scholarly journals A Complete Axiomatization of Quantified Differential Dynamic Logic for Distributed Hybrid Systems

2012 ◽  
Vol 8 (4) ◽  
Author(s):  
Andre Platzer
Keyword(s):  
Hybrid Systems ◽  
Dynamic Logic ◽  
Complete Axiomatization

scholarly journals Differential Dynamic Logic for Hybrid Systems

2008 ◽  
Vol 41 (2) ◽  
pp. 143-189 ◽  
Author(s):  
André Platzer
Keyword(s):  
Hybrid Systems ◽  
Dynamic Logic

scholarly journals Predicate Transformer Semantics for Hybrid Systems

2021 ◽  
Author(s):  
Jonathan Julián Huerta y Munive ◽  
Georg Struth
Keyword(s):  
Hybrid Systems ◽  
Vector Fields ◽  
Dynamic Logic ◽  
Invariant Sets ◽  
Deductive Verification ◽  
Semantic Framework ◽  
Verification Of Hybrid Systems ◽  
Predicate Transformer ◽  
Predicate Transformer Semantics

AbstractWe present a semantic framework for the deductive verification of hybrid systems with Isabelle/HOL. It supports reasoning about the temporal evolutions of hybrid programs in the style of differential dynamic logic modelled by flows or invariant sets for vector fields. We introduce the semantic foundations of this framework and summarise their Isabelle formalisation as well as the resulting verification components. A series of simple examples shows our approach at work.

scholarly journals A Logic for Verifying Metric Temporal Properties in Distributed Hybrid Systems

10.29007/smg4 ◽  
2018 ◽  
Author(s):  
Ping Hou ◽  
Yifei Chen
Keyword(s):  
Hybrid Systems ◽  
Dynamic Logic ◽  
Temporal Reasoning ◽  
Temporal Behavior ◽  
Final States ◽  
Conservative Extension ◽  
Metric Temporal Logic ◽  
Temporal Properties ◽  
Modular Verification ◽  
Base Logic

We introduce a logic for specifying and verifying metric temporal properties of distributed hybrid systems that combines quantified differential dynamic logic (QdL) for reasoning about the possible behavior of distributed hybrid systems with metric temporal logic (MTL) for reasoning about the metric temporal behavior during their operation. For our combined logic, we generalize the semantics of dynamic modalities to refer to hybrid traces instead of final states. Further, we prove that this gives a conservative extension of QdL for distributed hybrid systems. On this basis, we provide a modular verification calculus that reduces correctness of metric temporal behavior of distributed hybrid systems to generic temporal reasoning and then non-temporal reasoning, and prove that we obtain a complete axiomatization relative to the non-temporal base logic QdL.

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