There are two limiting cases of concurrency that can be treated in the situation calculus.
Two or more events, say and occur in a situation s and result in the same next situation Next(s). The fluents that hold in Next(s) are those determined by the effect axioms for e1 and e2 separately. Thus if we move a block and paint it concurrently, it will have both the new location and the new color in Next(s).
Two processes, starting, say from initial situations S0 and S0' take place and affect different sets of fluents. If nothing is said about the timing of the processes and no axioms of interaction are given, nothing can be inferred about the relative timing of the processes. Moreover, what can be inferred about the values of the fluents in successive situations is exactly what can be inferred by the processes taken separately. Thus Louis Pasteur was elected to the French Academy of Sciences in 1862 concurrently with certain battles of the American Civil War, but historians mention neither process in connection with the other. This is a limiting case, i.e. the case of zero interaction. Two theories of separate processes can be combined by taking the conjunction of their axioms. The combined theory is a conservative extension of each separate theory. It can be useful to elaborate the combined theory by giving axioms for the interaction. [McC95] and [MC98] treat elaborating theories of two non-interacting processes by adding axioms of interaction. Those articles treat Junior traveling in Europe and Daddy stacking gold blocks in New York. There is no interaction until we adjoin assertions about Junior losing an airplane ticket and asking Daddy for money, thus forcing Daddy to sell one of the blocks he was stacking.
We hope to combine the ideas of the two above-mentioned articles with those of this article in future work.