Logical thinking is very important for technical development and evolution of society. It also underlies critical distinction between humans and animals.
Beginning of Logic
Aristotle Logic
The basis of today's logic were derived from Aristotle (384-322 B.C.), the Greek philosopher who dealt with a lot of practical issues. He created formal logic and opened logical class for the first time in the history.
Aristotle stated that 'Of any subject, one must be either asserted or denied.' This notion was always basis of mathematics and logical thinking until, recently, fuzzy logic was informed by Lofti Zadeh in 1965
MATHEMATICS
Mathematics is a main tool of logic. Through deducting actual length, space, time, and existence to symbols called numbers, it made possible for us to manipulate world easily and simply. Invention of math replaced study of logic to study of math..
History of Math.
Math. has thousands years of history. From simple counting which already practiced as human history began to today's complex computings, we invented Algebra, Geometry, Calculas, probability and so on.
History of Mathematics Home Page
Math.,Logic, & Computer
Game theory
Game theory is what is called the theory of social situation by psychologists. Mainly game theory forcuses on how groups of people interact each other although the theory is often for parlor games such as poker or bridge.
Game theory is also widely used in Chess, Othello, and any other board games which require algorihm for the movements by computers. Game theory is possible by vast memory to simulate any possible movements of oppornent, and to switch the view point from "searching for the winning movements" to " elminating losing movements as many patterns as possible".
George Boole and Basis of Computer
George Boole (1815 - 1864) was an English mathematician who learned mathematics by himself. In his paper, "The Mathematical Analysis of Logic, Being an Essay Towards a Calculus of Deductive Reasoning", and "An Investigation of the Laws of Thought, on which are Founded the Mathematical Theories of Logic and Probability", he reduced logic to Boolean algebra. Then, about one hundreds years later, Boolean logic made it possible to produce the first computer. Although his great contribution toward math., logic, and computer, his theory was paid little attention during his life time.
Boolean Logic
Boole drew on the symbols and operations of algebra in creating his system of logic.
He restricted the use of numbers only 1 and 0. Any objects are expressed by combinations of 1 (universal set) and 0 (empty set) and AND, OR, and NOT. Boolean logic has led to the design of electronic computers because by switching curcuits, electronic computers can generate 0 and 1 all the time.
AND, OR and NOT
In the process of simplifying logic, he succeeded to express objects with AND, OR and NOT. Combinations of these can express almost any complex objects, and good example of this is algorithm of search engines.
Information Theory
Without Shannon's information theory, none of CD players, internet, and FAX machines are on market.
Fuzzy Logic
Attempting more human-like decision making.
The history of logic started with Aristotle. After 2000 years, in computalized society, the world is heading to fuzy where people seek "soft logic" in opposition of "hard logic". Science always refelcts the view of how people perceive the world at that time. Obviously, today, the world is getting smaller, and humans are attempting to integrate two opposing concepts rather than argueing which is more true. Especially, in human relations, this phenomina may contribute to resolve conflicts among nations.
URLs
Logic
Math., Logic, and Information System: topics dealing with logic, math., information theory, game theory, probability theory, possibility theory, Boolean logic, fuzzy logic with useful links-- tutorial, intermediate, long, links
http://peace.saumag.edu/Faculty/Kardas/Courses/CS/Student%20Pages/Fuzzy%20Logic.html
Mathematics
A brief history of algebra: A brief history of algebra, computing system. More than half of pages are spent modern algebra-- tutorial, basic,medium, links http://www.comlab.ox.ac.uk/oucl/users/jonathan.bowen/algebra/
History of Mathematics Homepage: History of math. from Greek era to today. List of mathematicians, and time table-- tutorial, intermediate, long, links http://aleph0.clarku.edu/~djoyce/mathhist/mathhist.html
Game Theory
HANDBOOK OF GAME THEORY: book review of HANDBOOK OF GAME THEORY, rational study of decision maker behavior--text, intermediate, medium, links http://www.ma.huji.ac.il/~hart/hgt/pref-i.html
GAME THEORY: short explaination of game theory-- text, basic,short, links http://pespmc1.vub.ac.be/ASC/GAME_THEOR.html
Learn About Game Theory: basic and advanced information about game theory with on-line games-- tutorial, intermediate, short, links
http://levine.sscnet.ucla.edu/general.htm
What is Game Theory? : basic introduction of basic theory and an instructive example-- text, basic, short, links
http://levine.sscnet.ucla.edu/whatis.htm
Boolean Logic
Picture of Boole: a big picture of Boole's face-- graphics, basic, short
http://www-groups.dcs.st-and.ac.uk/~hstory/BigPicture/Boole.jpeg
How to Use Boolean Logic : graphical presentation of AND, OR and NOT-- graphics, basic, short
http://www.newsbank.com/whatsnew/boolean/
Searching with Boolean Logic: search engine mechanisms using AND, OR and NOT-- graphics, basic, short
http://www.electionline.com/cpl-bin/help/boolops.cgi/317786158290f481
Information Theory
Information Theory: short introduction to information theory-- text, intermediate, short, links
http://www-isl.stanford.edu/people/yiannis/info.html
Heroes of Cyberspace: Claude Shannon: Brief biography of Claude Shannon and explanation of information theory-- text, intermediate, medium, links
http://www.info-nation.com/shannon.html
Claude Shannon's mathematical model of communication: a graphic explaining Claude Shannon's mathematical model of communication-- graphic, basic, short, links
http://coral.lili.uni-bielefeld.de/Classes/Summer96/Textdesc/funslides/node7.html
Notes on Computer-Generated Text: bibiography of Claude Shannon with his photograph-- text, basic, medium, links
http://www.nightgarden.com/infosci.htm
Fuzzy Logic
What is Fuzzy Logic?: simple description of what fuzzy logic is-- text, basic, short
http://home1.gte.net/darrenb/history.htm
Introduction: Basic of Fuzzy logic with graphics and how it is used in practical level-- tutorial, basic, short, links
http://www-dse.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/sbaa/report.intro.html
Fuzzy Logic: Excellent introductory site with history, overviews, demonstration and predictions-- tutorial, basic, short, links
http://www-dse.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/sbaa/report.html
Fuzzy Logic and Its Use: Q & A Session: Fuzzy logic self test with answers-- interactive, basic, short
http://www-dse.doc.ic.ac.uk:80/~nd/surprise_96/journal/vol3/sbaa/test.html
What Is...fuzzy logic: basic definition of Fuzzy Logic-- tutorial, basic, short, links
http://whatis.com/fuzzylog.htm
FAQ: Fuzzy Logic and Fuzzy Expert Systems--FAQ, basic, short,links
http://www.cs.cmu.edu/Groups/AI/html/faqs/ai/fuzzy/part1/faq.html
Fuzzy Logic Archive: Good connection to basics, FAQs, usenet, tutorials and fuzzy for beginners-- tutorial, intermediate, short, links
http://www.austinlinks.com/Fuzzy/
Just for Fun
Shannonizer: simple editing program which allow to change your words to ones like Mark Twain, etc.-- interactive, basic, short, links
http://www.nightgarden.com/shannon.htm
