Generalized Quantifiers and Conceptual Graphs

Conceptual graphs have been shown to be a logic that has a smooth mapping to and from natural language, in particular generally quantified statements, which is one of its advantages over predicate logic. However, classical semantics of conceptual graphs cannot deal with intrinsically vague generalized quantifiers like few, many, or most, which represent imprecise quantities that go beyond the capability of classical arithmetic. In this paper, we apply the fuzzy set-theoretic semantics of generalized quantifiers and formally define the semantics of generally quantified fuzzy conceptual graphs as probabilistic logic rules comprising only simple fuzzy conceptual graphs. Then we derive inference rules performed directly on fuzzy conceptual graphs with either relative or absolute quantifiers.