Rule-Based Mental Models

1. Rule-Based Mental Models Yongho Lee

2. Contents • Mental Models as Morphism • Mental Models as Rule Systems • The Performance of Rule-Based Modeling Systems • Illustration of the Performance of a Modeling System

3. 1. Mental Models as Morphism • A useful general definition of mental models must capture • A model must make it possible for the system to generate prediction even though knowledge of the environment is incomplete. • It must be easy to refine the model as additional information is acquired without losing useful information already incorporated. • The model must not make requirements on the cognitive system’s processing capabilities that are infeasible computationally. • Morphism • Mathematical structure • Homomorphism

4. 1. Mental Models as Morphism • The environment can in principle be described by a set of states and a transition function that specifies how the states can change over time. (Figure 2.1) • Let S be the set of states of the environment • Let O be the set of outputs of the cognitive system that act upon environment • 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)

5. 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. • Its hierarchical structure allows the system to make approximate predictions on the basis of incomplete knowledge of the environment. • As the model is refined, rules that represent useful probabilistic regularities can be retained as defaults.

6. 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 problem is solvable) could transform into . • The process of induction is directed by the goal of generating mental models that increasingly approximate an ideal. (Figure 2.5)

7. 2. Mental Models as RuleSystems • The condition-action rules, which have the general form, IF (condition 1, 2, … , n), THEN (action). • Satisfaction of the conditions depends on matches between the conditions 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, Regulation Schemas • System operating principles: notlearnable, not teachable

8. 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

9. 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

10. 4. Illustration of the Performance of a Modeling System Small / Black / Long horizontal axis / Animal

11. 4. Illustration of the Performance of a Modeling System

12. 4. Illustration of the Performance of a Modeling System Small / Black / Long horizontal axis / Animal / Head round

13. 4. Illustration of the Performance of a Modeling System

14. EOD

15. 1. Mental Models as Morphism Figure 2.1 Figure 2.3 Figure 2.2

16. 1. Mental Models as Morphism Figure 2.4 Figure 2.5

17. 2. Mental Models as RuleSystems Table 2.1 A. Synchronic 1. 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” concept B. Diachronic 1. Predictor If a person annoys a dog, then the dog will growl. 2. Effector If a dog chase you, then run away

18. 3. The Performance of Rule-Based Modeling Systems Figure 2.7