Disproving Using the Inverse Method by Iterative Refinement of Finite Approximations

International audienceIn first-order logic, forward search using a complete strategy such as the inverse method can get stuck deriving larger and larger consequence sets when the goal query is unprovable. This is the case even in trivial theories where backward search strategies such as tableaux methods will fail finitely. We propose a general mechanism for bounding the consequence sets by means of finite approximations of infinite types. If the inverse method also implements forward subsumption and globalization, then the search space under this approximation is finite. We therefore obtain a type-directed iterative refinement algorithm for disproving queries. The method has been implemented for intuitionistic first-order logic, and we discuss its performance on a variety of problems

A Climate for Change in the UN Security Council? Member States' Approaches to the Climate-Security Nexus

This research report is the first to systematically engage with the growing political agenda of the climate-security nexus and to place a particular focus on the relationship between the state and the only international organ with a mandate to maintain international peace and security: the United Nations Security Council (UNSC). Discussions that have been ongoing since 2007, scattered governmental positions and the difficulty of achieving an overview of the various understandings, topics, concerns and responses of the UNSC member states in relation to the climate-security nexus all indicate a need to address this topic. This report therefore assesses and maps if and how the UNSC members acknowledge the linkages between climate change and security and how they position themselves with respect to these debates in the UNSC. With a large international network of interdisciplinary and country-specialized partner scientists, the analysis relies on an extensive spectrum of official primary sources from member state governments, various ministry strategies (such as those addressing security and climate change), UNSC documents and interdisciplinary academic literature on the climate-security nexus. It is located in the context of substantiated planetary climate emergencies and existential threats as well as urgent calls for action from the UN and member state representatives, scientific networks in Earth System Sciences and youth protests. Based on broad empirical research findings, this report concludes that all 15 current UNSC member states acknowledge the climate-security nexus in complex, changing and partly country-dependent ways. The report formulates an outlook and recommendations for decision-makers and scholars with a particular focus on strengthening the science-policy interface and dialogue and emphasizing the urgent need for institutional, multilateral and scientifically informed change. It also illustrates how essential it is for the UNSC to recognize and adapt institutional working methods to the interrelations of climate change and security and their effects as a cross-cutting issue

Cut elimination in multifocused linear logic

We study cut elimination for a multifocused variant of full linear logic in the sequent calculus. The multifocused normal form of proofs yields problems that do not appear in a standard focused system, related to the constraints in grouping rule instances in focusing phases. We show that cut elimination can be performed in a sensible way even though the proof requires some specific lemmas to deal with multifocusing phases, and discuss the difficulties arising with cut elimination when considering normal forms of proofs in linear logic.Comment: In Proceedings LINEARITY 2014, arXiv:1502.0441

Space-efficient Planar Acyclicity Constraints - A Declarative Pearl

International audienceMany constraints on graphs, e.g. the existence of a simple path between two vertices, or the connectedness of the subgraph induced by some selection of vertices, can be straightforwardly represented by means of a suitable acyclicity constraint. One method for encoding such a constraint in terms of simple, local constraints uses a 3-valued variable for each edge, and an (N+1)-valued variable for each vertex, where N is the number of vertices in the entire graph. For graphs with many vertices, this can be somewhat inefficient in terms of space usage. In this paper, we show how to refine this encoding into one that uses only a single bit of information, i.e. a 2-valued variable, per vertex, assuming the graph in question is planar. We furthermore show how this same constraint can be used to encode connectedness constraints, and a variety of other graph-related constraints