# Differential Game Logic

 Title: Differential Game Logic Author: André Platzer Submission date: 2019-06-03 Abstract: This formalization provides differential game logic (dGL), a logic for proving properties of hybrid game. In addition to the syntax and semantics, it formalizes a uniform substitution calculus for dGL. Church's uniform substitutions substitute a term or formula for a function or predicate symbol everywhere. The uniform substitutions for dGL also substitute hybrid games for a game symbol everywhere. We prove soundness of one-pass uniform substitutions and the axioms of differential game logic with respect to their denotational semantics. One-pass uniform substitutions are faster by postponing soundness-critical admissibility checks with a linear pass homomorphic application and regain soundness by a variable condition at the replacements. The formalization is based on prior non-mechanized soundness proofs for dGL. BibTeX: @article{Differential_Game_Logic-AFP, author = {André Platzer}, title = {Differential Game Logic}, journal = {Archive of Formal Proofs}, month = jun, year = 2019, note = {\url{https://isa-afp.org/entries/Differential_Game_Logic.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License Status: [ok] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.