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Computer Brain--Math & Logic

[ Boolean Logic | Fuzzy Logic ]

O.gif (1023 bytes)ne strong AI approach to AI is by using logic as the basis of all development and research.  This school of thought originates from the view that AI can be achieved through systematic exploration that science demands.   Another reason why logic would be applied to AI development is because the system that inherits and tests AI, generally computers, are machines operating on both the logic of the physics that govern its inner workings as well as programming the computer to run the AI programs requires logic as well.

Boolean Logic

Invented by George Boole who developed an entire aspect of algebra on this topic, boolean logic is a simple and systematic way of thinking and reasoning.  In mathematics and philosophy, boolean logic can be applied to assess the validity of a mathematical expression or a sentence.  Let's start with a set of statements followed by a "true" if the statement is valid and "false" it is invalid.

  1. Apples are red--true.
  2. Violets are blue--true.
  3. Three plus three is equal to seven--false.

If the statements were linked together with "AND" or "OR" or negate the statement with "NOT"  in combinations of pairs, then the validity of the entire sentence can be established based on the validity of the sub-statements.   Thus,

Statement Basic Elements Final Value
Apples are red AND violets are blue. True AND True True
Apples are red AND Three plus three is equal to seven. True AND False False
Apples are red Or Three plus three is equal to seven. True OR False True
Apples are red OR Violets are blue. True Or True True
NOT Apples are red(i.e. Apples are not red.) AND violets are blue. False AND True False
...etc... ...etc... ...etc...

The combinations are not limited to pairs of statements linked by "AND" or "OR."  A sentence can have an unlimited number of statements all linked together by "AND" or "OR", but only two comparisons can be done at a time, so the statements are nested into parentheses(like in math where the statement in the innermost parentheses are evaluated first):

(Apples are red OR violets are blue) AND three plus three is equal to seven.  (True OR True) AND False = (True) AND False = True AND False False

The combination of statements allowed a sentences or a mathematical expressions to clearly express their meanings simplistically yet be powerful and effective.  Thus, this was an attempt to formalize thought and reasoning at the mathematics level.

Computer scientists don't use "true" or "false" to perform calculations.   Instead, they use a more abstract method involving the binary system with true represented as a "1" and false is represented as "0".  In the case of computers, "1" is considered "on", i.e. the existence of an electric current in a particular area of the computer, while "0" is the absence of electricity.  The routing of electricity by the computer and its interpretation through boolean logic that allows a computer to calculate and make decisions to serve the user.

Fuzzy Logic

Seemingly as rebellious as the hippies were in the 1960s, fuzzy logic was an attempt to break away from the traditional and inflexible thinking of logic programming and create a machine that acted more "organic."  What this means is that while a computer operates on logical principles, what it actually does does not have to be straightforward logic.  This kind of operation would allow a computer to make intelligent decisions based on incomplete information just as real organisms, especially a human being.

Fuzzy logic actually relates to boolean algebra in that instead of having only two values like "true" and "false", it has a range of values such as "always true", "sometimes true", "sometimes false", and "always false" to address statements that express something in general terms like "some apples are red."

In real life, most things cannot be entirely expressed accurately in a definite "either-this-or-that" statement.  This point is what separates computers from people: computers are digital machines that cannot definitely capture or represent something that is analog while a person, whether his/her brain is digital or not, can process analog information to a degree of accuracy good enough to make precise decisions.  In AI, fuzzy logic typically applied in pattern-recognition in which a picture or a sound recording does not have a clear representation of an object, but enough of it is there for the computer to recognize it using fuzzy logic.  Also, fuzzy logic can prevent computers from becoming lost in decision-making as it journeys from one decision to another without making much progress.  The special logic could allow computers to identify the faulty train of thought that cause the never ending loop, terminate the process, and still make a decision with a few pieces of information that could be processed.

 

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