This chapter is an intellectual autobiography centered on a lifelong commitment to the study of reasoning as a formal, epistemic, and mathematical phenomenon. My early fascination with concrete mathematics and discrete problem solving gradually evolved into a systematic engagement with logic in its proof-theoretical, model-theoretical, semantic, and operational dimensions. Throughout my career, I have worked on the foundations and development of non-classical logics, with particular emphasis on paraconsistent, paracomplete, modal, and many-valued systems, as well as on their interaction with probability theory, formal epistemology, and models of uncertain and defeasible reasoning. A central theme of my research has been the integration of symbolic and probabilistic approaches to inference, aiming to account for contradiction and inconsistency, partial information, evidential support, and causal relevance within rigorous formal frameworks. This chapter traces the intellectual path leading from early mathematical intuitions to the construction of logical systems and methodological tools designed to expand the expressive and inferential power of contemporary logic. It reflects on the motivations, conceptual challenges, and theoretical consequences of this trajectory, offering a unified perspective on reasoning beyond the limits of classical consistency.

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A Fascination for Reasoning

  • Walter Alexandre Carnielli

摘要

This chapter is an intellectual autobiography centered on a lifelong commitment to the study of reasoning as a formal, epistemic, and mathematical phenomenon. My early fascination with concrete mathematics and discrete problem solving gradually evolved into a systematic engagement with logic in its proof-theoretical, model-theoretical, semantic, and operational dimensions. Throughout my career, I have worked on the foundations and development of non-classical logics, with particular emphasis on paraconsistent, paracomplete, modal, and many-valued systems, as well as on their interaction with probability theory, formal epistemology, and models of uncertain and defeasible reasoning. A central theme of my research has been the integration of symbolic and probabilistic approaches to inference, aiming to account for contradiction and inconsistency, partial information, evidential support, and causal relevance within rigorous formal frameworks. This chapter traces the intellectual path leading from early mathematical intuitions to the construction of logical systems and methodological tools designed to expand the expressive and inferential power of contemporary logic. It reflects on the motivations, conceptual challenges, and theoretical consequences of this trajectory, offering a unified perspective on reasoning beyond the limits of classical consistency.