A focused framework for emulating modal proof systems

International audienceSeveral deductive formalisms (e.g., sequent, nested sequent, labeled sequent, hyperse-quent calculi) have been used in the literature for the treatment of modal logics, and some connections between these formalisms are already known. Here we propose a general framework, which is based on a focused version of the labeled sequent calculus by Negri, augmented with some parametric devices allowing to restrict the set of proofs. By properly defining such restrictions and by choosing an appropriate polarization of formulas, one can obtain different, concrete proof systems for the modal logic K and for its extensions by means of geometric axioms. In particular, we show how to use the expressiveness of the labeled approach and the control mechanisms of focusing in order to emulate in our framework the behavior of a range of existing formalisms and proof systems for modal logic

A data-driven and risk-based prudential approach to validate the DDMRP planning and control system

In this paper, we study the single-item dynamic lot-sizing problem in an environment characterized by stochastic demand and lead times. A recent heuristic called Demand Driven MRP, widely implemented using modern ERP systems, proposes an algorithm that is will effectively tackle this problem. Our primary goal is to propose a theoretical foundation for such a heuristic approach. To this aim, we develop an optimization model inspired by the main principles behind the heuristic algorithm. Specifically, controls are of the type (s(t), S(t)) with time varying thresholds that react to short-run real orders; in this respect, control is risk-based and data-driven. We also consider service levels derived as tail risk measures to ensure fulfillment of realized demand with a predetermined probability; in this respect, our approach is prudential. Finally, we use our model as a benchmark to theoretically validate and contextualize the aforementioned heuristic