# Walter Carnielli

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**Walter Alexandre Carnielli** (born on 11 January in 1952 in Campinas, Brazil) is a Brazilian mathematician, logician, and philosopher, full professor of Logic at the State University of Campinas (UNICAMP). With a Bachelor and a Ms.C. degree in mathematics at the State University of Campinas in Campinas he obtained his Ph.D. in 1984 in the same university under the supervision of Newton da Costa and subsequently stayed as a PostDoc at the University of California at Berkeley as a Research Fellow, following an invitation by Leon Henkin.

## Contents

## Areas of interest

### Many-valued logic and paraconsistent logic

Carnielli contributed to the proof theory and semantics of many-valued logics and paraconsistent logics. His tableau method for many-valued logics generalized all previous treatments of the subject [W. A. Carnielli. Systematization of the finite many-valued logics through the method of tableaux. The Journal of Symbolic Logic 52 (2), 1987, pp. 73–493]. His proposal of the possible-translations semantics (a new semantical interpretation for paraconsistent logics) contributed to a revival in the philosophial interpretation of paraconsistent logics [[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 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, and developed (with his collaborators A. M. Sette an P. A. Veloso) the modulated logics, a new kind of logics which allows the formalization of qualitative reasoning by means of special generalized quantifiers. His research also includes model theory, non-classical logics and foundations of quantum computation 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, Logic and Logical Philosophy, Journal of Applied Logic, CLE e-Prints, Reports on Mathematical Logic and *Journal of Applied Non-Classical Logics*. 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*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*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.
*The Journal of Symbolic Logic*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 2007 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*