Hilbertian Deductive Systems, Infon Logic, and Datalog

In the first part of the paper, we develop a general method for converting derivability problems, from a broad range of deductive systems, into the derivability problem in a quite specific system, namely the Datalog fragment of universal Horn logic. In this generality, the derivability problems may not be recursively solvable, let alone feasible; in particular, we may get Datalog “programs” with infinitely many rules. We then discuss what would be needed to obtain computationally useful results from this method. In the second part of the paper, we analyze a particular deductive system, primal infon logic with variables, which arose in the development of the authorization language DKAL. A consequence of our analysis of primal infon logic with variables is that its derivability problems can be translated into Datalog with only a quadratic increase of size.