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pro vyhledávání: '"JOOSTEN, JOOST J."'
The $Reflection$ $Calculus$ ($\mathcal{\mathbf{RC}}$) is the fragment of the polymodal logic $\mathcal{\mathbf{GLP}}$ in the language $L^+$ whose formulas are built up from $\top$ and propositional variables using conjunction and diamond modalities.
Externí odkaz:
http://arxiv.org/abs/2407.13619
We introduce a modal logic FIL for Feferman interpretability. In this logic both the provability modality and the interpretability modality can come with a label. This label indicates that in the arithmetical interpretation the axiom set of the under
Externí odkaz:
http://arxiv.org/abs/2406.18506
An important aim of this paper is to convey some basics of mathematical logic to the legal community working with Artificial Intelligence. After analysing what AI is, we decide to delimit ourselves to rule-based AI leaving Neural Networks and Machine
Externí odkaz:
http://arxiv.org/abs/2402.06487
We determine the strictly positive fragment $\mathsf{QPL}^+(\mathsf{HA})$ of the quantified provability logic $\mathsf{QPL}(\mathsf{HA})$ of Heyting Arithmetic. We show that $\mathsf{QPL}^+(\mathsf{HA})$ is decidable and that it coincides with $\math
Externí odkaz:
http://arxiv.org/abs/2312.14727
Autor:
Joosten, Joost J.
In this short paper we focus on human in the loop for rule-based software used for law enforcement. For example, one can think of software that computes fines like tachograph software, software that prepares evidence like DNA sequencing software or s
Externí odkaz:
http://arxiv.org/abs/2309.10678
Autor:
Müller, Moritz, Joosten, Joost J.
We discuss model-checking problems as formal models of algorithmic law. Specifically, we ask for an algorithmically tractable general purpose model-checking problem that naturally models the European transport Regulation 561, and discuss the reaches
Externí odkaz:
http://arxiv.org/abs/2307.05658
Autor:
Borges, Ana de Almeida, Bedmar, Mireia González, Rodríguez, Juan Conejero, Reyes, Eduardo Hermo, Buñuel, Joaquim Casals, Joosten, Joost J.
Publikováno v:
In Proceedings of the 13th ACM SIGPLAN International Conference on Certified Programs and Proofs (CPP 24), January 15--16, 2024, London, UK. ACM, New York, NY, USA, 12 pages
FV Time is a small-scale verification project developed in the Coq proof assistant using the Mathematical Components libraries. It is a library for managing conversions between time formats (UTC and timestamps), as well as commonly used functions for
Externí odkaz:
http://arxiv.org/abs/2209.14227
Autor:
Fernández-Duque, David, Joosten, Joost J., Pakhomov, Fedor, Papafilippou, Konstnatinos, Weiermann, Andreas
Japaridze's provability logic $GLP$ has one modality $[n]$ for each natural number and has been used by Beklemishev for a proof theoretic analysis of Peano aritmetic $(PA)$ and related theories. Among other benefits, this analysis yields the so-calle
Externí odkaz:
http://arxiv.org/abs/2112.07473
Publikováno v:
The Journal of Symbolic Logic 88(4): 1613-1638 (2023)
Vardanyan's Theorems state that $\mathsf{QPL}(\mathsf{PA})$ - the quantified provability logic of Peano Arithmetic - is $\Pi^0_2$ complete, and in particular that this already holds when the language is restricted to a single unary predicate. Moreove
Externí odkaz:
http://arxiv.org/abs/2102.13091
Interpretability logics are endowed with relational semantics \`a la Kripke: Veltman semantics. For certain applications though, this semantics is not fine-grained enough. Back in 1992, in the research group of de Jongh, the notion of generalised Vel
Externí odkaz:
http://arxiv.org/abs/2007.04722