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