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MODELS 

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Ontologies

Models (in general) are representations of objects, relations,
actions, or processes. Examples include a photograph of you, an
architect's scale model of a building, an engineer's drawing of an
electronic circuit. 

Models in AI too are representations of an agent's world.

Representing knowledge of something requires a language. 

A knowledge representation language consists of an ontology, i.e., a
set of primitives, that form the vocabulary of the language.  It also
consists of a grammar that defines how primitives may be combined into
larger structures.

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Representing Time

The simplest representation of time is called a "time-line."
Different timelines may represent "events" at different temporal
granularity.



Sept                 Sept                 Sept                 Sept
13                   14                   15                   16
|--------------------|--------------------|--------------------|---
Patient              Patient                                   Patient
enters               undergoes                                 is
hospital             surgery                                   discharged
                     
                     |
                     |
                     |
                     V
------------------------------------------
|                                        |
|                                        |
|                                        |
V                                        V

Sept
14
7:00                 8:00                 9:00
am                   am                   am
|--------------------|--------------------|---
Patient              Patient              Patient
undergoes            is given             undergoes
medical              anesthesia           surgery
examination

An event refers to something that happens in time. Multiple events in
a given time duration form an "event cluster."

Different timeslines may be organized in an abstraction/aggregation
hierarchy as indicated above. 

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Representing Space

A "point" is a location in space; a "region" is a set of points.  
A "direction" (in 3D) is a point on a unit sphere; (in 2D, direction
is a point on a unit circle). 
 
In an "adjacency matrix" representation, adjacent cells represent
objects (or parts of objects) and adjacency represents spatial
relations among objects:

      ----------------
      | X  |    | X  | 
      ----------------
      | X  |    | X  |
      ----------------
      | X  | X  | X  |
      ----------------   

In a standard quadtree representation, space is partitioned into
quadrents around X (or West-East) and Y (or North-South) axes:

    NW   |    NE
         |
         |
    ------------
         |
         |
    SW   |    SE


As the name suggests, a quadtree organizes spatial representations
in a tree. 

Your projects 3 and 4 use a quadtree spatial representation.

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Representing Causality

Causal processes are represented as directed acyclic graphs (called
DAGs). 

           state1
             |
             | transition1-2
             V
           state2
             |
             | transition2-3
             V
           state3
            /\
  tran3-4  /  \ tran3-5
          /    \
     state4     state5






Consider the following electrical circuit:


             Battery         Switch
                |              /
            ----||------------/  -----
            |   |                    |
            |                        |
            |         ^^             |
            ----------||--------------
                    Bulb


The two causal behaviors of this circuit may be represented as follows:

Behavior 1:

State 1
subs        loc        prop         val
electricity battery    voltage      1.5 volts
                 |
                 | Under-Condition State 2 of Behvaior 2
                 | Serially Connected Battery, Switch, Bulb
                 V
State 2
subs        loc        prop         val
electricity bulb       voltage      1.5 volts
                 |
                 | Using Function CreateLight of Bulb
                 | Relation Intensity == Voltage**2 (== means proportional to)
                 V
State 3
subs       loc        prop         val
light      bulb       intensity    6 lumens


Behavior B2

State1
comp(onent) mod(ality)
switch      off
        |
        | Due-to-ExternalStimulus
        |
        V
comp         mod
switch       on

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