A Generic Framework for Adaptive Vague Logics

A generic format for adaptive vague logics is presented. The concrete adaptive vague logics based on this format are able to (1) identify sentences as vague or non-vague in the context of a given set of premisses, and to (2) dynamically adjust the possible set of inferences in accordance with these identifications, i.e. vague sentences can only make use of vague inference rules, sentences contextually identified as non-vague can also use some extra set of classical logic rules. The generic format consists of a set of minimal criteria which the vague logic in casu must validate in order to be used as a basis for an adaptive vague logic. The criteria mainly focus on the way in which the logic should deal with a special ∆-operator (which can be interpreted as ‘completely true, ‘definitely true’, ‘clearly true’, etc.). It is proven that a wide range of famous logics for vagueness satisfy these criteria when extended with a specific ∆-operator, e.g. fuzzy basic logic and its well known extensions, cf. [5], superand subvaluationist logics, cf. [4], [6], and clarity logic, cf. [9]. Moreover, also a fuzzy logic is presented which can be used as a basis that can deal with higher-order vagueness. To make all this theory more concrete, some toy-examples of adaptive vague proofs are provided.