1,223 research outputs found
Concepts of Proof in Mathematics, Philosophy, and Computer Science
No full textA proof is a successful demonstration that a conclusion necessarily follows by logical reasoning from axioms which are considered evident for the given context and agreed upon by the community. It is this concept that sets mathematics apart from other disciplines and distinguishes it as the prototype of a deductive science. Proofs thus are utterly relevant for research, teaching and communication in mathematics and of particular interest for the philosophy of mathematics. In computer science, moreover, proofs have proved to be a rich source for already certified algorithms. This book provides the reader with a collection of articles covering relevant current research topics circled around the concept 'proof'. It tries to give due consideration to the depth and breadth of the subject by discussing its philosophical and methodological aspects, addressing foundational issues induced by Hilbert's Programme and the benefits of the arising formal notions of proof, without neglecting reasoning in natural language proofs and applications in computer science such as program extraction
Concepts of Proof in Mathematics, Philosophy, and Computer Science
No full textA proof is a successful demonstration that a conclusion necessarily follows by logical reasoning from axioms which are considered evident for the given context and agreed upon by the community. It is this concept that sets mathematics apart from other disciplines and distinguishes it as the prototype of a deductive science. Proofs thus are utterly relevant for research, teaching and communication in mathematics and of particular interest for the philosophy of mathematics. In computer science, moreover, proofs have proved to be a rich source for already certified algorithms.
This book provides the reader with a collection of articles covering relevant current research topics circled around the concept 'proof'. It tries to give due consideration to the depth and breadth of the subject by discussing its philosophical and methodological aspects, addressing foundational issues induced by Hilbert's Programme and the benefits of the arising formal notions of proof, without neglecting reasoning in natural language proofs and applications in computer science such as program extraction
On the relationship between fixed points and iteration in admissible set theory without foundation
No full textAbstract.: In this article we show how to use the result in Jäger and Probst [7] to adapt the technique of pseudo-hierarchies and its use in Avigad [1] to subsystems of set theory without foundation. We prove that the theory KPi0 of admissible sets without foundation, extended by the principle (Σ-FP), asserting the existence of fixed points of monotone Σ operators, has the same proof-theoretic ordinal as KPi0 extended by the principle (Σ-TR), that allows to iterate Σ operations along ordinals. By Jäger and Probst [6] we conclude that the metapredicative Mahlo ordinal φω00 is also the ordinal of KPi0+(Σ-FP). Hence the relationship between fixed points and iteration persists in the framework of set theory without foundatio
Labour co-determination and corporate governance in Germany: The economic impact of marginal and symbolic rights
No full textFor decades, some governments have fiercely opposed any statute of the Societas Europaea that foresaw German-type co-determined supervisory boards. Considering firms as pools of specific investors, we ask about the conditions that are necessary to secure the interests of specific human capitalists in an efficient way, if the real capital owners' right to residual control does not solve the ex-post bargaining problems over the sharing of quasi-rents. We disregard contract-theoretic approaches as solutions to the ex-post bargaining conflicts and suggest a constitutional approach to this major problem in the theory of the firm. From a constitutional perspective, the (non-executive) board members of the German Aufsichtsrat (Supervisory Board) - unlike the Betriebsrat (Works Council) - essentially dispose only of marginal, extremely symbolic, i.e., non-enforceable rights to represent worker investors. Legally, however, these rights are to be used first in the interests of the corporation and only secondarily in the interests of partial investors. Marginal and symbolic rights as well as fiduciary duties will make a difference in distributive bargaining, if they are legally imposed. Who is to be heard and to be involved in decision-making and what is counted as a legitimate argument or action - these are basically questions of political culture that in principle leave room for efficient international diversity. Option rights in the European directive on the Societas Europaea should thus be considered as an apt and wise decision. -- Seit Jahrzehnten wehren sich einige Regierungen vehement gegen die Schaffung einer Societas Europaea, welche mitbestimmte Aufsichtsräte nach deutschem Muster für europäische Aktiengesellschaften ermöglicht. Indem wir Firmen als Zusammenschluss spezifischer Investoren betrachten, fragen wir nach notwendigen Bedingungen, um die Interessen spezifischer Humankapitalgeber effizient abzusichern, wenn das residuale Kontrollrecht der Finanzkapitalgeber Ex-post-Verhandlungsprobleme über die Aufteilung der Quasirenten nicht zu lösen vermag. Wir sehen von vertragstheoretischen Lösungsansätzen zu Ex-post-Verhandlungsproblemen ab und empfehlen vielmehr eine konstitutionelle Annäherung an dieses Hauptproblem der Unternehmenstheorie. Aus konstitutioneller Sicht verfügen Arbeitnehmervertreter im Aufsichtsrat - im Gegensatz zum Betriebsrat - lediglich über marginale und eher symbolische, d.h. nicht die Interessen der Arbeitnehmerschaft zwingend durchsetzbare Rechte. Aus juristischer Sicht wiederum sollen diese Recht in erster Linie im Interesse des Unternehmens und erst nachrangig zur Durchsetzung von Partialinteressen verschiedener Investorengruppen genutzt werden. Marginale und symbolische Rechte ebenso wie treuhänderische Pflichten verändern die Ergebnisse von Verteilungsverhandlungen, wenn diese Rechte gesetzlich verankert sind. Wer muss gehört oder in den Entscheidungsprozess mit eingebunden werden und was gilt als legitimes Argument oder legitime Handlung - dies sind im Grunde Fragen der politischen Kultur, die im Prinzip Raum für effiziente internationale Vielfalt lassen. Optionsrechte in der europäischen Direktive der Societas Europaea sollten infolgedessen als angemessene und weise Entscheidung angesehen werden.
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Organizational Processes for Supporting Sustainable Security (Dagstuhl Seminar 12501)
No full textThis report documents the program and the outcomes of Dagstuhl Seminar 12501 "Organizational Processes for Supporting Sustainable Security" which ran from December 9 to 12, 2012 and was held in Schloss Dagstuhl--Leibniz Center for Informatics. During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. We also ran a number of collaborative sessions designed to promote the development of design principles for sustainably secure organizational processes. The first section
describes the seminar topics and goals in general. The following section contains abstracts of the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper
08302 Summary – Countering Insider Threats
No full textThis article summarizes the objectives and structure of a
seminar with the same title, held from July 20th to July 25th, 2008, at
Schloss Dagstuhl, Germany. The seminar brought together researchers
and policy-makers from all involved communities, to clarify what it is
that identifies an insider threat, and to develop a common vision of how
an insider can be categorized as well as an integrated approach that
allows a qualitative reasoning about the threat and the possibilities of
attacks. This report gives an overview of the discussions and presentations
during the week, as well as the outcome of these discussions
08302 Abstracts Collection – Countering Insider Threats
No full textFrom July 20 to July 25, 2008, the Dagstuhl Seminar 08302 ``Countering Insider Threats '' was held in Schloss Dagstuhl~--~Leibniz Center for Informatics.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
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