Joost Joosten - Selected Publications#

The bibliometrics are readily available on the regular platforms (like the free Google Scholar).

Here, a list of ten publications is given (some of more than 5 years old since they are more important than other more recent publications) with the reason why the author thinks the paper is relevant and where.

A. de Almeida Borges, J. J. Joosten. An Escape from Vardanyan’s Theorem. Journal of Symbolic Logic, Volume 88, Issue 4, Pages 1613 – 1638, 2023.

Quantified provability logic is undecidable. In this paper we carve out a decidable fragment of it and provide various modal and arithmetical semantics. The paper is relevant both in the community of Positive Logics and the community that works on Ordinal Analysis.

J. J. Joosten. Münchhausen Provability. Journal of Symbolic Logic, Volume 86 (3), pages 1006 – 1034, 2021.

A natural but tricky arithmetical interpretation of transfinite provability logic where levels of provability run in phase with levels of the Turing jumps.

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

This paper unifies modal syntactic, modal semantic, arithmetical semantics, fragments of arithmetic and Turing progressions. Even though many of the observations where partially already out there, this paper really combines them in a fitting framework. The Turing-Taylor expansions are nowadays called spectra and widely studied.

D. Fernández-Duque, J. J. Joosten, F. Pakhomov, K. Papafilippou, and A. Weierman. Arithmetical and Hyperarithmetical Worm Battles. Journal for Logic and Computation, Volume 32, Issue 8, Pages 1558 – 1584, December 2022.

A first evidence that transfinite polymodal provability logics indeed are applicable beyond Peano Arithmetic.

E. Goris, M. Bílková, J. J. Joosten and L. Mikec. Theory and application of labelling techniques for interpretability logics. Mathematical Logic Quarterly, Volume 68, Issue 3, Pages 352–374, August 2022.

This paper lays groundwork for those working in Interpretability logics. In the eighties, Critical successors where used and Goris and Joosten generalised this to full labels. Nowadays full labels are a standard technique in proofs for modal completeness and decidability.

A. de Almeida Borges, J. J. Conejero Rodríguez, D. Fernández Duque, M. González Bedmar, J. J. Joosten. To drive or not to drive: A logical and computational analysis of European transport regulations. Information and Computation, 280, 2021. After presenting a similar paper to a conference, the paper got invited for a special issue. Modal logic used to analyse real legal texts. Mainly Linear Temporal Logic and in later papers this has been followed by other frameworks.

E. Goris, and J. J. Joosten. Two new series of principles in the interpretability logic of all reasonable arithmetical theories. Journal of Symbolic Logic, 85(1), pages 1 - 25, 2020. A breaktrhough in a longstanding open problem. Two infinite series of new principles are provided whereas in previous decades new principles were discovered at an average of one principle per decade.

E. Hermo Reyes and J. J. Joosten, The logic of Turing progressions, Notre Dame Journal of Formal Logic, 61(1), pages 155 - 180, 2020.

The first time a modal logic is employed to directly denote Turing progressions and not just approximate them as in the case of GLP.

J. J. Joosten, J. Mas Rovira, L. Mikec and M. Vukovic. An Overview of Verbrugge Semantics, a.k.a. Generalised Veltman Semantics. In Dick de Jongh on Intuitionistic and Provability Logic, Outstanding Contributions to Logic, Bezhanishvili, N., Iemhoff, R. and Yang, F. editors. Springer, ISBN 9783031479205, 2024. The paper gives an overview and historical investigations. It seems to become a standard reference for those working in the field of interpretability logics (there has been an Arxiv version available for quite a while already).

J. J. Joosten, F. Soler Toscano and H. Zenil. Fractal Dimension versus Process Complexity. Advances in Mathematical Physics (online only), vol. 2016, Article ID 5030593, 21 pages, 2016. doi:10.1155/2016/5030593. The paper is the culmination of a longstanding collaboration of the three authors where they mined the computational universe looking for patterns through very large samples or exhaustive computations regarding small Turing machines and related discrete dynamic processes.