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.
  author  = {André Platzer},
  title   = {Differential Game Logic},
  journal = {Archive of Formal Proofs},
  month   = jun,
  year    = 2019,
  note    = {\url{http://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.