4,677 research outputs found

    Uniform Substitution for Differential Game Logic

    Full text link
    This paper presents a uniform substitution calculus for differential game logic (dGL). Church's uniform substitutions substitute a term or formula for a function or predicate symbol everywhere. After generalizing them to differential game logic and allowing for the substitution of hybrid games for game symbols, uniform substitutions make it possible to only use axioms instead of axiom schemata, thereby substantially simplifying implementations. Instead of subtle schema variables and soundness-critical side conditions on the occurrence patterns of logical variables to restrict infinitely many axiom schema instances to sound ones, the resulting axiomatization adopts only a finite number of ordinary dGL formulas as axioms, which uniform substitutions instantiate soundly. This paper proves soundness and completeness of uniform substitutions for the monotone modal logic dGL. The resulting axiomatization admits a straightforward modular implementation of dGL in theorem provers

    A Uniform Substitution Calculus for Differential Dynamic Logic

    Full text link
    This paper introduces a new proof calculus for differential dynamic logic (dL) that is entirely based on uniform substitution, a proof rule that substitutes a formula for a predicate symbol everywhere. Uniform substitutions make it possible to rely on axioms rather than axiom schemata, substantially simplifying implementations. Instead of nontrivial schema variables and soundness-critical side conditions on the occurrence patterns of variables, the resulting calculus adopts only a finite number of ordinary dL formulas as axioms. The static semantics of differential dynamic logic is captured exclusively in uniform substitutions and bound variable renamings as opposed to being spread in delicate ways across the prover implementation. In addition to sound uniform substitutions, this paper introduces differential forms for differential dynamic logic that make it possible to internalize differential invariants, differential substitutions, and derivations as first-class axioms in dL

    On the need for a global engineering initiative to mitigate climate change

    Full text link
    There is growing scientific evidence that the continued emission of greenhouse gases will eventually lead to catastrophic irreversible climate change and that, therefore, a global effort needs to be started to transition to a fully renewable economy. In this article, the engineering challenges of converting to emission-free power generation are reviewed and the feasibility of two proposed solutions, i.e. the ‘wind–water–solar’ and the ‘energy ship’ proposals, are discussed. It is concluded that a well-conceived and executed engineering effort needs to be initiated and guided by a Global Engineering Council for the purpose of examining and ranking various proposals and making specific recommendations
    corecore