Short answers, pulled from the story.
John McCarthy introduced the situation calculus in 1963 to solve a specific problem in artificial intelligence. He needed a way for machines to reason about changing worlds without getting lost in infinite possibilities.
Ray Reiter published his definitive formulation in 1991 that redefined what a situation actually meant within the logic system. His work shifted the focus from static snapshots to dynamic histories of actions while McCarthy originally viewed situations as complete states of the universe at an instant.
Ray Reiter solved this issue with successor state axioms in 1991 to allow the system to deduce all changes from a single formula per fluent. This eliminates the need for hundreds of separate frame axioms by handling inertia automatically through the structure of the axiom itself.
Richard Waldinger developed regression as a mechanism for proving consequences within the system. This technique expresses a formula containing a complex situation in terms of an earlier action and its predecessor to reduce formulas until they contain only the initial situation S0.
McCarthy released a revised version in 1986 that incorporated functional fluents. These changes laid the groundwork for automated reasoning systems used today by replacing predicates with functions to represent changing properties more flexibly.