Valeria Correa Vaz de Paiva 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

computer scientist A computer scientist is a person who is trained in the academic study of computer science. Computer scientists typically work on the theoretical side of computation, as opposed to the hardware side on which computer engineers mainly focus (al ...

. Her work includes research on logical approaches to

computation Computation is any type of arithmetic or non-arithmetic calculation that follows a well-defined model (e.g., an algorithm). Mechanical or electronic devices (or, historically, people) that perform computations are known as ''computers''. An es ...

, especially using

category theory Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Nowadays, cate ...

knowledge representation Knowledge representation and reasoning (KRR, KR&R, KR²) is the field of artificial intelligence (AI) dedicated to representing information about the world in a form that a computer system can use to solve complex tasks such as diagnosing a medic ...

and

natural language In neuropsychology, linguistics, and philosophy of language, a natural language or ordinary language is any language that has evolved naturally in humans through use and repetition without conscious planning or premeditation. Natural languages ...

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 ...

, and

functional programming In computer science, functional programming is a programming paradigm where programs are constructed by Function application, applying and Function composition (computer science), composing Function (computer science), functions. It is a declar ...

with a focus on foundations and type theories...

Education

De Paiva earned a bachelor's degree in mathematics in 1982, a master's degree in 1984 (on pure

algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary a ...

) and completed a doctorate at the

University of Cambridge , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...

in 1988, under the supervision of

Martin Hyland (John) Martin Elliott Hyland is professor of mathematical logic at the University of Cambridge and a fellow of King's College, Cambridge. His interests include mathematical logic, category theory, and theoretical computer science. Education H ...

. UCAM-CL-TR-213 Her thesis introduced

Dialectica space Dialectica spaces are a categorical way of constructing models of linear logic. They were introduced by Valeria de Paiva, Martin Hyland's student, in her doctoral thesis, as a way of modeling both linear logic and Gödel's Dialectica interpretat ...

s, a categorical way of constructing models of

linear logic Linear logic is a substructural logic proposed by Jean-Yves Girard as a refinement of classical and intuitionistic logic, joining the dualities of the former with many of the constructive properties of the latter. Although the logic has also be ...

, based on

Kurt Gödel Kurt Friedrich Gödel ( , ; April 28, 1906 – January 14, 1978) was a logician, mathematician, and philosopher. Considered along with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel had an imme ...

Dialectica interpretation In proof theory, the Dialectica interpretation is a proof interpretation of intuitionistic arithmetic (Heyting arithmetic) into a finite type extension of primitive recursive arithmetic, the so-called System T. It was developed by Kurt Gödel to pr ...

Career and research

She worked for nine years at PARC in

Palo Alto, California Palo Alto (; Spanish language, Spanish for "tall stick") is a charter city in the northwestern corner of Santa Clara County, California, United States, in the San Francisco Bay Area, named after a Sequoia sempervirens, coastal redwood tree kno ...

, and also worked at Rearden Commerce and

Cuil Cuil ( ) was a search engine that organized web pages by content and displayed relatively long entries along with thumbnail pictures for many results. Cuil said it had a larger index than any other search engine, with about 120 billion web pages.L ...

before joining Nuance. She is an honorary

research fellow A research fellow is an academic research position at a university or a similar research institution, usually for academic staff or faculty members. A research fellow may act either as an independent investigator or under the supervision of a pr ...

in computer science at the

University of Birmingham , mottoeng = Through efforts to heights , established = 1825 – Birmingham School of Medicine and Surgery1836 – Birmingham Royal School of Medicine and Surgery1843 – Queen's College1875 – Mason Science College1898 – Mason Univers ...

.Home page
University of Birmingham, retrieved 2015-07-24. She is currently on the Council of the Division for Logic, Methodology and Philosophy of Science and Technology of the International Union of History and Philosophy of Science and Technology (2020–2023).

Selected publications

* ''Applied Category Theory in Chemistry, Computing, and Social Networks''. (with Baez, Cho, Ciccala and Otter). Notices of the American Mathematical Society, vol. 69, number 2, February 2022. *''Term Assignment for Intuitionistic Linear Logic''. (with Benton, Bierman and Hyland). Technical Report 262,

University of Cambridge Computer Laboratory The Department of Computer Science and Technology, formerly the Computer Laboratory, is the computer science department of the University of Cambridge. it employed 35 academic staff, 25 support staff, 35 affiliated research staff, and about 15 ...

. August 1992. *''Lineales''. (with J.M.E. Hyland) In "O que nos faz pensar" Special number in Logic of "Cadernos do Dept. de Filosofia da PUC", Pontificial Catholic University of Rio de Janeiro, April 1991. *''A Dialectica-like Model of Linear Logic''. In Proceedings of Category Theory and Computer Science, Manchester, UK, September 1989. Springer-Verlag LNCS 389 (eds. D. Pitt, D. Rydeheard, P. Dybjer, A. Pitts and A. Poigne). *''The Dialectica Categories''. In Proc of Categories in Computer Science and Logic, Boulder, CO, 1987. Contemporary Mathematics, vol 92, American Mathematical Society, 1989 (eds. J. Gray and A. Scedrov)

References

{{DEFAULTSORT:De Paiva, Valeria Correa Vaz Year of birth missing (living people) Living people Brazilian mathematicians Brazilian computer scientists American computer scientists American women mathematicians Women logicians Brazilian women computer scientists Alumni of the University of Cambridge Brazilian logicians Category theorists 20th-century American mathematicians 21st-century American mathematicians Scientists at PARC (company) 20th-century women mathematicians 21st-century women mathematicians 20th-century American women 21st-century American women