/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

The author systematically examines one of the important issues of information — establishing the market price. He introduces the concept of «search» — where a buyer wanting to get a better price, is forced to question sellers. The article deals with various aspects of finding the necessary information.

Economics of Information

The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

Convergence of probability measures

What is modal logic

Naming and necessity

Confidence and decision

In recent years, much work has been dedicated by logicians, computer scientists and economists to understanding awareness, as its importance for human behaviour becomes evident. Although several logics of awareness have been proposed, little attention has been explicitly dedicated to change in awareness. However, one of the most crucial aspects of awareness is the changes it undergoes, which have countless important consequences for knowledge and action. The aim of this paper is to propose a formal model of awareness change, and to derive from it logics of awareness change. In the first part of the paper, the model of epistemic states of bounded agents proposed in Hill (Stud Log 89(1):81–109, 2008a) is extended with operations modelling awareness change. In the second part of the paper, it is shown how this model naturally extends the “standard” logic of awareness to yield a logic of awareness change.

Awareness Dynamics

We propose and operationalize normative principles to guide social decisions when individuals potentially have imprecise and heterogeneous beliefs, in addition to conflicting tastes or interests. To do so we adapt the standard Pareto principle to those preference comparisons that are robust to belief imprecision and characterize social preferences that respect this robust principle. We also characterize a suitable restriction of this principle. The former principle provides stronger guidance when it can be satisfied; when it cannot, the latter always provides minimal guidance.

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Robust Social Decisions

Contemporary decision theory places crucial emphasis on a family of mathematical results called representation theorems, which relate criteria for evaluating the available options (such as the expected utility criterion) to axioms pertaining to the decision-maker’s preferences (for example, the transitivity axiom). Various claims have been made concerning the reasons for the importance of these results. The goal of this article is to assess their semantic role: representation theorems are purported to provide definitions of the decision-theoretic concepts involved in the evaluation criteria (such as those of utility or subjective probability that feature in the subjective expected utility criterion). In particular, this claim shall be examined from the perspective of philosophical theories of the meaning of theoretical terms.

Representation theorems and the semantics of decision-theoretic concepts

In this paper we present a sequent calculus for propositional dynamic logic built using an enriched version of the tree-hypersequent method and including an infinitary rule for the iteration operator. We prove that this sequent calculus is theoremwise equivalent to the corresponding Hilbert-style system, and that it is contraction-free and cut-free. All results are proved in a purely syntactic way.

/pdf/a-contraction-free-and-cut-free-sequent-calculus-for-4cern7fiey.pdf

Brian Hill

Papers

Confidence and decision

Awareness Dynamics

Robust Social Decisions

Representation theorems and the semantics of decision-theoretic concepts

A Contraction-free and Cut-free Sequent Calculus for Propositional Dynamic Logic