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Paulo Guilherme Santos has a PhD in Mathematics by NOVA FCT and in Computer Science by Universität Tübingen. He was a visiting researcher at Carnegie Mellon University under a Fulbright scholarship. Since 2023, he is an Invited Assistant Professor at Lisbon Polytechnic University. PGS published 7 articles in journals. In addition, he has 1 section of a book and 1 book. PGS organized 5 event and received 10 awards and/or honors. Works in the area(s) of Exact Sciences with emphasis on Mathematics with emphasis on Pure Mathematics. In his professional activities interacted with 11 collaborator(s) co-authorship of scientific papers.
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Identification

Personal identification

Full name
Paulo Guilherme Domingos Canha Moreira Santos
Date of birth
1996/02/13
Gender
Male

Citation names

  • Santos, Paulo G.

Author identifiers

Ciência ID
7011-9F20-D8FD
ORCID iD
0000-0002-6686-005X

Email addresses

  • paulo.g.santos.logic@gmail.com (Professional)

Websites

Knowledge fields

  • Exact Sciences - Mathematics - Pure Mathematics

Languages

Language Speaking Reading Writing Listening Peer-review
Portuguese (Mother tongue)
English Advanced (C1) Advanced (C1) Advanced (C1) Advanced (C1)
French Elementary (A2) Elementary (A2) Elementary (A2) Elementary (A2)
German Beginner (A1) Beginner (A1) Beginner (A1) Beginner (A1) Beginner (A1)
Education
Degree Classification
2019/03 - 2023/06
Concluded
 Doutoramento em Matemática (Doutoramento)
Universidade Nova de Lisboa Faculdade de Ciências e Tecnologia, Portugal

Eberhard Karls Universität Tübingen, Germany
"On Notions of Provability " (THESIS/DISSERTATION)
2017/09 - 2019/06/21
Concluded
 Mestrado em Matemática e Aplicações (Mestrado)
Universidade Nova de Lisboa Faculdade de Ciências e Tecnologia, Portugal
 20
2014 - 2017
Concluded
 Licenciatura em Matemática (Licenciatura)
Universidade Nova de Lisboa Faculdade de Ciências e Tecnologia, Portugal
 17
Affiliation

Teaching in Higher Education

Category
Host institution 		Employer
2023/09 - Current Invited Adjunct Teacher (Polytechnic Teacher) Instituto Politécnico de Lisboa Instituto Superior de Contabilidade e Administração de Lisboa, Portugal
Instituto Politécnico de Lisboa Instituto Superior de Contabilidade e Administração de Lisboa, Portugal
2023/09 - 2024/02 Invited Assistant Professor (University Teacher) Universidade Nova de Lisboa Faculdade de Ciências e Tecnologia, Portugal
Universidade Nova de Lisboa Faculdade de Ciências e Tecnologia, Portugal
2022/03 - 2022/08 Assistant (University Teacher) Universidade Nova de Lisboa Faculdade de Ciências e Tecnologia, Portugal
Universidade Nova de Lisboa Faculdade de Ciências e Tecnologia, Portugal
2018/09 - 2018/09 Tutor (University Teacher) Universidade Nova de Lisboa Faculdade de Ciências e Tecnologia, Portugal
Universidade Nova de Lisboa Faculdade de Ciências e Tecnologia, Portugal
2017/09 - 2017/09 Tutor (University Teacher) Universidade Nova de Lisboa Faculdade de Ciências e Tecnologia, Portugal
Universidade Nova de Lisboa Faculdade de Ciências e Tecnologia, Portugal
Projects

Grant

Designation Funders
2016/01 - 2018/12 Hilbert's 24th Problem
Provided by PTCRIS: 141209
 Fundação para a Ciência e a Tecnologia
Outputs

Publications

Book
  1. Santos, Paulo. Diagonalization in Formal Mathematics. 2020.
    10.1007/978-3-658-29111-2
Book chapter
  1. Reinhard Kahle; Paulo Guilherme Santos. "Paradoxes, Intuitionism, and Proof-Theoretic Semantics". 2024.
    10.1007/978-3-031-50981-0_12
Journal article
  1. Reinhard Kahle; Isabel Oitavem; Paulo Guilherme Santos. "Numeral completeness of weak theories of arithmetic". Journal of Logic and Computation (2023): http://dx.doi.org/10.1093/logcom/exad075.
    10.1093/logcom/exad075
  2. Paulo Guilherme Santos; Wilfried Sieg; Reinhard Kahle. "A new perspective on completeness and finitist consistency". Journal of Logic and Computation (2023): http://dx.doi.org/10.1093/logcom/exad021.
    10.1093/logcom/exad021
  3. PAULO GUILHERME SANTOS; REINHARD KAHLE. "VARIANTS OF KREISEL’S CONJECTURE ON A NEW NOTION OF PROVABILITY". The Bulletin of Symbolic Logic 27 4 (2021): 337-350. https://doi.org/10.1017/bsl.2021.68.
    10.1017/bsl.2021.68
  4. Santos, Paulo G.. "k-Provability in PA". Logica Universalis (2021): http://dx.doi.org/10.1007/s11787-021-00278-1.
    10.1007/s11787-021-00278-1
  5. Malheiro, António; Santos, Paulo Guilherme. "A Note on a Unifying Proof of the Undecidability of Several Diagrammatic Properties of Term Rewriting Systems". ArXiv (2019): https://publons.com/wos-op/publon/58347553/.
  6. Vítor H. Fernandes; Paulo G. Santos. "Endomorphisms of semigroups of order-preserving partial transformations". Semigroup Forum (2018): https://doi.org/10.1007%2Fs00233-018-9948-z.
    10.1007/s00233-018-9948-z
  7. Paulo Guilherme Santos; Reinhard Kahle. "Diagonalização, Paradoxos e o Teorema de Löb". Revista Portuguesa de Filosofia 73 3-4 (2017): 1169-1188. https://doi.org/10.17990%2Frpf%2F2017_73_3_1169.
    10.17990/rpf/2017_73_3_1169
Thesis / Dissertation
  1. "On Notions of Provability". 2023. https://publikationen.uni-tuebingen.de/xmlui/handle/10900/148840.
    10.15496/PUBLIKATION-90180
Activities

Oral presentation

Presentation title Event name
Host (Event location)
2024 General notions of consistency Days in Logic 2024
IST
2023 'Provability Implies Provable Provability in FLINSPACE' LYMC2023,
Universidade Aberta
2023 'Provability Implies Provable Provability' using FLINSPACE TCA 2023
CAR Pocinho
2023 ¿-Reflexive Theories Seminário de Lógica Matemática
FCUL
2022 ‘Provability Implies Provable Provability’ in FLINSPACE Days in Logic 2022
Universidade do Algarve
2022 ‘Provability Implies Provable Provability’ in FLINSPACE Proof Society Autumn School and Workshop 2022
Utrecht University
2022 An Introduction to Numeral Completeness Algebra and Logic Seminar
FCT NOVA
2021/10 k-provability in PA Logica Universalis Webinar
Logica Universalis, Springer
2021/09 Numeral Completeness of Theories of Arithmetic Doktorandentreff
Technische Universität Darmstadt (Darmstadt, Germany)
2021/07 Numeral Completeness (https://youtu.be/8Dgcrj5W3lU) Celebrating 90 Years of Gödel's Incompleteness Theorems
Universität Tübingen (Tübingen, Germany)
2021/07 Yablo's Paradox Revisited (https://youtu.be/DukV0fiEfCo) Celebrating 90 Years of Gödel's Incompleteness Theorems
Universität Tübingen (Tübingen, Germany)
2021/02 k-provability in PA (https://youtu.be/3qVo0JtguGM) Carl Friedrich von Weizsäcker-Kolloquium
Carl Friedrich von Weizsäcker-Kolloquium Universität Tübingen (Tübingen, Germany)
2021/02 90 anos de incompletude Seminário de Alunos de Matemática
Seminário de Alunos de Matemática FCT-NOVA (Portugal)
2021/01 k-provability in PA
World Logic Day, IST
2021/01 90 anos de incompletude
Mathmasters at DM FCT-NOVA
2020/12 Arithmetical Numeral Completeness
FCUL (Portugal)
2020/01 Adapted Kreisel’s conjecture via reflexion principles on a new provability predicate Days in Logic
Faculdade de Ciências, Universidade de Lisboa (Lisbon, Portugal)
2019/12 Adapted Kreisel's conjecture via reflexion principles on a new provability predicate Algebra and Logic Seminar, FCT-NOVA
(Lisbon, Portugal)
2019/11 Yablo’s paradox revisited Circularity in Syntax and Semantics
2019/07 Kreisel’s Conjecture and Reflexion Principles: Two Variations of the Conjecture 5th International Workshop on Structure and Deduction
(Dortmund, Germany)
2019/07 A Computational Account Of Simplicity With A View Towards Hilbert’s 24th Problem Proof Computation, Complexity 2019
Mittag-Leffler Institute (Djursholm, Sweden)
2019/07 Speed-Up of Kreisel's Conjecture Via Reflexion Principles: Two Variations of the Conjecture Gödel's Legacy
(Vienna, Austria)
2018/10 A Self-Referential Interpretation of Yablo’s Paradox Using Linear Temporal Logic Algebra and Logic Seminar, FCT NOVA
FCT NOVA (Portugal)
2018/05 Towards an Axiomatic View do Double-Diagonalization: Mathematics and Yablo’s Paradox Algebra and Logic Seminar, FCT NOVA
FCT NOVA (Portugal)
2018/04 Diagonalization Algebra and Logic Seminar, FCT NOVA
FCT NOVA (Portugal)
2018/01 Diagonalization (http://w3.math.uminho.pt/DiL2018/program.html) Days in Logic 2018
Universidade de Aveiro (Aveiro, Portugal)
2017/08 Diagonalization (https://kgs.logic.at/madeira/program) International Summer School for Proof Theory in First-Order Logic in Funchal, Madeira
Universidade da Madeira (Funchal , Portugal)
2017/02 Diagonalization (https://www.math.tecnico.ulisboa.pt/~ggranja/Talentos/Oficina/17_horario_lisboa.pdf) Seminário Diagonal
ISEG (Portugal)
2016/07 On a Construction of Ockham Algebras (http://enspm16.spm.pt/files/outros/algebra_combinatoria.pdf) Encontro Nacional SPM
(Portugal)
2016/02 On a Construction of Ockham Algebras (https://www.math.tecnico.ulisboa.pt/~ggranja/Talentos/Oficina/16_horario_lisboa.pdf) Seminário Diagonal
FCT NOVA (Portugal)

Event organisation

Event name
Type of event (Role) 		Institution / Organization
2023 - Current TCA 2023, CAR Pocinho. Organized the parallel session Logic and Computation (2023)
Conference (Co-organisor)
2022 - Current LYMC2022, FCUL. Conference directed for Postdocs, PhD, and Master students of Lisbon Universities (2022)
2022 - Current ENSPM2022, Pol. Tomar. Organized the parallel session Young Researchers (2022)
Conference (Co-organisor)
2021 - Current LYMC 2021, NovaMath, FCT-NOVA. Conference directed for Postdocs, PhD, and Master students of Lisbon Universities (2021)
2022/01 - 2022/01 World Logic Day 2022 Portugal (2022 - 2022)
Conference (Co-organisor)
 Universidade Nova de Lisboa Faculdade de Ciências e Tecnologia, Portugal

Association member

Society Organization name Role
2018 - Current Association of Symbolic Logic

Course / Discipline taught

Academic session Degree Subject (Type) Institution / Organization
2023/09 - 2024/08 Matemática I, Matemática II, Assistent Professor (Professor Adjunto Convidado) at the Section of Mathematics at ISCAL IPL
2023/09 - 2024/02 Analysis I, Assistent Professor (Professor Auxiliar Convidado) at the Department of Mathemtics at NOVA FCT
2023/03 - 2023/08 Professor Assistente at the Department of Mathematics at NOVA FCT; Linear Algebra II
2018/09 - 2019/01 Álgebra Linear e Geometria Analítica Álgebra Linear e Geometria Analítica (Mestrado integrado) Universidade Nova de Lisboa Faculdade de Ciências e Tecnologia, Portugal
2018/09 - 2018/12 I taught Linear Algebra to first year students. Linear Algebra (Mestrado integrado) Universidade Nova de Lisboa, Portugal
2017/09 - 2018/01 Álgebra Linear e Geometria Analítica Álgebra Linear e Geometria Analítica (Mestrado integrado) Universidade Nova de Lisboa Faculdade de Ciências e Tecnologia, Portugal
2018 - 2018 I taught Linear Algebra to first year students.
2017/09 - 2017/12 I taught Linear Algebra to first year students. Linear Algebra (Mestrado integrado) Universidade Nova de Lisboa, Portugal
Distinctions

Award

2023 Member of the European Mathematical Society Young Academy (EMYA)
European Mathematical Society, Finland
2021 Melhor Estudante do Mestrado em Matenática e Aplicações, ramo MP
Universidade Nova de Lisboa Faculdade de Ciências e Tecnologia, Portugal
2020 BestMasters
Springer Nature, Luxembourg
2020 Bolsa Fulbright para Investigação com o apoio da FCT – Fundação para a Ciência e a Tecnologia
2020 Prémio de Lógica Amílcar Sernadas
Universidade de Lisboa Instituto Superior Técnico Departamento de Matemática, Portugal
2018 Best Student of the Bachelor in Mathematics 2018
Universidade Nova de Lisboa Faculdade de Ciências e Tecnologia, Portugal
2016 Novos Talentos em Matemática
Fundação Calouste Gulbenkian, Portugal
2015 Novos Talentos em Matemática
Fundação Calouste Gulbenkian, Portugal
2015 Caloiros da Nova
Universidade Nova de Lisboa Faculdade de Ciências e Tecnologia, Portugal

Other distinction

2019 Bolsa de Doutoramento
Fundação para a Ciência e a Tecnologia, Portugal