How AI Thinks in Shades of Gray


FUZZY THINKING: How AI Thinks in Shades of Gray is the first popular book to clearly explain the revolutionary new technology and worldview of fuzzy logic — and how the shift from black-and-white logic to thinking in shades of gray changes our lives and our AI future. Does outer space suddenly begin at exactly 100 kilometers above sea level? Does adulthood suddenly begin on one’s 18th birthday? Does life itself suddenly begin at conception or at 15 weeks after conception? Or are these fuzzy matters of degree?

Thirty years after its original publication in print, FUZZY THINKING returns in its first digital edition, produced in collaboration with Fearless Literary. Read the Foreword to the new edition below.


“Bart Kosko is a wonderful futurist with a polymathic combination of talents.”
— M.I.T. Professor Marvin Minsky

"Probably the best primer around for learning what Fuzzy Logic is all about."

"Fuzzy logic posits a world in which absolutes, such as those implied in the words "true" and "false", are less important and interesting than the matters of degree between them. "Fuzziness is grayness," and "the truth lies in the middle," according to Kosko, one of the pioneers of fuzzy logic theory, which he persuasively presents as a world view rooted more in Buddhist and Taoist assumptions than in the dichotomous Aristotelian tradition. He proposes FATs (Fuzzy Approximation Theorems) for the existence (and non-existence, as fuzziness demands) of God and as models of the abortion debate. In consumer terms, fuzzy logic is behind such "smart" machines as air conditioners and microwave ovens that gauge their operation to the conditions and demands of a given moment's task. Writing with style and risk, Kosko challenges assumptions, not about the existence of scientific authority, but about its nature."



BART KOSKO, Ph.D., J.D. s a professor of electrical and computer engineering, and law at the University of Southern California, and the 2023 winner of the Hebb Award in neural learning from the International Neural Network society. He holds degrees in philosophy, economics, mathematics, electrical engineering, and law, and has organized several conferences on machine learning, serves on the editorial board of several technical journals, and holds patents on machine learning and quantum computing, and has published numerous scientific articles and textbooks. He is an international best-selling author whose other books include Heaven in a Chip, Noise, the cyber-thriller novel Nanotime, and the global-warming thriller novel Cool Earth.





Everything is a matter of degree.

That credo is the fuzzy world view of shades of gray between the binary extremes of black and white. It reflects intelligent judgment both natural and artificial.

It also clashes now more than ever with the casual black-white thinking found all too often in much of science and politics and in most subjects in between: Does outer space suddenly begin at exactly 100 kilometers above sea level? Does adulthood suddenly begin on one’s 18th birthday? Does life itself suddenly begin at conception or at exactly 15 or 24 weeks after conception? Or are these matters of degree?

The shades-of-gray credo is also the title of the first chapter of Fuzzy Thinking. That book first appeared 30 years ago in 1993. It went on to appear in many translations both authorized and unauthorized. The book gave the term fuzzy thinking a cool cachet for a while in the 1990s.

Alas, it did not last.

The adjective fuzzy had returned to its old status as a cognitive slur by the fall of 2000. That was when the two candidates for the United States presidency accused each other of using “fuzzy math” in how they described or justified their proposed policies. The candidates did so even though their own home states supported research and development into literal fuzzy math. The New York Times on election day published my op-ed essay that detailed this national embarrassment.

But fuzzy thinking and fuzzy logic have not gone away.

Their theoretical foundations have only grown. And so have their applications. The book discusses many of the early applications of fuzzy logic. These applications produced smooth rule-based control of consumer electronics from cameras and washing machines to car subsystems from transmission control to anti-skid braking. The newer applications apply to larger-scale systems and to AI systems more generally. This growth is so extensive that we can refer to it as Fuzzy Logic 2.0.

The book Fuzzy Thinking lays the foundations for these advances and much more. For details the interested reader should visit my USC web page and browse the freely available videos and op-ed essays and the technical papers.

Modern fuzzy logic helps solve the central problem of modern black-box AI systems: How does an AI system explain itself?

This is the problem of XAI or explainable AI systems.

The most popular AI systems do not explain themselves at all. They train large-scale neural black boxes that map input patterns or questions to output classifications or answers. These input-output mappings are inscrutable in most cases. This holds because the mappings involve stunningly high mathematical dimensions and because they depend on equally stunningly large numbers of tunable parameters. These AI black boxes answer questions but they do not give a reliable confidence estimate of their answers. Nor do they give a logical or statistical audit trail of how a given input pattern maps to an output answer given what the network has learned versus what the network has simply guessed at.

Result: AI black boxes can hallucinate freely. A user has no systematic way to know when the AI black box guesses or hallucinates or how to separate out the hallucinatory spin from the data-based prediction. This problem has only increased with the exponential increase in computing power.

The fuzzy solution to the XAI problem is rules.

The rules themselves associate vague or fuzzy concepts in if-then form. A popular example from the book is the air-conditioning rule “If the air is cool then set the motor speed to slow.” Cool air and slow speeds are not binary concepts or properties. They are fuzzy because air temperatures are both cool and not cool to some degree just as motor speeds are both slow and not to some degree.

We now know that these rules correspond to mixed or combined probability curves. So a fuzzy system with 100 rules corresponds to a weighted mixture of 100 such probability curves. This result gives a type of uncertainty rapprochement between fuzz and probability or between vagueness and randomness. The result also gives in practice both a rule-based explanation and now a complete statistical description of which rules or subsystems contributed how much to each answer. This includes a total output confidence measure for each answer.

A fuzzy system can learn these rules by sampling from a trained neural black box. The sampling creates an explainable proxy system of the otherwise inscrutable AI black box. Fuzzy Thinking refers to this XAI technique as DIRO or “Data in, Rules out.”

The book also foresaw the modern use of fuzzy cognitive maps for large-scale causal models.

Causal reasoning is not black or white because most causes are partial and change over time. Complex events such as riots or thunderstorms have several partial causes that tend to swirl back on one another in rich tangles of feedback. Fuzzy cognitive maps allow these fuzzy causes to collide and produce dynamical equilibria that users can interpret as what-if predictions. Their fuzzy structure also allows any number of users to combine their fuzzy cognitive maps into a single richer map and use the combined map for causal predictions. This cognitive-mapping technique has become popular in the social sciences as well as in engineering.

But the central appeal of fuzzy logic remains its expressive power.

Factual claims such as “Grass is green” or “The air is cool” hold with an accuracy only somewhere between 0% or 100% even if they sometimes come with a probability disclaimer. And improving their accuracy takes work and not a mere binary declaration. Our most accurate statements of quantum electrodynamics have taken decades of work with pen and paper and with particle accelerators and supercomputers. Yet they offer precision to only a few decimal places. A pure binary factual truth would require precision to infinitely many decimal places.

Fuzzy or gray thinking is in this sense more than just a form of computer reasoning or artificial intelligence. It is a form of linguistic doubt or even skepticism. It is a form of computer or artificial reasonableness.Bart Kosko, Los Angeles, July 2023



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