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Starting with Hoare Logic over 50 years ago, numerous program logics havebeen devised to reason about the diverse programs encountered in the realworld. This includes reasoning about computational effects, particularly thoseeffects that cause the program execution to branch into multiple paths due to,.e.g nondeterministic or probabilistic choice.  The recently introduced Outcome Logic reimagines Hoare Logic with branchingat its core, using an algebraic representation of choice to capture programsthat branch into many outcomes. In this article, we expand on prior OutcomeLogic papers in order to give a more authoritative and comprehensive account ofthe metatheory. This includes a relatively complete proof system for OutcomeLogic with the ability to reason about general purpose looping. We also showthat this proof system applies to programs with various types of branching andthat it facilitates the reuse of proof fragments across different kinds ofspecifications.

Outcome Logic: A Unified Approach to the Metatheory of Program Logics with Branching Effects