Walter Alexandre Carnielli (born 11 January 1952 in

Campinas Campinas (, ''Plains'' or ''Meadows'') is a Brazilian municipality in São Paulo State, part of the country's Southeast Region. According to the 2020 estimate, the city's population is 1,213,792, making it the fourteenth most populous Brazilian ...

Brazil Brazil ( pt, Brasil; ), officially the Federative Republic of Brazil (Portuguese: ), is the largest country in both South America and Latin America. At and with over 217 million people, Brazil is the world's fifth-largest country by area ...

) is a Brazilian

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

logician Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...

, and

philosopher A philosopher is a person who practices or investigates philosophy. The term ''philosopher'' comes from the grc, φιλόσοφος, , translit=philosophos, meaning 'lover of wisdom'. The coining of the term has been attributed to the Greek th ...

, full professor of Logic at th
State University of Campinas (UNICAMP)
With Bachelor and Ms.C. degrees in mathematics at th
State University of Campinas
in

he obtained his Ph.D. in 1984 from the same university under the supervision of

Newton da Costa Newton Carneiro Affonso da Costa (born 16 September 1929 in Curitiba, Brazil) is a Brazilian mathematician, logician, and philosopher. He studied engineering and mathematics at the Federal University of Paraná in Curitiba and the title of his ...

and subsequently worked as a PostDoc at the

University of California at Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant univ ...

as a Research Fellow, following an invitation by

Leon Henkin Leon Albert Henkin (April 19, 1921, Brooklyn, New York - November 1, 2006, Oakland, California) was an American logician, whose works played a strong role in the development of logic, particularly in the theory of types. He was an active scholar ...

Areas of interest

Many-valued logic and paraconsistent logic

Carnielli contributed to the

proof theory Proof theory is a major branchAccording to Wang (1981), pp. 3–4, proof theory is one of four domains mathematical logic, together with model theory, axiomatic set theory, and recursion theory. Jon Barwise, Barwise (1978) consists of four correspo ...

and

semantics Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy Philosophy (f ...

many-valued logic Many-valued logic (also multi- or multiple-valued logic) refers to a propositional calculus in which there are more than two truth values. Traditionally, in Aristotle's logical calculus, there were only two possible values (i.e., "true" and "false" ...

s and

paraconsistent logic A paraconsistent logic is an attempt at a logical system to deal with contradictions in a discriminating way. Alternatively, paraconsistent logic is the subfield of logic that is concerned with studying and developing "inconsistency-tolerant" syste ...

s. His tableau method for many-valued logics generalized all previous treatments of the subject. His proposal of the possible-translations semantics (a new semantical interpretation for paraconsistent logics) contributed to a revival in the philosophical interpretation of paraconsistent logics.W. A. Carnielli (with M. E. Coniglio and J. Marcos). Logics of Formal Inconsistency. In: Handbook of Philosophical Logic, vol. 14, pp. 15–107. Eds.: D. Gabbay; F. Guenthner. Springer, 2007 The logics of formal inconsistency, which systematize a large class of paraconsistent logics, opened the way to the application of paraconsistency to computer science and to new philosophical investigations on paraconsistency.

Combinatorics, modulated logics, and combinations of logics

He also published on finite and infinite

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many appl ...

, and developed (with his collaborators A. M. Sette and P. A. Veloso) the modulated logics, a new kind of logics that allows the formalization of qualitative reasoning by means of special generalized quantifiers. His research also includes

model theory In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the s ...

, non-classical logics, foundations of

quantum computation Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though ...

, and combinations of logics.

Positions and awards

Carnielli served as a Director for the Centre for Logic, Epistemology and the History of Science at UNICAMP for three terms, and served as President of the Brazilian Logic Society. He was distinguished with an Alexander von Humboldt Grant for long term research stays in Germany, and served as en editor and/or a member of editorial boards of major journals, such as ''

Studia Logica ''Studia Logica'' (full name: Studia Logica, An International Journal for Symbolic Logic), is a scienific journal publishing papers employing formal tools from Mathematics and Logic. The scope of papers published in Studia Logica covers all scient ...

'', ''Logic and Logical Philosophy'',
Journal of Applied Logic
', ''CLE e-Prints'', ''Reports on Mathematical Logic'' and ''

Journal of Applied Non-Classical Logics ''Journal of Applied Non-Classical Logics'' is a peer-reviewed academic journal published by Taylor & Francis. It focusses on non-classical logic, in particular formal aspects (completeness, decidability, complexity), applications to artificial I ...

''. He is a recipient of the Telesio-Galilei Gold Medal Award 2012 in Philosophy and Mathematics.

Selected publications

Articles

*W. A. Carnielli. On coloring and covering problems for rook domains, ''

Discrete Mathematics Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous f ...

'' 57 (1985), pp. 9–16. *W. A. Carnielli. Systematization of the finite many-valued logics through the method of tableaux. ''

The Journal of Symbolic Logic ''The'' () is a grammatical article in English, denoting persons or things already mentioned, under discussion, implied or otherwise presumed familiar to listeners, readers, or speakers. It is the definite article in English. ''The'' is the m ...

'' 52 (2), 1987, pp. 73–493. *W. A. Carnielli (with Newton C. A. da Costa). Paraconsistent deontic logics. ''Philosophia – The Philos. Quarterly of Israel'' vol.16 numbers 3 and 4 (1988), pp. 293–305. *W. A. Carnielli. Hyper-rook domain inequalities. ''Studies in Applied Mathematics'' (Massachusetts Institute of Technology) 82,\ n.1 (1990), pp. 59–69. *W. A. Carnielli (with C. A. Di Prisco). Some results on polarized partition relations of higher dimension. ''Mathematical Logic Quarterly'' 39 (1993) pp. 461–474. *W. A. Carnielli (with P. A. S. Veloso). Ultrafilter logic and generic reasoning. In Computational Logic and Proof Theory (Vienna, 1997), pp. 34–53, Lecture Notes in Computer. Science 1289, Springer, Berlin, 1997. *W. A. Carnielli. Possible-translations semantics for paraconsistent logics. In: Frontiers in Paraconsistent Logic: Proceedings of the I World Congress on Paraconsistency, Ghent, 1998, pp. 159–72, edited by D. Batens et al., Kings College Publications, 2000. *W. A. Carnielli (with E. L. Monte Carmelo). K2,2-K1,n and K2,n-K2,n bipartite Ramsey numbers. ''Discrete Mathematics'', Vol. 223 (1-3), 2000, pp. 83–92. *W. A. Carnielli (with C. Sernadas and J. Rasga). Modulated fibring and the collapsing problem. ''

'' 67(4) 2002 pp. 1541–1569. *W. A. Carnielli (with J. Marcos). A taxonomy of C- systems . In: Paraconsistency- the Logical Way to the Inconsistent, Lecture Notes in Pure and Applied Mathematics, Vol. 228, pp. 01–94 2002. *W. A. Carnielli (with C. Caleiro, M. E. Coniglio and J. Marcos). Two’s company: The humbug of many logical values. In: Logica Universalis (Editor J.-Y. Béziau). Basel: Birkhäuser, 2005, p. 169-189. *W. A. Carnielli (with A. B.M. Brunner
Anti-intuitionism and paraconsistency
''Journal of Applied Logic'' Volume 3, Issue 1, March 2005, pages 161-184. *W. A. Carnielli (with M. E. Coniglio). Splitting Logics. In: We Will Show Them: Essays in Honour of Dov Gabbay. (Editors S. Artemov, H. Barringer, A. S. Avila Garcez, L. C. Lamb and J. Woods). London: King’s College Publications, 2005, v. 1, p. 389-414. *W. A. Carnielli (with M. E. Coniglio and J. Marcos). Logics of Formal Inconsistency. In: Handbook of Philosophical Logic, vol. 14, pp. 15–107. Eds.: D. Gabbay; F. Guenthner. Springer, 2007. *W. A. Carnielli (with M. E. Coniglio
Combining Logics. Stanford Encyclopedia of Philosophy
2007. *W. A. Carnielli (with J. Rasga and C. Sernadas). Preservation of Interpolation Features by Fibring. ''Mathematical Logic Quarterly'' Volume 18, Issue 1, 2008, pages 123-151. *W. A. Carnielli (with J. Rasga and C. Sernadas). Interpolation via translations. ''Mathematical Logic Quarterly'' Volume 55, Issue 5, 2009, pages 515-534. *W. A. Carnielli (with J. C. Agudelo). Paraconsistent Machines and their Relation to Quantum Computing.. ''Journal of Logic and Computation'' Volume 20, Issue 2, 2010, pages 573-595.

Books

*R. L. Epstein and W. A. Carnielli. ''Computability: computable functions, logic and the foundations of mathematics, with the timeline Computability and Undecidability''. Second edition. Wadsworth/Thomson Learning, Belmont, CA, 2000. *W. A. Carnielli and C. Pizzi. ''Modalità e multimodalità''. Franco Angeli, Milan, 2001. *W. A. Carnielli and R.L. Epstein ''Computabilidade: Funções Computáveis, Lógica e os Fundamentos da Matemática'' Winner of 200
Jabuti Award
a prestigious literary prize in Brazil. *W. A. Carnielli and C. Pizzi. ''Modalities and Multimodalities''. Springer-Verlag), 2008. *W. A. Carnielli, M. E. Coniglio, D. Gabbay, P. Gouveia and C. Sernadas. ''Analysis and Synthesis of Logics. How to Cut and Paste Reasoning Systems''. Applied Logic Series, Springer, 2008.

References

* Graduate Program in Philosophy-IFCH- UNICAMP * http://www.ifch.unicamp.br/pos/filosofia/index.php?texto=walter&menu=menudocente * Security and Quantum Information Group - (SQIG-IT) * http://www.it.pt/person_detail_p.asp?id=1896 * Alexander von Humboldt Foundation * http://www.humboldt-foundation.de/automat_db/pub_humboldtiana2.humboldtiana_index_pub?p_year=2000&p_group=1&p_fg2=2A
Walter Carnielli academic homepage''Pensadores da Matemática''
{{DEFAULTSORT:Carnielli, W. A. 20th-century Brazilian mathematicians Brazilian logicians 1952 births Living people Brazilian philosophers 20th-century Brazilian philosophers