THREE QUESTIONS TO WALTER CARNIELLI

1) When and how did you first hear about paraconsistent logic and start your work?
Around 1975 Ayda Arruda selected a group of students at the University of Campinas (Unicamp) to extracurricular study in logic, taking advan- tage of the fact that Newton da Costa was a guest professor at IMECC by that time. Itala D’Ottaviano was in this group, and as a young lecturer was my teacher in differential and integral calculus. The influence of professors Ayda Arruda, Newton da Costa, Andrés Raggio, and Rolando Chuaqui were crutial in my decision of changing algebra and number theory, my themes at the time, for logic.
I did not like paraconsistent logic, and I found the semantics of the calculi Cn, which was all that we had at the time, to be quite awkward. I decided to study logic, but avoiding touching on paraconsistent logic, and Newton da Costa never objected against this view. My PhD thesis, under his supervision , was on the foundations of many-valued logics in general, both propositional and first order. At the same time, I was much interested in number theory and combinatorial problems, and I could not decide which of the fields to follow. The only thing Newton asked of me was that, regardless of what I did, I would publish it in the best journal possible. I published my PhD thesis in the Journal of Symbolic Logic in 1987, and the treatment I proposed became a kind of "classical" reference. Newton da Costa was happy with that, and never demanded me to study paraconsistent logic.

2) How did you further develop your work on paraconsistent logic?
It started with my dissatisfaction with the work done at the time by da Costa, Elias Alves, and others. Great work, but not what I would have expected. In the 1990s I proposed the semantics of possible translations, and the special case of society semantics in the PhD thesis of Mamede Lima-Marques, of whom I was co-supervisor of graduate studies in Toulouse. All this in my opinion gave a much better justification for paraconsistent logics, and the work culminated in the logics of formal inconsistency (LFIs), a joint effort with João Marcos, my advisee at the time, and with Marcelo Coniglio, both of whom did a lot to revive the area of paraconsistency in Brazil, which was kind of dormant (not to say dead). TheLFIs offered a new and general approach to paraconsistent logcs that permitted better connections to computer science, linguistics, foundations of mathematics and even more acceptable philosophical interpretations of paraconsistency.

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In Berkeley in 1984.

3) How do you see the evolution of paraconsistent logic? What are the future challenges? I do not see paraconsistency as any revolution, but as an adaptation of standard logic in the direction of general human reasoning. Standard logic is quite good for making mathematics, but not for common reasoning, including contemporary scientific reasoning and quantum phenonena, reasoning in Artificial Intelligence and in Machine Learning. We need a lightweight logic.
The relationship between paraconsistency and rationality is an essen- tial topic that should be studied in all its aspects. The Centre for Logic, Epistemology, and History of Science at Unicamp recently approved my proposal for the creation of a ‘Laboratory of Logic and Rationality’. The idea is to form a nucleus that central- izes the study of areas such as the relation between probabilistic systems, Markov processes and alternative logics, argumentation schemes, automatic and pragmatic reasoning (with applications to AI and Machine Learning), computability and logic, infor- mation and logic, economics and logic, and, not the least, philosophy.
Recent work in collaboration with Abilio Rodrigues, Juliana Bueno-Soler and Marcelo Coniglio point to this direction. I was particularly delighted to have received the CAPES Prize for the best PhD dissertation in Philosophy for 2019, conferred to my student Bruno Mendonça and to myself, among hundreds of competitors. When a prize in Philosophy is given to a work in Logic those old times when some members of the philosophical comunity in Brazil doubted the "relevance of Logic for Philosphy" are happily behind.