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. The 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 M. Ying (1994) and G. Gerla et al. (1998, 2000). A second approach, that may be named "semantical", proposes to attach a similarity relation to a set of possible worlds rather than to propositions. This approach has its roots in works on approximate truth, or "truthlikeness", by I. Niiniluoto (1987), T. Weston (1987) and others in the 1980s, and more recently by E. Ruspini (1991).