Intelligence and Reasoning

Intelligence is the ability to choose actions to best meet specified goals.

Purpose
The purpose of this page is to describe and classify the theory of intelligence.

Introduction
Intelligence is just a word in the dictionary. What it means is different for different people. But I want to narrow it down to an underlying core concept.

I do not want to limit intelligence to human beings. Humans do many things that are not intelligent.

Intelligence is what it does. For humans it controls the body and makes decisions that keep the body alive. It is also driven by internal drives given to it by evolution. Intelligence is hijacked by these internal needs to work towards the preservation of the species.

By reducing this down to its primary functions we come up with the idea that intelligence makes decisions designed to meet specified goals.

There are many things not specifically included in this definition of intelligence
 * Consciousness
 * Art
 * Meaning

These things are important to human intelligence, but I do not see them as a necessary part of intelligence.

Functional Breakdown
Intelligence can be broken down functionally into,

Sensory Perception
Sensory perception is the input interface between the world and the intelligence. Of all the senses vision is the one that gives the most information about the environment.

It is hard to understand how vision works. A large amount of data must be processed. To have a plausable model of intelligence it helps to have a model of vision.

It may be possible to consider vision as a specific example of learning. But for simplicity I will firstly consider specific processing which may be useful.

Image Comparison
There is specific processing that would seem appropriate for vision. In particular the comparison of two images separated by a small amount of space (stereoscopic vision) or time (detection of movement). Would appear to be useful.

The nerves coming from the retina of the eye may be considered to produce an image. But also touch may also be considered to be send data that may considered to be an image.

To each point of a primary image we construct a vector that moves the point to the new image. The vectors are chosen so as to minimise the information content of the resulting structure.

Motion detection can then be applied to,
 * The whole image.
 * Areas of the image.

Motion detection comes in three forms.
 * Movement
 * Rotations
 * Distance/Size

A difference in size between images would result in vectors that change by a constant amount in the X and Y planes.

Change in size may indicate movement towards or away from the object.

Rotations (include change of viewing angle) are characterized by.
 * X, Y planes - A pattern of increasing or decreasing vectors perpendicular to a line.
 * Z plane - A pattern of increasing or decreasing vectors parallel to a line.

Stereoscopic Imaging
The X axis displacement of the eyes causes displacement of the image of objects. The displacement is inversely proportional to the distance. This variation in displacement in object image position indicates variation in depth, which gives depth perception.

X,Y rotation should not be seen in stereoscopic images.

Time Change Imaging
Z axis rotation also indicates change of depth in time change image comparison.

X,Y rotation indicates rotation of the object relative to the viewer.

Change in depth (Z-axis movement towards or away from the viewer) causes change in size.

Recognition
Image comparison may be used for recognition. A stored image compared with a target image would give an array of mapping vectors.

These mapping vectors may then be corrected for,
 * Position
 * Rotation
 * Size

The resulting vectors should then be zero vectors. The sum of the squares of the lengths of the vectors measure how similar are. Areas of longer vectors can then be analyzed for local movement.

Object Model
Out of this modeling surfaces corresponding to objects may be identified, and recognised, leading to an object view of the world.

Learning
Learning is theoretically the deduction of probabilities of future events. However probability turns out not to be as neat and precise a concept as we may want. Probability is a function of,
 * Input data
 * Prior assumptions.

So probability is subjective. It depends on the intelligences experience and prior assumptions. These assumptions are built into the native language of the intelligence.

Also real probabilities are very hard to calculate. A true probability is based on weighing every possible model. In practice probability is calculated based on a set of assumptions that make the calculation possible.

In practice calculation of probabilities is not always required. Learning can be based purely on the compression of data. Models that compress data more have more predictive power.

We would like all knowledge to be built on the bedrock of certain and absolute facts. In fact all knowledge floats on a lava of prior assumptions.

Measurement
Learning may be broken down into two areas,


 * Inductive Inference
 * Inductive Regression

The difference is really only that Inductive Regression is the application of Inductive Inference to quantities (real numbers).

When you look at real numbers from a mathematicians point of view they are strange beasts. They are uncountable, and most real numbers will never be seen. Inductive Inference deals effectively with real numbers only for smooth and continuous things.

Perhaps there is another area of inference based on the Fractal nature of things?

Search
Inductive Inference and Inductive Regression give us the theory of how to measure probabilities. However to apply this theory we must restrict our goals to achievable results.

Symbolic Learning
For symbolic learning we know that compression may be achieved by the replacement of repeated symbols by strings of symbols. These replacement rules can then be compared, using the difference algorithm, to create second order replacement rules (replacement rules applied to replacement rules). By applying these rules with a particular set of restrictions, second order replacement rules can be used to implement variables.

Replacement along with second order replacement forms a simple univeral language of logic. By writing some rules it is possible to define mathematics.

Some simple algorithms allow us to construct replacement rules that minimise the size of strings. From suitable data input arithmatic and mathematics can be learned.

Analysis
Analysis is working out the consequences of the model. It includes,
 * Checking for Internal Consistency
 * Deriving useful facts and skills

Simulation of Possible Outcomes
For quantative models, analysis may be limited to applying learning and the decision making process to the simulation of likely events.

Simulation consists of applying random data to the learned model to generate a plausable reality. The intelligence can then uses its decision making process to try various actions out in the simulation. Learning can then be applied to the results of the simulation.

In addition to simulation in time order, the intelligence may perform simulation in reverse order, starting with the desired goal and attempting to meetup with a state that can be reached by simulation forward.

Analysis in Symbolic Logic
In symbolic logic analyis includes the derivation and proving of theorems and the solving of difficult equations.

What makes a good theorem? I give two measures,
 * Simplicity
 * The minimum number of steps needed to prove it.

A simple theorem is better than a complex theorem because it is more easily applied.

A theorem that takes many steps to prove has the effect of leap frogging over many intervening steps to a result that may be useful to us.

So we can imagine a theorem generator that applies axioms and existing theorems that searches for new theorems that are good.

Axiom Theorem System
However that does not appear to be the way humans do it. Humans learn theorems by observing them in data. Then afterwards a theorem proof is constructed to prove or disprove the plausible theorem based on axioms.

Axioms are also learned theorems. A more accurate picture is then,
 * Learning gives a group of plausible theorems.
 * Starting with simple therorems we attempt to prove/disprove complex theorems.
 * The set of simplest theorems from which the other theorems can be derived become the axioms.

This process gives a small set of axioms that describe our world. This gives greater compression of the data, so greater probability of being correct.

Decision
Decision is the choosing of actions which optimize the internal goals. The internal goal is the "happiness" at a particular point in time. The descision process aims to maximise the integral of the happiness over time. Decision making is then the process of predicting the happiness over time and choosing actions that maximise it.

The internal goals should include the search for knowledge.

In order to search for knowledge the intelligence must measure knowledge. This is the uncertainty in the probabilities in the domain of the model. In addition to the probability of an event the intelligence needs to know how certain that probability is. This is the measure of uncertainty.

The search for knowledge drives experimentation.

Optimization of Goals
In the quantative domain decision making may be guided by gradient ascent to look for a local maximum that represents a good series of actions to take.

Symbolic Decision making
Symbolic decision making uses Constraint Logic Programming to sift through the possiblities to obtain a solution.

Summary
Intelligence is a somewhat fuzzy and imperfect thing. I cant imagine a perfect intelligence. I do not think that there are absolute probabilities or perfect truths involved here.

Instead intelligence is that which works to achieve its goals. For humans these goals may once have been only to avoid being eaten by lions. If the humans knowledge and intelligence worked well enough for that then it succeeded in its goal.

Nowadays we strive for scientific truth and mathematical rigor. But these are extra things built on top of intelligence. They are not a natural or fundamental part of it.