Name Walter Carnielli Role Mathematician | Academic advisor Newton da Costa | |

Books Modalities and Multimodalities |

## Cle4science colloquia walter carnielli

**Walter Alexandre Carnielli** (born 11 January 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

- Cle4science colloquia walter carnielli
- Walter carnielli formal plenitude and curry s paradox sketch of an expanded theory for arithmetic
- Many valued logic and paraconsistent logic
- Combinatorics, modulated logics, and combinations of logics
- Positions and awards
- Articles
- Books
- References

## Walter carnielli formal plenitude and curry s paradox sketch of an expanded theory for arithmetic

## 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 and 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.

## Articles

*Discrete Mathematics*57 (1985), pp. 9–16.

*The Journal of Symbolic Logic*52 (2), 1987, pp. 73–493.

*Philosophia – The Philos. Quarterly of Israel*vol.16 numbers 3 and 4 (1988), pp. 293–305.

*Studies in Applied Mathematics*(Massachusetts Institute of Technology) 82,\ n.1 (1990), pp. 59–69.

*Mathematical Logic Quarterly*39 (1993) pp. 461–474.

*Discrete Mathematics*, Vol. 223 (1-3), 2000, pp. 83–92.

*The Journal of Symbolic Logic*67(4) 2002 pp. 1541–1569.

*Journal of Applied Logic*Volume 3, Issue 1, March 2005, pages 161-184.

Mathematical Logic Quarterly *Volume 18, Issue 1, 2008, pages* 123-151.

*Mathematical Logic*

Quarterly *Volume 55, Issue 5, 2009, pages 515-534.*

*Journal of Logic and Computation*Volume 20, Issue 2, 2010, pages 573-595.

## Books

*Computability: computable functions, logic and the foundations of mathematics, with the timeline Computability and Undecidability*. Second edition. Wadsworth/Thomson Learning, Belmont, CA, 2000.

*Modalità e multimodalità*. Franco Angeli, Milan, 2001.

*Computabilidade: Funções Computáveis, Lógica e os Fundamentos da Matemática*Winner of 2007 Jabuti Award, a prestigious literary prize in Brazil.

*Modalities and Multimodalities*. Springer-Verlag), 2008.

*Analysis and Synthesis of Logics. How to Cut and Paste Reasoning Systems*. Applied Logic Series, Springer, 2008.