invalid inferences;
they establish validity by ensuring that a conclusion holds over all the models of the premises.
These procedures can be implemented in a formal system; however current psychological theories based on
formal rules (and most artificial intelligence programs) do not use them."

"Mental models provide a unified account of deductive, probabilistic, and modal reasoning.
People deduce that a conclusion is necessary – it must be true -- if it holds in all of their models of the premises;
they infer that it is probable -- it is likely to be true -- if it holds in most of their models of the premises,
and they infer that it is possible -- it may be true -- if it holds in at least one of their models of the premises.
Mental model researchers have investigated the role of models in many domains of reasoning including the following:

Reasoning with sentential connectives such as "or" and "and".
Reasoning based on conditional assertions.
Reasoning with quantifiers such as "all", "some", and "none", including syllogistic reasoning and reasoning with multiple quantifiers.
Counterfactual reasoning and reasoning about hypothetical or imaginary cases.
Informal everyday inferences and arguments.
Relational reasoning, including spatial reasoning and temporal reasoning.
Modal reasoning about what is possible and what is necessary.
Probabilistic reasoning.
Wason's selection task.

Current challenges to model theorists are to explain causal reasoning, deontic reasoning about what is permissible and impermissible,
defeasible reasoning in which the facts demand a change in one's beliefs, and the strategic thinking that occurs in making decisions
and in reasoning about another individual's inferences."



3. A Specific Example for the Use of Mental Models

3.1. Categorical Syllogisms
Definition: A categorical syllogism is an argument consisting of exactly three categorical propositions
(two premises and a conclusion) in which there appear a total of exactly three categorical terms,
each of which is used exactly twice.

categorical term
A word or phrase that designates a class. Each categorical term divides the world into two parts: the original class and its complement;
the things to which the term applies and those to which it does not.

One of those terms must be used as the subject term of the conclusion of the syllogism,
and we call it the minor term of the syllogism as a whole. The major term of the syllogism is whatever is employed
as the predicate term of its conclusion. The third term in the syllogism doesn't occur in the conclusion at all, but
must be employed in somewhere in each of its premises; hence, we call it the middle term.

Since one of the premises of the syllogism must be a categorical proposition that affirms some relation between its middle
and major terms, we call that the major premise of the syllogism. The other premise, which links the middle and minor terms,
we call the minor premise.

Consider, for example, the categorical syllogism:

                    No geese are felines.
                    Some birds are geese.
                    ------------------------
 (Therefore)  Some birds are not felines.

Clearly, "Some birds are not felines" is the conclusion of this syllogism. The major term of the syllogism is "felines" (the predicate term of its conclusion),
so "No geese are felines" (the premise in which "felines" appears) is its major premise. Simlarly, the minor term of the syllogism is "birds,"
and "Some birds are geese" is its minor premise. "geese" is the middle term of the syllogism.


3.2. Failures (?) of Human Reasoning
Here is this categorical syllogism (The Athletic Bankers Problem, S2).

                                All Bankers are Athletes
                                No Consultant is a Banker.
                                ---------------------------

What is the consequence?
           (Take a few minutes to contemplate).
How did you obtain the result?

Here is another (the Beekeepers Problem, S1)

                                Some Artists are Beekeepers
                               All beekeepers are Chemists
                               -------------------------------

What is the consequence?
            (Take a few minutes to contemplate).
How did you obtain the result?


3.3




3.4. The Method of "Deduction"
In human reports about problem solving and reasoning most subjects mention the use of
    graphical representations (diagrams) and other visualizations (like seeing the solution from a bird's perspective).
In logic problems, typically they use Venn-diagrams (1) often found as a sketch on the margin (2) oral report
    upon questioning. The total percentage is 95-100 % (!). [probably suitable as an autism test and math prodigy test..]

What are Euler circles or Venn-diagrams:
Here is an applet I borrowed from the Web.
http://www.nova.edu/~hammack/MathDL/Venn/
http://sue.csc.uvic.ca/~cos/venn/VennEJC.html

Traditionally, the Venn method was refused within mathematics and logic (especially in education).
Today it has formal theories and thought to be more respectable.


3.5. A Mental Models Explanation
of Both the Results and the Methods of Syllogistic Reasoning
(after P.N. Johnson-Laird 1983: Mental Models)

Mental representation of a syllogism is based on "mental tokens" (we can think of them as pebbles [little peices of stone children play with])

The idea is to represent sets by their members,
and each member as a simple, concrete entity.
Propositions are modeled as concrete relations ("bondages") between the entitites.
Entire problems are represented as the totality of such relations that apply to the members.

The obtained representation supports (underlies) effortless visualizations of the type
    exemplified by Venn diagrams - it is possible to directly "see" it.
    (i.e. a mental model is itself not a visual representation; yet a visual representation can be directly
    "read out" from a mental model)

In the examples above:
"All Bankers are Athletes"

b = a b = a b = a            note that the assignment is not unique - variability is possible, e.g.       a       a

b = a b = a b = a b = a

b = a b = a       a       a

 

"No Consultant is a Banker"

c
c
c
        b
        b
        b
        b

Solution consists of (a) merging, taking into accont the various ways in which it can be done depending on variants, e.g.

(1) c c         b = a         b = a         b = a         b = a               a

(2) c c            c            a         b = a         b = a         b = a         b = a

(3) c            a c            a         b = a         b = a         b = a         b = a               a

(b) readout

            No        c     is             a                ; immediately obtained ("visible") from (1)
            Some    c     are not     a                ; immediately visible from (1) or (2)
            Some    c     are           a                ; immediately visible from (2)
         * Some    a     are not     c                ; immediately visible from (3) - or visible with an effort from (1) & (2)

Exercise:
Syllogism 1 (easy, there is less room for variation with consequences).


Support for the theory
(1) domain dependence. Note that the elements are simply any words with A,B, and C.
        From separate tests it is known that same task with Banker is easier than with B.
        A plausible interpretation is that B has no definite suggestion for modeling, Banker does.
(2) form effect - B-A-C-B needs to be "revolved" into the "right position" - increased response time; effort; more error arises
(3) same errors follow [with similar frequency] as in actual logical task                [Johnson-Laird even quantifies MM errors]
(4) same errors (and for the same reason), as in the Venn method reported on the first person basis.



4. The Nature of Mental Representation
Mental model: A case in analogical representation?
E.g. pictures are analogous to what they represent (they "look the same" - which invokes infinite regress)
Mental models are not pictures, but more fundamental structures.

More generally, a mental model is a case in "personified" or "tokenized" representation:
    objects of the representation are examples (tokens) of objects of the domain to be represented.

This property of ental models can be used as basis for a quite general scheme of mental representation.
Not the input generated by the target domain but the components of the latter are "represented".
By the way: Representation is a wrong word here - as we learned from metaphor theory and embodiment.
In embodied perception, there is nothing in the stimuli ("input") that resembles the (components of) the target domain.

Deficiency of input thesis
Since percepts are not suitable for representing the target domain, our image of the target domain is not (directly) based on them.
Mental models will never be formed by sensory information alone.
(The propositional use of mental models is a clear example here - there is nothing sensory, just a triggering of internal model formation.)

Mental models thesis:
Situated (episodic) perceptual input serves the buildup of mental models in the mind.
The target domain is constructed in and by the mental models. The perceived invariance of the target domain
    is due to the invariance of these mental models, onto which the percepts that underlie experience are mapped in
    an integrative form (note that here we distiuguish between a percept as a mental-physological entity and its "subjective" form or experience).
Mental models (must) constitute skeletons independent of sensory information, which only serves to supplement, evoke or actualize them.
(e.g. The competent infant is probably equipped by object detectors, or - as in case of agency - the proto-forms of such detectors.)


Generalization of Mental Models in the Causal Theory
It is clear that the above picture, though based on mental models as discussed here,
        goes way beyond what is included in the usual concept.
To accommodate this picture, we need a significant extension of the Mental Models theory.
The extension is centered around the notion of causality.

(i) the MM theory is mostly about reasoning in particular, and - although it has suggestions - it says nothing in concrete
    about mental representation and mentation in general, or about the relation between mental models and perception.
(ii) in a Johnson-:Laird type mental model theory one of the perennial questionable issues is that of the mental operation.
    In other words, MM-s are entirely static structures that need external processing, not very different from logic itself,
    which the MM framework is devised to replace.

properties in common between the target domain and a mental model under various conceptions
    in a visual representation:                  observational proberties, the rest is subordinated to this
    in a logical representation:                 relational properties, the rest is subordinated to this
    in a mental model, causal version      causal properties, and the rest follows from this


Causal Mental Models
A causal mental model is a generative representation.
A causal mental model is a material object with causal powers.

Mental models of the J-L style are inert tokens (as visible in the "pebbles") metaphor.
Mental models of the causal style are incporporations of actors with the same causal abilities as observed in the target domain.

Causal mental models support the representation of narratives by representing (constructing) the agents and constraints of the narrative.
Meaning is obtained through the narratives of mental models as discussed when discussing narratives.