Uniform Substitution for Differential Game Logic

@article{Platzer2018UniformSF,
  title={Uniform Substitution for Differential Game Logic},
  author={Andr{\'e} Platzer},
  journal={ArXiv},
  year={2018},
  volume={abs/1804.05880}
}
This paper presents a uniform substitution calculus for differential game logic (dGL). Church's uniform substitutions substitute a term or formula for a function or predicate symbol everywhere. After generalizing them to differential game logic and allowing for the substitution of hybrid games for game symbols, uniform substitutions make it possible to only use axioms instead of axiom schemata, thereby substantially simplifying implementations. Instead of subtle schema variables and soundness… 
Constructive Game Logic
TLDR
Constructive Game Logic is developed, which extends Parikh's Game Logic with constructivity and with first-order programs à la Pratt’s first- order dynamic logic (DL), and provides the most general account of a Curry-Howard interpretation for any program logic to date, and the first at all for Game Logic.
Uniform Substitution At One Fell Swoop
TLDR
This paper proves soundness and completeness of one-pass uniform substitutions for dGL and introduces a uniform substitution mechanism that proceeds in a linear pass homomorphically along the formula.
Constructive Hybrid Games
Hybrid games combine discrete, continuous, and adversarial dynamics. Differential game logic () enables proving (classical) existence of winning strategies. We introduce constructive differential
Overview of Logical Foundations of Cyber-Physical Systems
TLDR
This chapter provides an informal overview of differential dynamic logic (dL), which provides logical specification and rigorous reasoning techniques for hybrid systems and explains how safety guarantees obtained in the land of verified models reach the level of CPS execution unharmed.
Thesis Proposal Practical End-to-End Verification of Cyber-Physical Systems
TLDR
This thesis addresses implementation and soundness gaps by using constructive logic and programming languages as the foundation of an end-to-end verification toolchain of cyber-physical systems called Constructive Differential Game Logic ( CdGL).
Proposal Practical End-to-End Verification of Cyber-Physical Systems
TLDR
This thesis addresses implementation and soundness gaps by using constructive logic and programming languages as the foundation of an end-to-end verification toolchain of cyber-physical systems called Constructive Differential Game Logic (CdGL).
Deductive Software Verification: Future Perspectives: Reflections on the Occasion of 20 Years of KeY
This paper describes the story of the first nine years of the KeY project, its original goals, the people involved, its setbacks, but also its occasional failures and blind alleys. It is deliberately
A Retrospective on Developing Hybrid System Provers in the KeYmaera Family - A Tale of Three Provers
TLDR
This chapter provides a retrospective on the developments of three theorem provers for hybrid systems, which share a common core logic, yet no line of code, and differ vastly in prover implementation technology.

References

SHOWING 1-10 OF 12 REFERENCES
L O ] 1 6 A pr 2 01 8 Uniform Substitution for Differential Game Logic
This paper presents a uniform substitution calculus for differential game logic (dGL). Church’s uniform substitutions substitute a term or formula for a function or predicate symbol everywhere. After
A Complete Uniform Substitution Calculus for Differential Dynamic Logic
  • A. Platzer
  • Computer Science
    Journal of Automated Reasoning
  • 2016
This article introduces a relatively complete proof calculus for differential dynamic logic (dL) that is entirely based on uniform substitution, a proof rule that substitutes a formula for a
Propositional game logic
  • R. Parikh
  • Philosophy
    24th Annual Symposium on Foundations of Computer Science (sfcs 1983)
  • 1983
We define a propositional logic of games which lies in expressive power between the Propositional Dynamic Logic of Fischer and Ladner [FL] and the µ-calculus of Kozen [K]. We show that the logic is
Differential Game Logic
  • A. Platzer
  • Computer Science
    ACM Trans. Comput. Log.
  • 2015
TLDR
The logic dGL is proved to be strictly more expressive than the corresponding logic of hybrid systems by characterizing the expressiveness of both.
KeYmaera: A Hybrid Theorem Prover for Hybrid Systems (System Description)
TLDR
This work integrates real quantifier elimination following an iterative background closure strategy to overcome the complexity of real arithmetic and implements a generalized free-variable sequent calculus and automatic proof strategies that decompose the hybrid system specification symbolically.
Formally verified differential dynamic logic
TLDR
The soundness theorem for differential dynamic logic is formalized, a logic for verifying hybrid systems theorem prover KeYmaera X, and the metatheory is extended to include features used in practice, such as systems of differential equations and functions of multiple arguments.
KeYmaera X: An Axiomatic Tactical Theorem Prover for Hybrid Systems
TLDR
KeYmaera X is a theorem prover for differential dynamic logic, a logic for specifying and verifying properties of hybrid systems, that allows users to specify custom proof search techniques as tactics, execute them in parallel, and interface with partial proofs via an extensible user interface.
Differential Hybrid Games
  • A. Platzer
  • Mathematics, Economics
    ACM Trans. Comput. Log.
  • 2017
TLDR
This article augments differential game logic with modalities for the combined dynamics of differential hybrid games and introduces differential game invariants and differential game variants for proving properties of differential games inductively.
Playing Hybrid Games with KeYmaera
TLDR
A case study in which a robot satisfies a joint safety and liveness objective in a factory automation scenario, in which the factory may perform interfering actions independently, is verified.
A Decision Method For Elementary Algebra And Geometry
By a decision method for a class K of sentence (or other expressions) is meant a method by means of which, given any sentence θ, one can always decide in a finite number of steps whether θ is in K;
...
...