The history of logic tells us that the binary-based logic proposed by Aristotle was, and continues to be, a pervasive force. Logic does, however, have a complex history and, in more recent years, the concept of ‘fuzzy-logic’ has emerged as a counter to the rigidity of Aristotelian logic and decision making. Fuzzy logic is an attempt to bridge the gap between mathematics and the fuzzy way humans naturally talk, think, and interact with the world.
Edy Portmann is a transdisciplinary researcher and professor of soft and cognitive computing at the Human-IST Institute of the University of Fribourg, Switzerland. As president of the Swiss-based FMsquare Foundation, Portmann is a fuzzy-logic evangelist on a mission to raise awareness of the importance of non-Aristotelian thinking in science and technology.
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Hello and welcome to Research Pod. Thank you for listening and joining us today.
In this episode we look at Edy Portmann’s research, a transdisciplinary researcher and professor of soft and cognitive computing at the Human-IST Institute of the University of Fribourg, Switzerland. As president of the Swiss-based FMsquare Foundation, Portmann is a fuzzy-logic evangelist on a mission to raise awareness of the importance of non-Aristotelian thinking in science and technology.
As early as the 1990s, during his apprenticeship as an automotive electrician and electronics technician, Portmann was introduced to the concept of fuzzy logic, which is a more varied approach to classical logic that accounts for infinite values between 0 and 1. His first encounter with the concept of this ‘fuzzy’ form of many-valued logic was when Portmann was discussing a famous race car with colleagues at work. In fact, the case was so thorny that the Supreme Court in London had to make a ruling on the integrity of the car.
The court case was about the legendary car known as Old Number One, which a car enthusiast wanted to buy for 10 million pounds. He had doubts whether this car was ‘genuine’, and believed the car was significantly different from the one that won the races due to the repairs and modifications it had undergone over time. The seller declared that it was the genuine car, arguing that ‘racing cars are usually altered in the course of their lifetime as a result of improvements, modifications, use, as well as accidents‘ – so, who was right?
As early as 1465, a new conversation arose in Leuven. The scholar Peter de Rivo held that, ‘whether in the present or in the future, everything either is or is not‘. This view originated in Aristotle’s principle of bivalence which stipulates that there are only two states, but Rivo’s argument was sharply rejected by his colleagues. The problem is that the underlying principle of bivalence only allows a single semantic truth value for a statement: that is, something must either be ‘true’ or ‘false’. There can be no middle ground with Aristotelian reasoning, which is why the judge in the case of the race car was struggling. Was there no way for them both to be right?
Lao Tzu, a Chinese philosopher from 6th century BCE who is commonly credited as the founder of Taoism, believed that our world is made up of opposites. His texts emphasise the fuzzy virtues of ‘effortless action’ and ‘naturalness’ beyond the logic of empirical binaries.
Lao Tzu perceives our world through balance, wherein opposing forces are paradoxically in total equilibrium with each other. Think about this for a moment: There is no ‘true’ without a ‘false’, because without the term true we would not comprehend the term false fully, either. We need opposites to understand meaning.
In the Middle Ages, most Western scholars tended to accept Aristotle’s principle, yet some thinkers continued to push the question. For example, some 170 years before the dispute in Leuven, first scholars toyed with a non-binary value straight from Aristotle. In the 20th century, this would spur the logician Jan Łukasiewicz to revolt against with his three-valued logic, a precursor of the fuzzy logic, hinted at in a lecture as early as in 1918.
The electrical engineer and computer scientist Lotfi Zadeh developed this notion of fuzzy logic in his highly cited paper on ‘fuzzy sets’, which included a mathematical formulation of this problem. Zadeh’s proposed solution to the binary principle is based on flexibility between set boundaries, which enables an exact capture of the imprecise by combining classical logic with the ‘fuzziness’ of human experience. As Zadeh hinted himself, ‘everything is a matter of degree’.
Going back to the Supreme Court case, the judge could now draw on this vagueness specification. He realised that the race car could not be considered truly genuine, but that it was also wrong to consider it merely a replica. In the end, however, he sided with in the seller in interpreting ‘genuine’ as ‘authentic’.
Would it not be a step forward if our Artificial Intelligence could interpret human language and its semantics in a similar holistic way to the judge in the case of Old Number One? Portmann asks himself such questions as a non-Aristotelian researcher and in doing so, follows the soft computing tradition of Zadeh, who also invented ‘computing with words and perceptions’ as a further development of fuzzy logic.
Portmann also shows why we should be moving from measurement-based to perception-based computing by highlighting a cultural difference between Westerners and people from the Congo. If you put a vertical line next to a horizontal line of the same length and ask which one is longer, Westerners tend to choose the horizontal one, while the Suku in the Congo overwhelmingly say the vertical line is longer.
This difference may be environmental; Suku live in grasslands where the horizon is visible at all times and so they are able to easily detect even the smallest elevations in the distance. Since verticality makes a stronger impression on them, they may also focus more on it.
From this example, we learn that culture and experience also influence our minds on a subconscious level. We would like to think that our decisions are made on rational and objective bases, and yet we cannot escape our habits of thought. We live with deep-rooted and invisible biases.
Fuzzy logic is an attempt to bridge the gap between mathematics and the fuzzy way humans naturally talk, think, and interact with the world. With his logic, Zadeh presented a mathematical model that can deal with ambiguity and uncertainty in a human way. Rather than creating sharp boundaries for real-world concepts, Zadeh’s boundaries are fuzzy. Thus, an element is not simply in or out of the set, as in classical set theory, but is somewhere on an infinite continuum in-between.
When Portmann assisted Zadeh as his last postdoctoral fellow, the model was evolving into computing with words and perceptions, a methodology for making inferences, calculations, and decisions based rooted not only in measurement, but also perception based on data and information described in natural, or ‘human’, language. There are good reasons for this attempt to calculate with words: Much of our knowledge is described in natural language, words are less precise than numbers, and precision has its price.
So, if there is a tolerance for inaccuracy, it can be better described by using words instead of exact numbers. According to Portmann, a calculation with words and underlying perceptions can be seen as a non-Aristotelian formalism for dealing with imprecise data and information. In other words, Portmann builds on non-linear models that more closely reflect the non-binary complexity of our world, blending logic with human experience and in turn opening the door to a major expansion of the role of perception and natural languages in science and technology.
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