On syntactical and semantical approaches to similarity-based approximate reasoning

In this paper we survey and compare two different logical approaches to similarity-based approximate reasoning that have been proposed recently in the literature. A first one, that may be named syntactical, is based on attaching similarity degrees directly to pairs of propositions. Such an approach has been followed mainly by Ying, Gerla and colleagues. A second approach, that may be named semantical, proposes to attach a similarity relation on a set of possible worlds rather than on propositions. This approach has its roots in works on approximate truth, or truthlikeness, by Niiniluoto, Weston and others in the eighties, and more recently by Ruspini.