Rule-Based Mental Models

Yongho Lee

Contents

1. Mental Models as Morphism

2. Mental Models as Rule Systems

3. The Performance of Rule-Based Modeling Systems

4. Illustration of the Performance of a Modeling System

1. Mental Models as Morphism

A useful general definition of mental models must capture

1) A model must make it possible for the system to generate prediction even though

knowledge of the environment is incomplete.

2) It must be easy to refine the model as additional information is acquired without

losing useful information already incorporated.

3) The model must not make requirements on the cognitive system’s processing capa-

bilities that are infeasible computationally.

Morphism

Mathematical structure

Homomorphism

1. Mental Models as Morphism

The environment can in principle be described by a set of states and a transition func-

tion that specifies how the states can change over time. (Figure 2.1)

1) Let S be the set of states of the environment

2) Let O be the set of outputs of the cognitive system that act upon environment

3) Let T be the transition function of the environment

A categorizatino function P defined in terms of the detected properties. (Figure 2.2)

Simple detectors, which take on binary values, encode properties of states of the world.

A model transition function, T’, which is intended to mimic the transition function T

operating in the world. (Figure 2.3)

1. Mental Models as Morphism

The process of model construction can be viewed as the progressive refinement of a

quasi-homomorphism. (Figure 2.4)

The initial layer of the model will divide the world into broad categories that allow

approximate predictions with many exceptions.

The induction process will be guided by failures of the current model.

New exceptions to the current model will always be possible.

The concept of a q-morphism captures several basic aspects of a pragmatic account of

the performance of cognitive systems.

1) Its hierarchical structure allows the system to make approximate predictions on the

basis of incomplete knowledge of the environment.

2) As the model is refined, rules that represent useful probabilistic regularities can be

retained as defaults.

1. Mental Models as Morphism

A model typically preserves only some aspects of the world. is the problematic initial state, is the state that would satisfy the goal, and T(S(t), O(t))

is the transition function allowing potential sequence of state changes that (if the prob-

lem is solvable) could transform into .

The process of induction is directed by the goal of generating mental models that in-

creasingly approximate an ideal. (Figure 2.5)

2. Mental Models as Rule Systems

The condition-action rules, which have the general form, IF (condi-tion 1, 2, … , n), THEN (action). Satisfaction of the conditions depends on matches between the con-ditions and active information in memory. Active information, in contrast to stored information, is declarative knowledge currently being processed by the system. The actions of matched rules determine what the system will do; that is, the rules incorporate procedural information.

Empirical rules (Table 2.1)

Inferential rules: Specialization rules, Unusualness rules, Statistical rules, Regula-

tion Schemas

System operating principles: not learnable, not teachable

3. The Performance of Rule-Based Modeling Systems

Competing to represent the environment

Match : description of the current situation

Strength : history of past usefulness

Specificity : greatest degree of completeness

Support : greatest compatibility

Competition, Support, and Coherence (Figure 2.7)

Radically different interpretation

Categorization and implicit representation of probability

Mutually exclusive

Encoding : beam balance test

3. The Performance of Rule-Based Modeling Systems

Automatic Spreading Activation

Inevitably spreads (ex. nurse – doctor)

No process capacity

Continues spreading indefinitely

Extremely rapid (40ms)

Rule directed Spreading Activation

Bull – Cow – Milk : no second-order priming effect

few immediate associates – stops dead

4. Illustration of the Performance of a Modeling System

Small / Black / Long horizontal axis / Animal

4. Illustration of the Performance of a Modeling System

4. Illustration of the Performance of a Modeling System

Small / Black / Long horizontal axis / Animal / Head round

4. Illustration of the Performance of a Modeling System

EOD

1. Mental Models as Morphism

Figure 2.1

Figure 2.2Figure 2.3

1. Mental Models as Morphism

Figure 2.4

Figure 2.5

2. Mental Models as Rule Systems

Table 2.1

A. Synchronic1. Categorical If an object is a dog, then it is a animal. If an object is a dog, then it can bark. 2. Associative If an object is a dog, then activate the “cat” conceptB. Diachronic1. Predictor If a person annoys a dog, then the dog will growl.2. Effector If a dog chase you, then run away

3. The Performance of Rule-Based Modeling Systems

Figure 2.7