The Logic of Approximate Dependence

In my joint paper [3] with Rohit Parikh we investigate a logic arising from finite information. Here we consider another kind of limited information, namely information with a small number of errors, and prove a related completeness theorem. We point out that this approach naturally leads to considering multi-teams in the team semantics that lies behind [3]. The idea of finite information logic [1] is that when quantifiers, especialy the existential quantifiers, express choices in social context, the choices are based on finite information about the parameters present. In this paper we consider a different kind of restriction. We do not restrict the information available but we allow a small number of errors. In social sofware a few errors can perhaps be allowed, especially if there is an agreement about it. Consider the sentences This paper was written while the author was visiting the Computer Science Department of the University of California, Santa Cruz. The author is grateful to his host Phokion Kolaitis for the invitation and for the hospitality. The author is grateful for helpful discussions on this topic with P. Galliani, L. Hella, and P. Kolaitis. The author also thanks J. Kivinen, Jixue Liu, H. Toivonen and M. Warmuth for helpful suggestions. Research partially supported by grant 40734 of the Academy of Finland.