Modal Semantics for Knowledge Bases Dealing with Vague Concepts

The paper investigates the characterisation of vague concepts within the framework of modal logic. This work builds on the su-pervaluation approach of Fine and exploits the idea of a precisiication space. A simple language is presented with two modalities: a necessity operator and an operatorìt is unequivocal that' which is used to articulate the logic of vagueness. Both these operators obey the schemas of the logic S5. I show how this language can be used to represent logical properties of vague predicates which have a variety of possible precise interpretations. I consider the use within KR systems of number of diierent entailment relations that can be speciied for this language. Certain vague predicates (such as`tall') may be indeenite even when there is no ambiguity in meaning. These can be accounted for by means of a three-valued logic, incorporating a def-initeness operator. I also show the relationship between observable quantities (such as height) and vague predicates (such as`tall') can be represented via axioms involving precise comparative relations (such as`taller'). I consider how Williamson's `logic of clarity' can be combined with the semantics for un-equivocality and how the clarity operator can be related to observables.