A fuzzy logic approach to non-scalar hedges
pp. 233-248
in: David Makinson, Jacek Malinowski, Heinrich Wansing (eds), Towards mathematical philosophy, Berlin, Springer, 2009Abstract
In (Journal of Philosophical Logic, 2: 458–508, 1973), George Lakoff proposes a fuzzy semantics for the non-scalar hedges technically, strictly speaking, and loosely speaking. These hedges are able to modify the meaning of a predicate. However, Lakoff's proposal is problematic. For example, his semantics only contains interpretations for hedged predicates using semantic information provided by selection functions. What kind of information these functions should provide for non-hedged predicates remains unspecified. This paper presents a solution for this deficit and other problems by means of a generic first-order fuzzy logic FL h . A wide range of fuzzy logics can be used as a basis for FL h . Next to a fully specified semantics, this solution also incorporates a proof theory for reasoning with these hedges. FL h makes use of a special set of selection functions. These functions collect the kind of information a reasoner can retrieve from concepts in his or her memory when interpreting a (non-)hedged predicate. Despite this non-standard element, FL h remains a conservative modification of its underlying fuzzy logic.
