Uniform Substitution for Dynamic Logic with Communicating Hybrid Programs

03/30/2023

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by   Marvin Brieger, et al.

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This paper introduces a uniform substitution calculus for dℒ_CHP, the dynamic logic of communicating hybrid programs. Uniform substitution enables parsimonious prover kernels by using axioms instead of axiom schemata. Instantiations can be recovered from a single proof rule responsible for soundness-critical instantiation checks rather than being spread across axiom schemata in side conditions. Even though communication and parallelism reasoning are notorious for necessitating subtle soundness-critical side conditions, uniform substitution when generalized to dℒ_CHP manages to limit and isolate their conceptual overhead. Since uniform substitution has proven to simplify the implementation of hybrid systems provers substantially, uniform substitution for dℒ_CHP paves the way for a parsimonious implementation of theorem provers for hybrid systems with communication and parallelism.