Differential_Game_Logic swMATH ID: 32245 Software Authors: André Platzer Description: Differential Game Logic. 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. Homepage: https://www.isa-afp.org/entries/Differential_Game_Logic.html Related Software: KeYmaera; Transformer semantics; Quantales; KeYmaera X; KAD; Algebraic_VCs; Kleene Algebra; Ordinary Differential Equations; Archive Formal Proofs; Bellerophon; Coquelicot; C-CoRN; RODAS; Isabelle/HOL Cited in: 3 Publications Cited by 3 Authors 2 Platzer, André 1 Huerta y Munive, Jonathan Julián 1 Struth, Georg Cited in 2 Serials 1 Journal of Automated Reasoning 1 ACM Transactions on Computational Logic Cited in 3 Fields 3 Computer science (68-XX) 2 Mathematical logic and foundations (03-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year