In spite of its delicate name BELLE represents the concept of brute force. In spite of the brutal force in its name, CHAOS represents the concept of sophistication, selectivity. Both of these oddly named entities are American computer chess programs, and they met in a showdown here in a playoff round at the end of the third World Computer Chess Championship.

BELLE designed by Ken Thompson and Joe Condon at the Bell Telephone Labs in Murray Hill, N.J., is the fastest gun in computer chess -- but inclined to shoot first and ask questions later, if at all. When choosing a move, it examines approximately 160,000 positions per second -- or 28.8 million possibilities in the three minutes it takes, on the average, to make a move. But at that speed, it examines positions. rather crudely.

CHAOS, designed by a team at the University of Michigan, is a Hamlet of computer chess slow and thoughtful, inclinded to doubts and hesitations. It tooks at a position much more subtly than BELLE and evaluates the possibilities by a much more carefully calibrated set of criteria. But that takes time, and in its alloted three minutes per move CHAOS can examine only a fraction of the possibilities that BELLE dashes through.

Sunday, when BELLE met CHAOS -- at the Brucknerhaus concert hall in this Austrian city where the Danube encounters the footballs of the Alps -- it was a symbolic confrontation of the two basic philosophies of computer chess -- overwhelming force vs. selective search, the machine gun vs. the derringer. They met in a special playoff round added after the conclusion of the tournament when the final score left them tied at 3 1/2 points apiece. The all-American playoff round was reached after the two finalists had shaken off challengers from the Soviet Union, Europe and Canada, as well as the powerful American program Duchess, from Duke University, which went into the last round of the tournament with a perfect score but then was crushed by BELLE's steamrollr attack. CHAOS slipped into the playoff by giving the coup de grace to the Russian program Kaissa, which had begun the tournament well with two cliffhanger victories, but faded in the closing rounds.

Once the showdown came, the result was what usually happens when a Hamlet type goes one-on-one against a Hercules type: BELLE tore CHAOS into little pieces while CHAOS was still smiling an electronic smile at the subtlety of one of its moves. And so the proponents of finesse in chess programming are en route back to their drawing boards, while the devotes of brute force gloat in anticipation of the even more powerful hardware they will have for the next world championship in 1983. 'Megabyte' Masters

A computer chess championship is a blend of academic convention, grand prix race and trade fair. Most of the hard-core chess programmers, who have been at work since the 1960s building machines that play games, are basically scientists engaged (they hope) in the creation of artificial intelligence. Between rounds, they get together for informal exchanges of ideas and long conversations studded with strange jargon -- sentences full of "megabyte," node," depth of search" and "cutting down your tree." This final expression has nothing to do with lumber of forests: It describes the way possibilities branch out as a computer moves deeper and deeper into a chess situation, and ways of keeping that proliferation within bounds.

Along with the scientists at the tournament were a sprinkling of professional chess players, who tend to look on the machines that play their game with a mixture of fear and contempt -- the way jockeys might look on an Alfa Romeo Buzzing around a horse track.

The feeling was heightened this year because of the $100,000 Fredkin Prize, will be awarded to the first computer program to win the world championship from a human being. There is no time limit on the prize, and nobody expects it to be awarded in the next few years, but it was a prime topic of idle conversation at the tourament. Opinion was divided sharply on whether it will be won in this century, with some computer people and quite a few chess people suggesting that it never will happen.

Hans Berliner, an authority on chess and on computers and the head of the committee supervising the prize, expressed the mainstream opinion when he announced the award in Pittsburgh: "It will take more than five years and probably longer. By 1990, I think there is a 50-50 chance that it will happen. From that point on, the odds will get gradually better. And 20 years from now it is almost a certainly." The Human Factor

The best programs in the world championship tournament are now able to beat about 99.5 percent of human chess players. Some members of the other .5 percent were at the tournament:

International master David Levy, who won a match against the former computer champion, Chess 4.9. He is lining up bets for another manputer champion, Chess 4.9. He is lining up bets for another man-vs.-computer match in the mid-1980s -- but he is not so sure he will win that one.

German grandmaster Helmut Pfleger, who thinks that computers will never be able to beat grandmasters consistently because "there are some kinds of perception that you cannot put into a computer program." But he admits that playing against a computer "can make you nervous."

Fridric Olafsson of Iceland, president of the International Chess Federation, who is having informal discussions with Levy about the status of computers in international chess.

Olafsson seems to be seriously considering a proposal by Levy to allow a team of computers to compete in the next chess olympiad two years from now. The olympiad is a tournament of national teams, and under Levy's proposal computers would play as though their team represented an independent nation.

"I don't think we'd finish in the top 20," says Levy. "Probably we'd be about one-third of the way from the bottom. But it might be enough to make people start taking computer chess seriously. Of course, it would be hard for the teams that finish below us. Think of them having to go home and say, 'We were doing all right until we ran into the that computer team.'"

In the United States, computers have been playing against humans in tournaments at least occasionally since the late 1960s. And the U.S. Chess Federation is trying to work out a standard policy for handlng them. In a letter from the USCF -- read at the funding meeting here of the International Computer Chess Association -- competition rules were announced. They will allow computers to continue playing in human tournaments, under strict conditions and limitatoins, for at least another year. The Software Hard Sell

At this year's world championship, there was a new element that had hardly been noticeable at the last, three years ago in Toronto: computer chess as a commercial product. About one-third of the people or programs connected with the championship seemed also to be connected with the small game-playing machine computers that have been breaking into the consumer market. David Levy has a company, Intelligent Games Inc., whose computer program, operating on a television screen, is about to hit the European market and will be marketed in America next year. Mychess, the program of America's David Kittinger, played for the world championship but is also being sold in disc format for home computers of fairly high capacity (36,000 bytes). Another American programmer, Tony Scherzer, put his micropropgram BeBe in the tournament largely to promote his company, Sys-10, which develops and markets the Chess Champion line of home chess computers. BeBe did not become a champion at this tournament, but it drew all its games against some very muscullar competition. Scherzer had mixed feelings about this result, but finally shruggled. "I guess the ads can say that we were undefeated in the world computer championship," he said.

Europeans have been slower than Americans and Japanese in developing marketable computer games. Sidney Samole, the president of Fidelity Electronics of Miami, which dominates the computer games mass market in the United States, said that his company expects to sell $75 million worth of game-playing computers this year -- chiefly the various models of Chess Challenger, but also similar machines that will play checkers, backgammon or one to four hands in a bridge four-some. About one-third of Fidelity's sales are in Europe, Samole said, with a particularly strong market in the German-speaking countries.

Germany has produced its first home chess computer, designed by German programmer Thomas Nitche, who had a program in the world championship. The first German program is called Mephisto, after an English chess automation that won a tournament in 1878. The orignial Mephisto was a fraud (it was actually operated by chess master Isider Gunsberg), but the electronic one looks like a strong contender. As a sort of prelude to future marketplace battles, Mephisto had an impromptu match with the Chess Challengr's Sensory Voice Model.

At the International Computer Chess Association meeting, some of the more academic members seemed disturbed by the intrusion of commerce into the pure pursuit of an artificial intelligence. Tentative efforts were made to draw a line between the two kins of computer chess -- for example, by requiring an entry fee in the next world championship from those who are now willing to let others examine their programs. The results of these efforts were inconclusive.

"The expense for this world championship were $50,000," said Sidney Samole. "In three years, the next one will cost $150,000, and a lot of the free-and-easy information being handed out in bull sessions will be trade secrets by then."