4 citations · 5 across the 5 of their papers we have counts for
6 papers
The omega-rule interpretation of transfinite provability logic
David Fernández-Duque, Joost J. Joosten
In this paper we consider transfinite provability logics where for each ordinal in some recursive well-order we have a corresponding modal provability operator. The modality [xi] w…
Complexity fits the fittest
J. J. Joosten
In this paper we shall relate computational complexity to the principle of natural selection. We shall do this by giving a philosophical account of complexity versus universality.…
Pi^0_1 ordinal analysis beyond first order arithmetic
J. J. Joosten
In this paper we give an overview of an essential part of a Pi^0_1 ordinal analysis of Peano Arithmetic (PA) as presented by Beklemishev. This analysis is mainly performed within t…
On the necessity of complexity
Joost J. Joosten
Wolfram's Principle of Computational Equivalence (PCE) implies that universal complexity abounds in nature. This paper comprises three sections. In the first section we consider th…
On provability logics with linearly ordered modalities
Lev D. Beklemishev, David Fernández-Duque, Joost J. Joosten
We introduce the logics GLP(Λ), a generalization of Japaridze's polymodal provability logic GLP(ω) where Λis any linearly ordered set representing a hierarchy of provability operat…
Empirical Encounters with Computational Irreducibility and Unpredictability
Hector Zenil, Fernando Soler-Toscano, Joost J. Joosten
There are several forms of irreducibility in computing systems, ranging from undecidability to intractability to nonlinearity. This paper is an exploration of the conceptual issues…