Uniform Substitution for Differential Game Logic
This paper presents a uniform substitution calculus for differential game logic ( Open image in new window ). 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-critical side conditions on the occurrence patterns of logical variables to restrict infinitely many axiom schema instances to sound ones, the resulting axiomatization adopts only a finite number of ordinary Open image in new window formulas as axioms, which uniform substitutions instantiate soundly. This paper proves soundness and completeness of uniform substitutions for the monotone modal logic Open image in new window . The resulting axiomatization admits a straightforward modular implementation of Open image in new window in theorem provers.
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