Papers

• Homologated software should come with a formal dialogue fragment.
  Position paper presented and discussed at the Transatlantic Dialogue on Humanity and AI Regulation Event https://pamplin.vt.edu/security-privacy-trust/news/transatlantic-dialogue.html


• To drive or not to drive: A logical and computational analysis of European transport regulations.
  Joint work with Ana de Almeida Borges, Juan José Conejero Rodríguez, David Fernández Duque and Mireia González Bedmar. Information and Computations, 2020. https: //doi.org/10.1016/j.ic.2020.104636


• The Second Order Traffic Fine: Temporal Reasoning in European Transport Regulations
  Joint work with Ana de Almeida Borges, Juan José Conejero Rodríguez, David Fernández Duque and Mireia González Bedmar. In 26th International Symposium on Temporal Representation and Reasoning (TIME 2019), Leibniz Inter- national Proceedings in Informatics (LIPIcs), Volume 147, ISBN 978-3-95977-127-6, pages 6:1-6:16, editors Johann Gamper and Sophie Pinchinat and Guido Sciavicco, Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2019.


• To Drive or Not to Drive
  A Formal Analysis of Requirements (51) and (52) from Regulation (EU) 2016/799
  Joint work with Joint work with David Fernández Duque, Mireia González Bedmar, Daniel Sousa, and Guillermo Errezil Alberdi. In TransJus Working Papers Publication Number 4, Special Edition, Personalidades jurídicas difusas y artificiales, Institut de Recerca TransJus, Barcelona, ISSN 2462-263X, Pages 159-171, 2019.


• Turing jumps through provability
  


• Predicativity through transfinite reflection
  Joint work with Andrés Cordon Franco, David Fernández Duque and Félix Lara Martín.


• The Selfish Algorithm
  Joint work with Eduardo Hermo Reyes.


• Turing-Taylor expansions for arithmetic theories
  Studia Logica, 104 (6), pages 1225-1243, 2016.


• When logic lays down the law
  Joint work with Bjørn Jespersen, Ana de Almeida Borges, Jorge del Castillo Tierz, Eric Sancho Adamson, Juan José Conejero Rodríguez, Aleix Solé Sánchez and Nika Pona.


• Fractal dimension versus computational complexity
  Joint work with Fernando Soler-Toscano and Hector Zenil, Submitted.


• The omega-rule interpretation of transfinite provability logic
  Joint work with David Fernández-Duque, Annals of Pure and Applied Logic 169 (4), pages 333-371, 2018.


• Models for transfinite provability logic
  Joint work with David Fernández-Duque, Journal of Symbolic Logic, 78(2), pages 543-561, 2013.


• Π⁰₁ ordinal analysis beyond first order arithmetic
  Joost J. Joosten, Mathematical Communications, 18(1), pages 109-121, 2013.


• Turing Progressions and their well-orders
  Joint work with David Fernández-Duque; In How the world computes, Lecture Notes in Computer Science, Springer, Volume 7318, p212-221, 2012.


• Speedup and Slowdown Phenomena in Turing Machines(Software)
  Joint work with Fernando Soler-Toscano and Hector Zenil; Wolfram Demonstrations Project, 2012.


• Hyperations, Veblen progressions and transfinite iteration of ordinal functions
  Joint work with David Fernández-Duque; Annals of Pure and Applied Logic, 164 (7,8), pages 785-801, 2013.



• On provability logics with linearly ordered modalities
  Joint work with Lev D. Beklemishev and David Fernández-Duque; Accepted for publication in Studia Logica, 2013.



• Well orders in the transfinite Japaridze algebra
  Joint work with David Fernández-Duque, Submitted 2012


• Well orders in the transfinite Japaridze algebra II: Turing Progressions and their well-orders
  Joint work with David Fernández-Duque, Submitted 2012.



• On the necessity of complexity
  Joost J. Joosten, book chapter, in Irreducibility and Computational Equivalence: 10 Years After the Publication of Wolfram's A New Kind of Science. (11-24). Springer, Heidelberg New York Dordrecht London, H. Zenil editor, ISBN 978-3-642-35481-6, 2013.



• Kripke models for transfinite provability logic.
  Joint work with David Fernández-Duque; In T. Bolander, T. Bräuner, S. Ghilardi and L. Moss, editors, Advances in Modal Logic, vol. 9, pp. 185-199. College Publications, 2012.



• Complexity fits the fittest
  Joost J. Joosten, book chapter in Emergence, Complexity and Computation in Nature. Springer Verlag, I. Zelinka, A. Sanayei, H. Zenil H., O. E. Rossler, editors, to appear, doi 10.1007/978-3-319-00254-5 3, ISBN 978-3-319-00253-8, 2013.



• Additive protocols for safe and informative communication between card players
  Joint work with many others; Australasian Journal of Combinatorics, Volume 54, Pages 163-175, 2012.



• Empirical Encounters with Computational Irreducibility and Unpredictability
  Joint work with Fernando Soler-Toscano and Hector Zenil, Minds & Machines, Volume 22, Issue 3, Pages 149-165, 2012.



• Hidden variables simulating quantum contextuality increasingly violate the Holevo bound
  Joint work with Adán Cabello; In Unconventional Computing, Springer LNCS 6714 (64-76), ISSN 0302-9743. Proceedings of the 10th International Conference UC 2011, Turku, Finland 2011.



• Secure communication of local states in multi-agent systems
  Joint work with many others; Pre-proceedings of the Workshop on Logics in Security, affiliated to ESSLLI 2010, Copenhagen.


• Program-size versus Time complexity, Slowdown and speed-up phenomena in the micro-cosmos of small Turing machines 2010.
  Presented at the Conference Physics and Computation 2010, Luxor, Egypt. Published at the International Journal of Unconventional Computing, vol. 7, no. 5, pp. 353-387, 2011.



• Turing Machine Enumeration: NKS versus Lexicographical (Software) 2010.
  Wolfram Demonstrations Project.



• Interpretability logics and large cardinals in set theory 2010.
  Proceedings of the IV Jornadas Ibericas de Filosofia de la Ciencia, Logica y Lenguaje, Sevilla 2009.



• Complejidad descriptiva y computacional en máquinas de Turing pequeñas 2010.
  Joint work with many others; Proceedings of the V Jornadas Ibericas de Filosofia de la Ciencia, Logica y Lenguaje, Lisbon 2010.



• Consistency statements and iterations of computable functions in $I \Sigma_1$ and PRA. 2010.
  Archive for Mathematical Logic. Accepted for publication, June 2010.



• A New Principle in the Interpretability Logic of all Reasonable Arithmetical Theories 2010.
  Joint work with Evan Goris; Logic Journal of the Interest Group in Pure and Applied Logic. Advanced Access published December 24, 2009, doi:10.1093/jigpal/jzp082.



• Self Provers and Sigma_1 Sentences 2010.
  Joint work with Evan Goris; Logic Journal of the Interest Group in Pure and Applied Logic. Advanced Access published January 29, 2010, doi:10.1093/jigpal/jzp096.



• Provability and Interpretability Logics with Restricted Substitutions 2010.
  Joint work with Thomas Icard; Submitted to the Notre Dame Journal of Formal Logic.



• Interpretability in PRA 2009.
  Joint work with Marta Bilkova and Dick de Jongh; Annals of Pure and Applied Logic 161 (2), 128-138; 2009.



• Modal Matters in Interpretability Logics 2008.
  Joint work with Evan Goris; Logic Journal of the Interest Group in Pure and Applied Logic} 16: 371-412; 2008.



• Semantics for sub-intuitionistic logics 2006.
  Chapter in Miscellanea Logica VII (21-34). Univerzita Karlova v Praze, Filozofick\'a fakulta; ISBN 978-80-7308-261-1.



• Propositional proof systems and fast consistency provers 2006.
  Notre Dame Journal of Formal Logic, 48 (3), 381-398; 2007.



• Credit cards, computationele complexiteit en consistentie uitspraken



• What is Flamenco 2005.

See also the ProvokatoR magazine.


• A finitary treatment of the closed fragment of Japaridze's provability logic. Joint work with Marco Vervoort and Lev Beklemishev; Journal on Logic and Computation, 15(4), 447-463, 2005.



• Het hoofd van een filosoof De FilosooF, 2005.


• PhD thesis, November 2004:
  dvi-format, ps-format, pdf-format.
  There is also a nice webversion of my PhD thesis which is publised by Igitur.




• How to derive principles of interpretability logic, A toolkit (With Albert Visser)
  In J. van Benthem, A. Troelstra, F. Veltman and A. Visser, editors, Liber Amicorum for Dick de Jongh. Institute for Logic, Language and Computation, 2004. ISBN: 90 5776 1289, http://www.illc.uva.nl/D65/



• Smart Labels (With Evan Gorris and Marta Bilkova)
  In J. van Benthem, A. Troelstra, F. Veltman and A. Visser, editors, Liber Amicorum for Dick de Jongh. Institute for Logic, Language and Computation, 2004. ISBN: 90 5776 1289, http://www.illc.uva.nl/D65/



• Materiae Modales in Logicis Interpretabilitatis, pdf-format.



• Characterizations of interpretability (preliminary version, jointly with Albert Visser)
  ps-format, pdf-format.



• Comparing IΣ₁ and PRA
  ps-format, pdf-format.



• IΣ₁ according to PRA
  ps-format, pdf-format.


• Modal matters in Interpretability Logics
  Joint work with Evan Goris; ps-format, pdf-format.



• Formalized Interpretability in Primitive Recursive Arithmetic, Spring 2003,
  Also published in the proceedings of the ESSLLI 2003 student session. ps-format, pdf-format.



• The Closed Fragment of the Interpretability Logic of PRA with a Constant for IΣ₁, February 2003, ps-format, pdf-format.




• Two Proofs of Parson's Theorem, November 2002.ps-format, pdf-format.




• Arithmetics, Personal Notes of a Course by Lev Beklemishev. October 2001. ps-format, pdf-format.



• The Interpretability Logic of all Reasonable Arithmetical Theories,
  the new conjecture.
  Jointly with Albert Visser; October 1999. Also published in Erkenntnis, 2000. The .ps format is of slightly better quality. ps-format, pdf-format.




• Towards the Interpretability Logic of All Reasonable Arithmetical Theories, Masters Thesis, December 1998. ps-format, pdf-format. html-version



• Here are some old notes on arithmetical problems I have once studied a bit. Arithmetic



• And here is a very old page related to my Master's Thesis. Interpretability Logics