Provability Logic and the Completeness Principle

In this paper, we study the provability logic of intuitionistic theories of arithmetic that prove their own completeness. We prove a completeness theorem for theories equipped with two provability predicates $\Box$ and $\triangle$ that prove the schemes $A\to\triangle A$ and $\Box\triangle S\to\Box S$ for $S\in\Sigma_1$. Using this theorem, we determine the logic of fast provability for a number of intuitionistic theories. Furthermore, we reprove a theorem previously obtained by M. Ardeshir and S. Mojtaba Mojtahedi determining the $\Sigma_1$-provability logic of Heyting Arithmetic

Kinematics of the South Atlantic rift

The South Atlantic rift basin evolved as branch of a large Jurassic-Cretaceous intraplate rift zone between the African and South American plates during the final breakup of western Gondwana. By quantitatively accounting for crustal deformation in the Central and West African rift zone, we indirectly construct the kinematic history of the pre-breakup evolution of the conjugate West African-Brazilian margins. Our model suggests a causal link between changes in extension direction and velocity during continental extension and the generation of marginal structures such as the enigmatic Pre-salt sag basin and the S\~ao Paulo High. We model an initial E-W directed extension between South America and Africa (fixed in present-day position) at very low extensional velocities until Upper Hauterivian times ($\approx$126 Ma) when rift activity along in the equatorial Atlantic domain started to increase significantly. During this initial $\approx$17 Myr-long stretching episode the Pre-salt basin width on the conjugate Brazilian and West African margins is generated. An intermediate stage between 126.57 Ma and Base Aptian is characterised by strain localisation, rapid lithospheric weakening in the equatorial Atlantic domain, resulting in both progressively increasing extensional velocities as well as a significant rotation of the extension direction to NE-SW. Final breakup between South America and Africa occurred in the conjugate Santos--Benguela margin segment at around 113 Ma and in the Equatorial Atlantic domain between the Ghanaian Ridge and the Piau\'i-Cear\'a margin at 103 Ma. We conclude that such a multi-velocity, multi-directional rift history exerts primary control on the evolution of this conjugate passive margins systems and can explain the first order tectonic structures along the South Atlantic and possibly other passive margins.Comment: 46 Pages, 22 figures. Submitted to Solid Earth (http://www.solid-earth.net). Abstract shortened due to arXiv restrictions. New version contains revisions and amendments as per reviewers requests. Supplementary data is available at http://datahub.io/en/dataset/southatlanticrif

Simulating the Emergence of Task Rotation

In work groups, task rotation may decrease the negative consequences of boredom and lead to a better task performance. In this paper we use multi agent simulation to study several organisation types in which task rotation may or may not emerge. By looking at the development of expertise and motivation of the different agents and their performance as a function of self-organisation, boredom, and task rotation frequency, we describe the dynamics of task rotation. The results show that systems in which task rotation emerges perform better than systems in which the agents merely specialise in one skill. Furthermore, we found that under certain circumstances, a task that leads to a high degree of boredom was performed better than a task causing a low level of boredom.Organisation, Task Rotation, Work Groups, Psychological Theory, Multi Agent Simulation

When Does a Newcomer Contribute to a Better Performance? A Multi-Agent Study on Self-Organising Processes of Task Allocation

This paper describes how a work group and a newcomer mutually adapt. We study two types of simulated groups that need an extra worker, one group because a former employee had left the group and one group because of its workload. For both groups, we test three conditions, newcomers being specialists, newcomers being generalists, and a control condition with no newcomer. We hypothesise that the group that needs an extra worker because of its workload will perform the best with a newcomer being a generalist. The group that needs an extra worker because a former employee had left the group, will perform better with a specialist newcomer. We study the development of task allocation and performance, with expertise and motivation as process variables. We use two performance indicators, the performance time of the slowest agent that indicates the speed of the group and the sum of performance of all agents to indicate labour costs. Both are indicative for the potential benefit of the newcomer. Strictly spoken the results support our hypotheses although the differences between the groups with generalists and specialists are negligible. What really mattered was the possibility for a newcomer to fit in.Task Allocation, Group Processes, Psychological Theory, Small Groups, Self-Organisation

On the Existence of Pushouts of Realizability Toposes

We consider two preorder-enriched categories of ordered PCAs: $\mathsf{OPCA}$, where the arrows are functional morphisms, and $\mathsf{PCA}$, where the arrows are applicative morphisms. We show that $\mathsf{OPCA}$ has small products and finite biproducts, and that $\mathsf{PCA}$ has finite coproducts, all in a suitable 2-categorical sense. On the other hand, $\mathsf{PCA}$ lacks all nontrivial binary products. We deduce from this that the pushout, over $\mathsf{Set}$, of two nontrivial realizability toposes is never a realizability topos.Comment: 19 pages; revised argument in Section 6, added remarks and reference