My sense is that common sense tends to be axiomatic. To avoid pitfalls, a degree of wisdom may also be required in that axioms may not apply in all contexts. [See Axiomatic System].
A major problem is that science often demonstrates that intuition, and "common sense", often lead to incorrect conclusions. Neil Degrasse Tyson covers this topic for the general public in his book Death By Black Hole:
Chapter 3, "Seeing Isn't Believing", hints at the pitfalls of generalizing from too little evidence. It begins by making the point that although we know the Earth is round, it appears flat when one observes only a small, local portion of it.
A very famous example comes from mathematician Abraham Wald:
During World War II, Wald was a member of the Statistical Research Group (SRG) where he applied his statistical skills to various wartime problems. These included methods of sequential analysis and sampling inspection. One of the problems that the SRG worked on was to examine the distribution of damage to aircraft to provide advice on how to minimize bomber losses to enemy fire. There was an inclination within the military to consider providing greater protection to parts that received more damage but Wald made the assumption that damage must be more uniformly distributed and that the aircraft that did return or show up in the samples were hit in the less vulnerable parts. Wald noted that the study only considered the aircraft that had survived their missions—the bombers that had been shot down were not present for the damage assessment. The holes in the returning aircraft, then, represented areas where a bomber could take damage and still return home safely. Wald proposed that the Navy instead reinforce the areas where the returning aircraft were unscathed, since those were the areas that, if hit, would cause the plane to be lost.
Source: Abraham Wald (wiki)
My sense is that "confidence levels" may be the main technique driving toward algorithmic "common sense", specifically in that the algorithm is questioning it's assumptions.