Cut Elimination for a Logic with Induction and Co-induction

Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles are based on a proof theoretic (rather than set-theoretic) notion of definition. Definitions are akin to logic programs, where the left and right rules for defined atoms allow one to view theories as "closed" or defining fixed points. The use of definitions and free equality makes it possible to reason intentionally about syntax. We add in a consistent way rules for pre and post fixed points, thus allowing the user to reason inductively and co-inductively about properties of computational system making full use of higher-order abstract syntax. Consistency is guaranteed via cut-elimination, where we give the first, to our knowledge, cut-elimination procedure in the presence of general inductive and co-inductive definitions.Comment: 42 pages, submitted to the Journal of Applied Logi

An Open Challenge Problem Repository for Systems Supporting Binders

A variety of logical frameworks support the use of higher-order abstract syntax in representing formal systems; however, each system has its own set of benchmarks. Even worse, general proof assistants that provide special libraries for dealing with binders offer a very limited evaluation of such libraries, and the examples given often do not exercise and stress-test key aspects that arise in the presence of binders. In this paper we design an open repository ORBI (Open challenge problem Repository for systems supporting reasoning with BInders). We believe the field of reasoning about languages with binders has matured, and a common set of benchmarks provides an important basis for evaluation and qualitative comparison of different systems and libraries that support binders, and it will help to advance the field.Comment: In Proceedings LFMTP 2015, arXiv:1507.0759

Temporary measures in Italy: buying or losing time?

In this paper we examine the effects of temporary measures on the Italian budget in the period 1997-2006 and assess their appropriateness. We also analyse the role of extraordinary operations which reduced the level of public debt in the same time frame while leaving the net worth of the public sector broadly unchanged. Our analysis suggests that temporary measures and extraordinary operations were used mainly to comply formally with EU fiscal rules without incurring the economic and political costs of more structural adjustment. Policy-makers bought time in a worsening cyclical context, expecting the recovery to be imminent. Ex post information reveals that the timing of this strategy was wrong. In a broader temporal perspective, the use of extraordinary operations has made it possible to postpone more permanent actions which would have improved the sustainability of Italian public finances. It is difficult not to conclude that precious time has been lost designing an equitable distribution across generations of the expected costs of the upcoming demographic transition.temporary measures, economic cycle, budgetary policies.

Real-time determinants of fiscal policies in the euro area: Fiscal rules, cyclical conditions and elections

We examine the impact of four factors on the fiscal policies of the euro-area countries over the last two decades: the state of public finances, the European fiscal rules, cyclical conditions and general elections. We rely on information actually available to policy-makers at the time of budgeting in constructing our explanatory variables. Our estimates indicate that policies have reacted to the state of public finances in a stabilizing manner. The European rules have significantly affected the behaviour of countries with excessive deficits. Apart from these cases, the rules appear to have reaffirmed existing preferences. We find a relatively large symmetrical counter-cyclical reaction of fiscal policy and strong evidence of a political budget cycle. The electoral manipulation of fiscal policy, however, occurs only if the macroeconomic context is favourable.fiscal policy, real-time information, euro-area countries, stabilisation policies, fiscal rules, political budget cycle

Scheduling of an aircraft fleet

Scheduling is the task of assigning resources to operations. When the resources are mobile vehicles, they describe routes through the served stations. To emphasize such aspect, this problem is usually referred to as the routing problem. In particular, if vehicles are aircraft and stations are airports, the problem is known as aircraft routing. This paper describes the solution to such a problem developed in OMAR (Operative Management of Aircraft Routing), a system implemented by Bull HN for Alitalia. In our approach, aircraft routing is viewed as a Constraint Satisfaction Problem. The solving strategy combines network consistency and tree search techniques

Dealing with unexpected shocks to the budget

In this paper we assess the impact of unexpected shocks to real interest rates and GDP on government budgets for nine European Union countries. Shocks are estimated as onestep-ahead forecast errors arising from a recursive bivariate VAR model. To assess the impact on the budgets we use available information on budgetary sensitivities with respect to the business cycle and estimate the sensitivities to changes in interest rates on the basis of the maturity structure of public debts. Our analysis is relevant, in particular, to define what safety margins are needed to avoid the deficit exceeding the 3 per cent Maastricht threshold. The approach followed in this paper differs in two respects from standard analyses aiming at defining budgetary positions that satisfy the Stability and Growth Pact. First, whereas the latter examine only fluctuations in economic activity, we also consider fluctuations in interest rates. Second, whereas standard analyses focus on deviations from trends and define margins for the medium-term cyclically adjusted balance, we examine unexpected shocks and define margins for nominal balances. The results point to significant differences in the required margins across countries, depending on the amplitude of past shocks, the magnitude of automatic stabilizers and the size and maturity structure of the debt. In the case of Italy, the country with the highest debt/GDP ratio and the largest fraction of short-term debt, the impact of unexpected shocks to interest rates may be quite substantial. However, when shocks to interest rates and GDP are considered jointly, other countries (Belgium and Finland) seem to require larger margins.budgeting, Stability and Growth Pact, forecast errors

The short-term impact of government budgets on prices: evidence from macroeconomic models

This paper reviews the existing empirical evidence on the short-term impact on prices of fiscal variables and assesses it against new results from harmonised simulations, conducted with six well-established econometric models used by the ECB and five national central banks (NCBs) of the Eurosystem. The outcome is also compared with results from the European Commission and the OECD models. Overall, a broad consensus appears on the impact on prices of changes in individual government budget items in the euro area. In all cases, changes in government demand and in direct taxes paid by households have a limited impact on prices in the first year while, in contrast, changes in indirect taxes and employers' social security contributions have a relatively large impact. The second year results show that the effects on prices usually take some time to materialise fully; in particular, they often become large for the public consumption shock. JEL Classification: E17, E31, E62euro area, Fiscal Policy, model simulations, prices