Zero-one laws with respect to models of provability logic and two Grzegorczyk logics

It has been shown in the late 1960s that each formula of first-order logic without constants and function symbols obeys a zero-one law: As the number of elements of finite models increases, every formula holds either in almost all or in almost no models of that size. Therefore, many properties of models, such as having an even number of elements, cannot be expressed in the language of first-order logic. Halpern and Kapron proved zero-one laws for classes of models corresponding to the modal logics K, T, S4, and S5 and for frames corresponding to S4 and S5. In this paper, we prove zero-one laws for provability logic and its two siblings Grzegorczyk logic and weak Grzegorczyk logic, with respect to model validity. Moreover, we axiomatize validity in almost all relevant finite models, leading to three different axiom systems

New Perspectives on Games and Interaction

This volume is a collection of papers presented at the 2007 colloquium on new perspectives on games and interaction at the Royal Dutch Academy of Sciences in Amsterdam. The purpose of the colloquium was to clarify the uses of the concepts of game theory, and to identify promising new directions. This important collection testifies to the growing importance of game theory as a tool to capture the concepts of strategy, interaction, argumentation, communication, cooperation and competition. Also, it provides evidence for the richness of game theory and for its impressive and growing application

Data and Language in Organizations: Epistemological Aspects of Management Support Systems

This book contributes to the literature on management decision support systems (DSS). DSS research is motivated by the observation that much of what managers do involves unstructured problem solving. For the reason, the structured, procedural models implemented in management information systems (MIS) have had little impact on actual managerial practice. Actually, the terms "decision" and "problem solving" over-simplify the image of managerial activity, if what is meant is choosing from a set of well-defined alternatives. Management also includes such aspects as reality testing, problem finding, scenario generation, and just plain muddling through. A broader conception of management cognition -- of which decision making is only a part -- is therefore adopted. The challenge to technology development is to support these unstructured managerial activities. The emphasis is to amplify managerial cognition and to improve decision effectiveness. However, to achieve this we must go beyond platitudes and come to a better understanding of what managers actually do. The activity of managers is almost entirely linguistic. Computers, as symbolic processors, ought to be an effective complement. However, a fundamental problem, stressed repeatedly throughout the book, is semantic change. The context of managers is always changing, whereas computational inference depends on fixed semantics. Herein Lies the basis for a theory of management support systems. The theory takes the form of an applied epistemology: how do managers know their world and detect its changes? Thus, while this book is oriented towards improving information technology, its attention is primarily to the content of management information and only secondarily to technology. Technological innovations abound. What is needed now is a better understanding of what these technologies are to do

Abstract Consequence and Logics - Essays in Honor of Edelcio G. de Souza

Edelcio G. de Souza is a Brazilian logician and philosopher who has researches in the domains of abstract logic, non-classical systems, philosophy of science and the foundations of mathematics. This book is in his honor with the purpose of celebrating his 60th birthday. It contains some articles connected with the above topics and other subjects in logical investigations