A framework for combining fuzzy modifiers

The author previously (1993) presented QUAL, a logic for reasoning with modifiers related to fuzzy quantification, usuality, and likelihood. Within QUAL, one may express syllogisms like “Most birds can fly; Tweety is a bird; therefore, it is likely that Tweety can fly”. A limitation on QUAL (as with any similarly conventional) formalism is that it does not allow for a formula to have more than one likelihood (or truth) value. Without this, it is not possible to represent a situation, for example, where one line of reasoning leads to “likely P”, while another leads to “rather unlikely P”, whence it is also not possible to prescribe a way in which these two likelihood determinations might be combined. The present work shows how this limitation may be overcome, by introducing the notion of a path logic. In path logics derivations are represented as being “situated in time.” In effect, propositions are viewed as being derived one at a time. Different occurrences of the same formula in a derivation path become labelled as temporally distinct. By defining valuations on members of derivation paths, one may then have different occurrences of the same formula taking different likelihood values. Accordingly, the path logic serves as a framework within which one may formulate various methods of modifier combination, as well as various reason maintenance techniques