In The Revision Theory of Truth (MIT Press), Gupta and Belnap (1993) claim as an advantage of their approach to truth “its consequence that truth behaves like an ordinary classical concept under certain conditions— conditions that can roughly be characterized as those in which there is no vicious reference in the language.” To clarify this remark, they define Thomason models, nonpathological mo...

Article history: Received 30 November 2007 Available online 31 August 2011 JEL classification: D82 D83

Philosopher: Today, I suggest we discuss the important concepts of common knowledge and common belief. As far as I know, the first one to give a formal analysis of these concepts was the philosopher David Lewis, in his book Convention [131]. One of his examples is traffic conventions, about the role of common knowledge in how one behaves in road traffic. To explain this properly, I wonder if yo...

But game theory as we presently know it can not proceed without the fulcrum of common knowledge. Robert Wilson (1985) In the universal belief space [Mertens and Zamir (1985)] which incorporated all situations of incomplete information concerning a state space S , we de ne a `knowledge operator' in terms of beliefs. From this operator we derive (in the usual way) the concept of common knowledge ...

This two-part paper details a theory of solvability for the power flow equations in lossless power networks. In Part I, we derive a new formulation of the lossless power flow equations, which we term the fixed-point power flow. The model is stated for both meshed and radial networks, and is parameterized by several graph-theoretic matrices – the power network stiffness matrices – which quantify...

A special final coalgebra theorem, in the style of Aczel’s [2], is proved within standard Zermelo-Fraenkel set theory. Aczel’s AntiFoundation Axiom is replaced by a variant definition of function that admits non-well-founded constructions. Variant ordered pairs and tuples, of possibly infinite length, are special cases of variant functions. Analogues of Aczel’s Solution and Substitution Lemmas ...

Monotone systems of polynomial equations (MSPEs) are systems of fixedpoint equations X1 = f1(X1, . . . , Xn), . . . , Xn = fn(X1, . . . , Xn) where each fi is a polynomial with positive real coefficients. The question of computing the least non-negative solution of a given MSPE X = f (X) arises naturally in the analysis of stochastic models such as stochastic context-free grammars, probabilisti...

Future 4th Generation (4G) wireless multiuser communication systems will have to provide advanced multimedia services to an increasing number of users, making good use of the scarce spectrum resources. Thus, 4G system design should pursue both highertransmission bit rates and higher spectral efficiencies. To achieve this goal, multiple antenna systems are called to play a crucial role. In this ...