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Compositional Proofs in Differential Dynamic Logic dL

Simon Lunel, Benoit Boyer, Jean-Pierre Talpin
2017 2017 17th International Conference on Application of Concurrency to System Design (ACSD)  
In this paper, we address the specification of hybrid system using Platzer's differential dynamic logic (dL).  ...  Prior notions of composition in dL were not associative. (2) We provide a theorem which characterizes necessary conditions to automate the proof that composed components satisfy the composition of their  ...  Differential Dynamic Logic (dL) This section briefly introduces the differential dynamic logic (dL), defined by A. Platzer [1] .  ... 
doi:10.1109/acsd.2017.16 dblp:conf/acsd/LunelBT17 fatcat:nvkzk7b74vgmxgfbo6zfqlr4ty

Logics of Dynamical Systems

Andre Platzer
2012 2012 27th Annual IEEE Symposium on Logic in Computer Science  
We study the logic of dynamical systems, that is, logics and proof principles for properties of dynamical systems.  ...  Index Terms-logic of dynamical systems, dynamic logic, differential dynamic logic, hybrid systems, axiomatization, deduction  ...  The logics and proof systems we consider are compositional.  ... 
doi:10.1109/lics.2012.13 dblp:conf/lics/Platzer12 fatcat:uyo3s7frizgt7d2haga3yylifa

Towards a Hybrid Dynamic Logic for Hybrid Dynamic Systems

André Platzer
2007 Electronical Notes in Theoretical Computer Science  
We introduce a hybrid variant of a dynamic logic with continuous state transitions along differential equations, and we present a sequent calculus for this extended hybrid dynamic logic.  ...  With these extensions, our hybrid dynamic logic advances the capabilities for compositional reasoning about (semialgebraic) hybrid dynamic systems.  ...  This differential dynamic logic, dL, is suitable for verifying hybrid dynamic systems.  ... 
doi:10.1016/j.entcs.2006.11.026 fatcat:6r6ztgkqqfchdm24rfxjuwkpze

Logical Analysis of Hybrid Systems [chapter]

André Platzer
2012 Lecture Notes in Computer Science  
programs (HPs) . . . . . . . ..2.2 Statements and control structures definable with hybrid programs ..2.3 Operators and meaning in differential dynamic logic (dL ) . ..3.1 Comparison of DAL with DA-programs  ...  Rule schemata of the free-variable calculus for differential dynamic logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.12 Correspondence of dynamic proof rules and transition semantics  ... 
doi:10.1007/978-3-642-31623-4_3 fatcat:b7gnxodcqfgsfgj7an4aiptazm

Dynamic Logics of Dynamical Systems [article]

André Platzer
2012 arXiv   pre-print
We explain the dynamical system models, dynamic logics of dynamical systems, their semantics, their axiomatizations, and proof calculi for proving logical formulas about these dynamical systems.  ...  Differential dynamic logics have been implemented in automatic and interactive theorem provers and have been used successfully to verify safety-critical applications in automotive, aviation, railway, robotics  ...  The logics and proof systems we consider are compositional.  ... 
arXiv:1205.4788v1 fatcat:2ahunsfdzfamdiwzd66m5e4wzq

Differential Dynamic Logic for Hybrid Systems

André Platzer
2008 Journal of automated reasoning  
elimination for real arithmetic to dynamic logic.  ...  Keywords dynamic logic · differential equations · sequent calculus · axiomatisation · automated theorem proving · verification of hybrid systems Introduction Ensuring correct functioning of complex physical  ...  Formulas of Differential Dynamic Logic The formulas of dL are defined as in first-order dynamic logic [35] .  ... 
doi:10.1007/s10817-008-9103-8 fatcat:rr2zob6u6jdnzftqjysgybtvyq

A Program Logic to Verify Signal Temporal Logic Specifications of Hybrid Systems: Extended Technical Report [article]

Hammad Ahmad, Jean-Baptiste Jeannin
2021 arXiv   pre-print
Differential dynamic logic (dL) was introduced to reason about the end states of a hybrid program.  ...  In this paper, we bridge the gap between the two different logics by introducing signal temporal dynamic logic (STdL) -- a dynamic logic that reasons about a subset of STL specifications over executions  ...  CONCLUSION In this work, we introduce signal temporal dynamic logic (STdL), a logic that extends and combines differential dynamic logic (dL) with a fragment of signal temporal logic (STL).  ... 
arXiv:2103.08117v2 fatcat:cmydhnwxyfhzze22embx6dgumu

dTL2: Differential Temporal Dynamic Logic with Nested Temporalities for Hybrid Systems [chapter]

Jean-Baptiste Jeannin, André Platzer
2014 Lecture Notes in Computer Science  
The differential temporal dynamic logic dTL 2 is a logic to specify temporal properties of hybrid systems.  ...  It extends differential temporal dynamic logic dTL with nested temporalities.  ...  Based on dynamic logic, differential dynamic logic only reasons about the end state of a system.  ... 
doi:10.1007/978-3-319-08587-6_22 fatcat:e44egzjn75frlg265ml7e4rweq

ARCH-COMP20 Category Report: Hybrid Systems Theorem Proving

Stefan Mitsch, Jonathan Julián Huerta y Munive, Xiangyu Jin, Bohua Zhan, Shuling Wang, Naijun Zhan
2020 International Workshop on Applied Verification of Continuous and Hybrid Systems  
S) Scripted in which a significant part of the verification is done with dedicated proof scripts or problem-specific proof tactics.  ...  unambiguity and precision of program semantics, and iii) The mathematical rigor of logical reasoning principles.  ...  This material is based upon work supported by the AFOSR under grant number FA9550- We thank the entire Logical Systems Lab at Carnegie Mellon University for their many contributions and suggestions to  ... 
doi:10.29007/bdq9 dblp:conf/arch/MitschMJZWZ20 fatcat:kygslehltnbzdnsqbcohb5spuu

Overview of Logical Foundations of Cyber-Physical Systems [article]

André Platzer
2019 arXiv   pre-print
Differential dynamic logic (dL) provides logical specification and rigorous reasoning techniques for hybrid systems.  ...  The logic dL is implemented in the theorem prover KeYmaera X, which has been instrumental in verifying ground robot controllers, railway systems, and the next-generation airborne collision avoidance system  ...  are fascinating and useful, but presently only implemented in previous-generation theorem provers Quesel, 2008, Renshaw et al., 2011]. Acknowledgements.  ... 
arXiv:1910.11232v1 fatcat:uqhuwcyi25gr7aq75qvgfmzfe4

A logic of proofs for differential dynamic logic: toward independently checkable proof certificates for dynamic logics

Nathan Fulton, André Platzer
2016 Proceedings of the 5th ACM SIGPLAN Conference on Certified Programs and Proofs - CPP 2016  
This paper presents a differential dynamic logic with such an explicit representation of proofs.  ...  The resulting logic extends both the syntax and semantics of differential dynamic logic with proof terms -syntactic representations of logical deductions.  ...  We thank the members of the Logical Systems Lab at Carnegie Mellon University for helpful discussions related to this work. We also thank the anonymous reviewers for their suggestions and comments.  ... 
doi:10.1145/2854065.2854078 dblp:conf/cpp/FultonP16 fatcat:srmlvx5csjd5xbdozezl3zwlgm

Integrating runtime validation and hardware-in-the-loop (HiL) testing with V & V in complex hybrid systems

S.D. Dewasurendra, A.C. Vidanapathirana, S.G. Abeyratne
2019 Journal of the National Science Foundation of Sri Lanka  
compositional and (3) the HA based test generation method is compositional, sound and complete relative to firstorder logic of differential equations.  ...  The study formally proves that (1) the proposed HA based formal verification method is compositional, sound and complete relative to first-order logic of differential equations, (2) the modular tests are  ...  Differential dynamic logics for verification of continuous-variable dynamics A proof calculus for Differential Dynamic Logic (dL) (first order dynamic logic for reals) and its temporal extension, developed  ... 
doi:10.4038/jnsfsr.v47i4.9678 fatcat:jlqubuqeznauxnp2ifvu6r6oam

Logic and Compositional Verification of Hybrid Systems [chapter]

André Platzer
2011 Lecture Notes in Computer Science  
The continuous dynamics of hybrid systems can be modeled by differential equations, the discrete dynamics by a combination of discrete state-transitions and conditional execution.  ...  In this tutorial, we survey state-of-the-art verification techniques for hybrid systems. In particular, we focus on a coherent logical approach for systematic hybrid systems analysis.  ...  In the fully symbolic domain of differential dynamic logic, however, we can do better. There is a sound compositional proof system that works fully symbolically [30, 32] .  ... 
doi:10.1007/978-3-642-22110-1_4 fatcat:7dipdx5p4rbj5k5qcvog5kphea

KeYmaera X: An Axiomatic Tactical Theorem Prover for Hybrid Systems [chapter]

Nathan Fulton, Stefan Mitsch, Jan-David Quesel, Marcus Völp, André Platzer
2015 Lecture Notes in Computer Science  
KeYmaera X is a theorem prover for differential dynamic logic (dL), a logic for specifying and verifying properties of hybrid systems.  ...  The prover kernel contains a list of sound dL axioms that are instantiated using a uniform substitution proof rule.  ...  Differential dynamic logic (dL) [10, 11, 12] is a first-order multimodal logic for specifying and proving properties of hybrid programs.  ... 
doi:10.1007/978-3-319-21401-6_36 fatcat:cyfct4v6kbhprnkcv4zq25mo64

Differential Dynamic Logic dℒ [chapter]

André Platzer
2010 Logical Analysis of Hybrid Systems  
Dynamic Logic dL Differential Dynamic Logic dL Differential Dynamic Logic dL .5 Proof Calculus Differential Dynamic Logic dL Differential Dynamic Logic dL Differential Dynamic  ...  Dynamic Logic dL Differential Dynamic Logic dL Differential Dynamic Logic dL Differential Dynamic Logic dL Differential Dynamic Logic dL  ...  We prefix each formula in the proof of φ with A and show that this gives a proof of A φ . i∃ is not needed in the proof due to the absence of free logical variables.  ... 
doi:10.1007/978-3-642-14509-4_2 fatcat:awfwcd5vqvc4lhmcfgpysr65bm
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