Social Interaction, Knowledge, and Social Software

In [31] a theory of human computation, analogous to Turing’s theory of machine computation is discussed. The issue there is whether there might be an analogue to Church’s thesis in this human domain. Examples of human algorithms discussed include the making of scrambled eggs. By comparison, Lynn Stein in this volume discusses the making of a peanut butter and jelly sandwich. Neither she nor us in this volume have any concern with Church’s thesis as such, although that might prove to be a fascinating topic for a future paper. Rather the issue here is interaction, which occurs most naturally in multi-agent algorithms, unlike the making of scrambled eggs or peanut butter sandwiches where one agent normally suffices. Such multi-agent algorithms, examples of which are building a house, or playing bridge, are examples of what we shall call Social Software after [32]. In that paper, one of us asked “Is it possible to create a theory of how social procedures work with a view to creating better ones and ensuring the correctness of the ones we do have?” The present paper will survey some of the logical and mathematical tools that have been developed over the years that may help address this question. Social procedures occur at two levels. One is the purely personal level where an individual is able to perform some complex action because social structures have been set up to enable such an action. Taking a train (which requires a system) or even a bath (where the city must supply not only the water but also a system of pipes to carry it) are examples of such situations where an individual is doing something simple or complex which is enabled by existing social structures. Procedures which are truly social are those which require more than one individual even in their execution. A piano duet is a simple example, but holding an election or passing a bill through the Senate are more complex ones. Computer programs, whether sequential or distributed, have logical and algorithmic properties which can be analyzed by means of