Computer Science Department
School of Computer Science, Carnegie Mellon University


A Complete Axiomatization of Differential Game Logic
for Hybrid Games

André Platzer

January 2013
Revised July 2013

This report is an updated version of Computer Science Department
Technical Report CMU-CS-13-100

This report also supersedes Computer Science Deparment
Technical Report CMU-CS-12-105.

Also appears as: Differential Game Logic
, 2015


Keywords: Game logic, hybrid dynamical systems, hybrid games, axiomatization

Differential game logic (dGL) is a logic for specifying and verifying properties of hybrid games, i.e. games that combine discrete, continuous, and adversarial dynamics. Unlike hybrid systems, hybrid games allow choices in the system dynamics to be resolved adversarially by different players with different objectives. The logic dGL can be used to study the existence of winning strategies for such hybrid games, i.e. ways of resolving the player's choices in some way so that he wins by achieving his objective for all choices of the opponent. Hybrid games are determined, i.e. one player has a winning strategy from each state, yet their winning regions may require transfinite closure ordinals. The logic dGL, nevertheless, has a sound and complete axiomatization relative to any expressive logic. Separating axioms are identified that distinguish hybrid games from hybrid systems. Finally, dGL is proved to be strictly more expressive than the corresponding logic of hybrid systems.

52 pages

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