Turning Around the Ideas of ‘Meaning’ and ‘Complement’

Abstract

Since the inception of fuzzy sets in 1965, Lotfi A. Zadeh viewed them by specifying the meaning of their linguistic labels in a given universe of discourse. Anyway, it lacked to clarify the same concept of meaning in a way able to separate those words that can be submitted to scientific scrutiny from those that cannot, as well as to show which it is, into meaning, the actual role of the membership function of a fuzzy set. Once rooted in the Wittgenstein’s ‘identification’ of meaning and linguistic use, meaningful predicates can be seen as those represented by quantities whose measures are the membership functions. Closed such question, it still lacks to completely study the meaning of connectives that, in fuzzy logic, are not universal as they are in classical logic, but context-dependent and purpose-driven; hence and like fuzzy sets, should be carefully designed at each case. When fuzzy logic was theoretically introduced, from the mid-sixties to the last eighties of the XX century, crisp deductive logic ideas were prevalent over those of conjectural ordinary reasoning to represent, for instance, what is ‘not properly covered under a linguistic label’ and only the concept of pseudo-complement was considered, even if antonyms are essential for linguistic variables, a basic tool in the applications of fuzzy logic. Fifty years later, when fuzzy logic comes to be surpassed by Zadeh’s ‘Computing with Words’, perhaps some thoughts at the respect could be suitable towards its applicability to represent complex linguistic statements in common sense reasoning. This paper just tries to reflect on one of the subjects fuzzy logic perhaps manages in a too simplistic way, almost uniquely by means of the strong negation 1-id, and from an analogous point of view to that of logic that not always is close to ordinary reasoning. It refers to a general concept of ‘complement’, a concept that tries to ‘collectivize’ all that does not properly lay under a given concept but should not to be forgot since it completes what is taken into account. In the, say traditional treatment of set’s complement, it lacks the consideration of what actually happens in language, the true background of what fuzzy logic tries to represent, where ‘opposites’ play a role that is, at least, weakly but equal or more important that that played by ‘not’. Fuzzy logic’s praxis just considers both negation and antonym through their membership functions, avoids a deep semantic analysis of both concepts, has not criteria to decide when membership functions should, or should not, be functionally expressed from the membership function of the initial linguistic label, as well as how it can be done with the known models of negation functions. The process followed by fuzzy logic’s practitioners for designing opposites and negation is often too lose and quickly done for well adjusting representation to what is been represented. The point of view taken in this paper is not mathematical in nature, but is just a first trial to reflect on what can surround a linguistic concept of ‘complement’, of what is either ‘not’, or is ‘opposite’, to what is qualified by a predicate. The paper only tries to open the eyes of theoreticians towards the true ground on which fuzzy logic is anchored, the natural language’s practice; fuzzy logic cannot be neither a mathematical subject, nor one of just a computational interest, but a discipline of the imprecise similar to an experimental science.

To Professor Christer Carlsson.