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On the logos : a naïve view on ordinary reasoning and fuzzy logic
Trillas E., Springer International Publishing, New York, NY, 2017. 213 pp. Type: Book (978-3-319560-52-6)
Date Reviewed: Apr 9 2018

There are many books that you read to get answers to questions and doubts, and there are few books that leave you with more questions and doubts than before reading them. Yet, you can still be satisfied with such books because they give you the idea of the exciting dynamism of science, which does not fear to attack consolidated assumptions and to question them from their very foundations. Trillas’ volume is one such book.

It is about ordinary reasoning, that is, reasoning carried out by laypeople. Whilst a common approach for studying ordinary reasoning essentially reduces it to some formal logic, based on a number of axiomatic properties that are taken for granted because of their apparent obviousness, Trillas takes almost nothing for granted. Very few axioms define a “basic algebra of fuzzy sets” (BAF) upon which very disparate topics are discussed, from deduction to analogy, creative reasoning, speculations, uncertainty, and so on. This way, not only classical logic and fuzzy logic can be seen, but also particular cases of BAF; Trillas’ approach enables discussion of topics that are usually left outside of formal theories, although they are integral parts of common reasoning.

The book starts with a reconsideration of the concept of a fuzzy set. In much literature, fuzzy sets are actually identified with their membership functions (actually, there is no distinction between these two concepts). Trillas proposes a different view, in which membership functions are (approximate) measures of the meaning of fuzzy sets, the latter being collectives generated by linguistic labels. In a sense, this point of view is revolutionary: fuzzy sets are no more characterized by membership functions (just like classical sets are characterized by characteristic functions), but are measured by membership functions; therefore, several membership functions can be associated with the same fuzzy set. If accepted, this new point of view has a far-reaching impact in the research on fuzzy set theory, as well as on fuzzy modeling and applications.

The book proceeds with short chapters in which specific arguments are discussed in a semiformal style. The essence of the argumentation is that ordinary reasoning cannot be studied on a purely algebraic basis and extreme care must be taken before introducing any additional property in the theory or model that is developed, because any addition may make sense for some types of reasoning but lose significance or even be dangerous for other types. Surprisingly, this warning applies also for properties that are usually considered as universal (an example: commutativity of conjunction). This is quite a problem that calls for further investigation and, as the same author wishes, a new holistic approach in automated reasoning to understand the sense of natural language sentences before choosing the right operations to grab the meaning of the words within.

The second part of the book, “Gathering Questions,” is a “dark jungle of more or less ambiguous ideas” where the reader cannot help but reflect on many issues concerning classical, fuzzy, and less orthodox reasoning schemes.

This is not a technical book. It is more of a philosophical text that touches several issues that daily confront people involved in artificial intelligence, natural language understanding, and fuzzy modeling. Due to its thought-provoking nature, sometimes re-reading is necessary in order to fully understand the author’s thoughts. Reading this book may raise feelings of a disparate nature: excitement, perplexity, enlightenment, and incompleteness. In all cases, the ingenuous will surely find stimuli for further thinking and meditation.

Reviewer:  Corrado Mencar Review #: CR145958 (1806-0286)
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