Logics of Dynamical Systems

We study the logic of dynamical systems, that is, logics and proof principles for properties of dynamical systems. Dynamical systems are mathematical models describing how the state of a system evolves over time. They are important in modeling and understanding many applications, including embedded...

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Bibliographic Details
Published in:2012 27th Annual IEEE Symposium on Logic in Computer Science pp. 13 - 24
Main Author: Platzer, A.
Format: Conference Proceeding
Language:English
Published: IEEE 01.06.2012
Subjects:
Acceleration
Automata
axiomatization
Complexity theory
deduction
differential dynamic logic
Differential equations
dynamic logic
hybrid systems
logic of dynamical systems
Mathematical model
Semantics
Vehicle dynamics
ISBN:1467322636, 9781467322638
ISSN:1043-6871
Online Access:Get full text
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Summary:We study the logic of dynamical systems, that is, logics and proof principles for properties of dynamical systems. Dynamical systems are mathematical models describing how the state of a system evolves over time. They are important in modeling and understanding many applications, including embedded systems and cyber-physical systems. In discrete dynamical systems, the state evolves in discrete steps, one step at a time, as described by a difference equation or discrete state transition relation. In continuous dynamical systems, the state evolves continuously along a function, typically described by a differential equation. Hybrid dynamical systems or hybrid systems combine both discrete and continuous dynamics. This is a brief survey of differential dynamic logic for specifying and verifying properties of hybrid systems. We explain hybrid system models, differential dynamic logic, its semantics, and its axiomatization for proving logical formulas about hybrid systems. We study differential invariants, i.e., induction principles for differential equations. We briefly survey theoretical results, including soundness and completeness and deductive power. Differential dynamic logic has been implemented in automatic and interactive theorem provers and has been used successfully to verify safety-critical applications in automotive, aviation, railway, robotics, and analogue electrical circuits.
ISBN:1467322636
9781467322638
ISSN:1043-6871
DOI:10.1109/LICS.2012.13