Name
Abstract | ||
|---|---|---|
We prove the completeness of an axiomatization for differential equation invariants. First, we show that the differential equation axioms in differential dynamic logic are complete for all algebraic invariants. Our proof exploits differential ghosts, which introduce additional variables that can be chosen to evolve freely along new differential equations. Cleverly chosen differential ghosts are the proof-theoretical counterpart of dark matter. They create new hypothetical state, whose relationship to the original state variables satisfies invariants that did not exist before. The reflection of these new invariants in the original system then enables its analysis. We then show that extending the axiomatization with existence and uniqueness axioms makes it complete for all local progress properties, and further extension with a real induction axiom makes it complete for all real arithmetic invariants. This yields a parsimonious axiomatization, which serves as the logical foundation for reasoning about invariants of differential equations. Moreover, our results are purely axiomatic, and so the axiomatization is suitable for sound implementation in foundational theorem provers. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1145/3209108.3209147 | LICS'18: PROCEEDINGS OF THE 33RD ANNUAL ACM/IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE |
Keywords | DocType | Volume |
differential equation axiomatization,differential dynamic logic,differential ghosts | Conference | abs/1802.01226 |
Citations | PageRank | References |
2 | 0.37 | 10 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| André Platzer | 1 | 1425 | 82.57 |
| Yong Kiam Tan | 2 | 107 | 12.93 |