Two ways to common knowledge

It is not clear what a system for evidence-based common knowledge should look like if common knowledge is treated as a greatest fixed point. This paper is a preliminary step towards such a system. We argue that the standard induction rule is not well suited to axiomatize evidence-based common knowledge. As an alternative, we study two different deductive systems for the logic of common knowledge. The first system makes use of an induction axiom whereas the second one is based on co-inductive proof theory. We show the soundness and completeness for both systems.

Intuitionistic common knowledge or belief

Starting off from the usual language of modal logic for multi-agent systems dealing with the agents’ knowledge/belief and common knowledge/belief we define so-called epistemic Kripke structures for intu- itionistic (common) knowledge/belief. Then we introduce corresponding deductive systems and show that they are sound and complete with respect to these semantics.

[Growth: what is normal?]

Growth is an inherent property of life, which has to be checked and controlled by any general physician following children. Therefore, the common knowledge about the normal pattern/course of growth is essential in order to act proactively whenever the child's growth does not progress adequately.

John Calvin's Impact on Church and Society, 1509-2009. Essays for the 500th birthday of Calvin

A tribute to the monumental influence of John Calvin in the 500 years since his birth. / What legacies, still enduring today, have John Calvin and Calvinism given to the church and society in Europe and North America? An international group of scholars tackles that question in this volume honoring Calvin's 500th birthday. These chapters together provide a comprehensive and accessible introduction to Calvin's life and thought, the history of the Reformation in Switzerland and worldwide, and his continuing relevance for ecclesial, social, and political questions today. / Contributors: Philip Benedict, James D. Bratt, Emidio Campi, Wulfert de Greef, Christopher Elwood, Eva-Maria Faber, Eric Fuchs, Ulrich H. J. Krtner, Christian Link, Christian Moser, Andrew Pettegree, Christoph Strohm, Mario Turchetti./ The essays in this book fit beautifully together to provide a solid, complete work that gives precise insight into the many different facets of Calvin and Calvinism. The high-level research found here clearly shows the great impact that Calvin has had on both church and society. It is a great pleasure to see Calvin here anew. Eberhard Busch / University of Gttingen / That John Calvin made a deep and lasting impact on many aspects of history is common knowledge but the character of the man and the nature of his influence are perhaps as controversial as any that can be named. It is thus a challenge to examine even a fraction of the many ways that Calvins life and thought have contributed to the shaping of later ages in both church and society. This volume offers essays on key points from an appropriately international group of authors appreciative but critical, drawing on a rich range of recent scholarship, presented in a pleasing and accessible form. It is a fine place for the new reader of Calvin to get a glimpse of his impact, while offering a fresh summary of some significant issues for more advanced students of the Reformer. Elsie Anne McKee / Princeton Theological Seminary / Hirzel and Sallmann have succeeded in gathering essays by an illustrious circle of experts both historians and theologians on important areas of Calvins thought and impact. Ranging from an insignificant city at the edge of the Swiss Confederation in the 1530s to the Accra Confession of 2004, these essays will serve to correct popular misconceptions. A fine introduction for a broader readership that wants more than mere armchair theology. Peter Opitz / University of Zurich

New evidence for the symbiosis between Tuber aestivum and Picea abies

The Burgundy truffle (Tuber aestivum Vittad.), an ectomycorrhizal fungus living in association with host plants, is one of the most exclusive delicacies. The symbiosis with deciduous oak, beech, and hazel dominates our concept of truffle ecophysiology, whereas potential conifer hosts have rarely been reported. Here, we present morphological and molecular evidence of a wildlife T. aestivum symbiosis with Norway spruce (Picea abies Karst.) and an independent greenhouse inoculation experiment, to confirm our field observation in southwest Germany. A total of 27 out of 50 P. abies seedlings developed T. aestivum ectomycorrhizae with a mean mycorrhization rate of 19.6 %. These findings not only suggest P. abies to be a productive host species under suitable biogeographic conditions but also emphasize the broad ecological amplitude and great symbiotic range of T. aestivum. While challenging common knowledge, this study demonstrates a significant expansion of the species' cultivation potential to the central European regions, where P. abies forests occur on calcareous soils.