Uniform Substitution for Differential Refinement Logic

Abstract

This paper introduces a uniform substitution calculus for differential refinement logic dRL. The logic dRL extends the differential dynamic logic dL such that one can simultaneously reason about properties of and relations between hybrid systems. Refinements are useful e.g. for simplifying proofs by relating a concrete hybrid system to an abstract one from which the property can be proved more easily. Uniform substitution is the key to parsimonious prover microkernels. It enables the verbatim use of single axiom formulas instead of axiom schemata with soundness-critical side conditions scattered across the proof calculus. The uniform substitution rule can then be used to instantiate all axioms soundly. Access to differential variables in dRL enables more control over the notion of refinement, which is shown to be decidable on a fragment of hybrid programs.

IJCAR 2024

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Cited by in corpus (5)

• Verification of Autonomous Neural Car Control with KeYmaera X
• The Significance of Symbolic Logic for Scientific Education
• Refactoring-as-Propositions: Proved Refactoring of Hybrid Systems via Proved Refinements
• A Deductive Refinement Calculus for Differential-Algebraic Programs
• Heterogeneous Dynamic Logic: Provability Modulo Program Theories