Adaptive Fuzzy Logics for Contextual Hedge Interpretation

The setting is that of an agent who needs to find out in which sense a predicate may have been used in a set of sentences received from a source. The agent should take into account both the logical constraints of the set of sentences and relevant semantic information concerning the predicate stored in his semantic memory. I present several adaptive fuzzy hedge logics. Each of these logics checks whether an occurrence of a hedgeable predicate may be interpreted in some specific sense, i.e. as being hedged by technically, strictly speaking, loosely speaking, or simply non-hedged. The basis for the logics is the fuzzy hedge logic Gh. This logic integrates a modified version of George Lakoff’s fuzzy semantics for the hedges technically, strictly speaking, and loosely speaking, cf. Lakoff (1973). The integration involves the introduction of a special set of selection functions. These functions collect the kind of information the agent can retrieve from fuzzy concepts in his semantic memory when interpreting a hedgeable predicate. As the logics are adaptive logics, they have a dynamic proof theory, cf. (Batens 2004; Batens 2007). This enables them to deal with non-monotonic interpretation dynamics. The logics are all sound and complete with respect to the standard [0, 1]-semantics.