The expressive power of modal logic with inclusion atoms

Modal inclusion logic is the extension of basic modal logic with inclusion atoms, and its semantics is defined on Kripke models with teams. A team of a Kripke model is just a subset of its domain. In this paper we give a complete characterisation for the expressive power of modal inclusion logic: a class of Kripke models with teams is definable in modal inclusion logic if and only if it is closed under k-bisimulation for some integer k, it is closed under unions, and it has the empty team property. We also prove that the same expressive power can be obtained by adding a single unary nonemptiness operator to modal logic. Furthermore, we establish an exponential lower bound for the size of the translation from modal inclusion logic to modal logic with the nonemptiness operator.Comment: In Proceedings GandALF 2015, arXiv:1509.0685

Changes in Finland's International Investment Position, 1985-1998. A Brief Statistical Analysis

This paper attempts to describe and compare developments in the components of Finland’s net international investment position (NIIP). The data consist of sectoral flows and valuation items over the period 1985 – 1998, which is, for analytical purposes, broken down into two subperiods: before and after the Finnish markka was floated. The study focuses on the main sectors, ie banks, corporations and the central government. Valuation items (changes in exchange rates and equity prices) are also important in the decomposition of the NIIP, particularly as regards recent history of equity prices. The mean and variability of each item is estimated, and for some items also bivariate robust variance tests are carried out. The major feature in Finland’s balance of payments has been nonresidents’ increased interest in Finnish equities as an object of investment. This phenomenon, along with the boom in share prices, has in recent years raised the equity holdings of foreigners to the rank of most significant item in Finland’s international investment position. Another important feature in the BOP is the rapid growth of the central government’s foreign debt due to the deep recession of 1991 - 1994. In respect to Finland, it is important to note the different stories told by developments in NIIP vs net external debt components: NIIP figures indicate that ownership of corporations based in Finland has indeed become global and that the value of shares has been increasing, whereas net external debt figures indicate that the economy has succeeded in restoring external indebtedness to pre-recession levels. The results also confirm that the Finnish banks still contribute prominently to variations in Finnish BOP flows. As regards the late 1980s and early 1990s, this can be inferred from the highly bank-oriented structure of Finnish financial markets, but the same holds true during the 1990s as well in the period of recovery from economic crisis.balance of payments; international investment position; net external debt

The European Natural Gas Market: Imports to Rise Considerably

Since the late 1990s, natural gas has been the second most important source of energy in the European Union after oil. Current forecasts predict that the demand for natural gas will continue to rise over the long term. As the production of natural gas in the EU has already passed its peak and will drop in coming years, natural gas imports will have to rise considerably. To ensure according supplies is possible in the long run, as approximately 80% of the world's natural gas reserves are located within the economic reach of the EU-primarily in the former Soviet Union and Middle East. A supply of imported natural gas adequate to cover declines in EU production is contractually guaranteed through 2020. Additional projects will permit an increase in natural gas consumption in the EU of 20 to 30%. By 2020, 80% of the EU's supply will come from imports. Russia will remain by far the largest supplier, followed by Norway and Algeria. Security concerns are raised by the importation of natural gas from a small handful of suppliers. While the regional diversification of imports is only possible to a limited extent, the construction of a pipeline to connect Europe with natural gas rich nations on the Caspian Sea and in the Middle East would be a step in the right direction. The expansion of capacities for production, transport and storage of liquified natural gas (LNG) could also help to augment diversification.Natural gas, LNG, Import dependence, Reserves, Pipelines