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

Offline and online data: on upgrading functional information to knowledge

This paper addresses the problem of upgrading functional information to knowledge. Functional information is defined as syntactically well-formed, meaningful and collectively opaque data. Its use in the formal epistemology of information theories is crucial to solve the debate on the veridical nature of information, and it represents the companion notion to standard strongly semantic information, defined as well-formed, meaningful and true data. The formal framework, on which the definitions are based, uses a contextual version of the verificationist principle of truth in order to connect functional to semantic information, avoiding Gettierization and decoupling from true informational contents. The upgrade operation from functional information uses the machinery of epistemic modalities in order to add data localization and accessibility as its main properties. We show in this way the conceptual worthiness of this notion for issues in contemporary epistemology debates, such as the explanation of knowledge process acquisition from information retrieval systems, and open data repositories

The Basic Principles of Uncertain Information Fusion. An organized review of merging rules in different representation frameworks

We propose and advocate basic principles for the fusion of incomplete or uncertain information items, that should apply regardless of the formalism adopted for representing pieces of information coming from several sources. This formalism can be based on sets, logic, partial orders, possibility theory, belief functions or imprecise probabilities. We propose a general notion of information item representing incomplete or uncertain information about the values of an entity of interest. It is supposed to rank such values in terms of relative plausibility, and explicitly point out impossible values. Basic issues affecting the results of the fusion process, such as relative information content and consistency of information items, as well as their mutual consistency, are discussed. For each representation setting, we present fusion rules that obey our principles, and compare them to postulates specific to the representation proposed in the past. In the crudest (Boolean) representation setting (using a set of possible values), we show that the understanding of the set in terms of most plausible values, or in terms of non-impossible ones matters for choosing a relevant fusion rule. Especially, in the latter case our principles justify the method of maximal consistent subsets, while the former is related to the fusion of logical bases. Then we consider several formal settings for incomplete or uncertain information items, where our postulates are instantiated: plausibility orderings, qualitative and quantitative possibility distributions, belief functions and convex sets of probabilities. The aim of this paper is to provide a unified picture of fusion rules across various uncertainty representation settings

Managed Floats to Damp Shocks like 1982-5 and 2006-9: Field and Laboratory Evidence for Chinese Interest in a Single World Currency

This paper’s field evidence is: (1) many official sectors rapidly forget the damage of the 1982-85 exchange rate liquidity crisis and reverted to what caused that crisis, namely a closed economy clean floats perspective; and (2) the 2006-2008/9 exchange rate liquidity shock would have been more drastic but for central bank currency swaps. This evidence is bolstered by a laboratory experiment that incorporates more aspects of real world complexity and more different sorts of official and private sector agents than are feasible in econometric or algebraic investigations and employs a new central bank cooperation-conflict model of exchange rate determination , and is within an umbrella theory of Pope, namely SKAT, the Stages of Knowledge Ahead Theory. SKAT allows for risk effects from stages omitted in normal models, including those from (a) difficulties of agents in evaluating alternatives in a complex environment in which the assumed maximization of expected utility is impossible; and (b) preference for safety and reliability is not trivialized. Our joint field plus laboratory evidence indicates that official sectors should maintain an international exchange rate oriented perspective, or better yet, a single world currency as recommended by Zhou Xiaochuan, head of the People’s Bank of China. To avoid rapid forgetting of havoc from isolationist clean floats and the value of stable exchange rates, a new syllabus, as under the SKAT umbrella, is fundamental in the education of official sector members in order to furnish them with a coherent alternative intellectual framework to current university education that excludes liquidity crises.clean float, managed float, IMF imposed conditions, exchange rate regime, exchange rate volatility, experiment, SKAT the Stages of Knowledge Ahead Theory, monetary policy, transparent policy, exchange rate shocks, central bank cooperation, central bank conflict