Weight structures for approximate reasoning with weighted expressions

One method of constructing an 'approximate reasoning' system is to use a 'classical' system of many-valued logic and attach to each logical expression a 'weight' which assesses the validity of this expression. Several such systems have been described in the literature, with varying interpretations concerning structure and semantics of weights. In this paper, a 'canonical' principle for defining the fundamental relations model and semantic consequence for logics with weighted expressions is described, which not only allows a large variety of truth-value and weight structures, but furthermore allows to transfer the results of 'classical' model theory to the resulting logics in a natural way.