Modeling sorites reasoning with adaptive fuzzy logic

We present and discuss a new solution for reasoning with sorites series and their related paradoxes. We argue that a suitable logic for sorites series should be able to apply specific classical logic rules like modus ponens until and unless it becomes apparent that these applications generate unacceptable results. When the latter happens, the logic should be able to retract those applications of classical logic rules that are problematic. The formal core of our solution consists of several adaptive logics based on a Łukasiewicz fuzzy logic extended with the Baaz’ Δ-operator and a non-singleton interval of designated values. The natural dynamics characteristic of adaptive logics allows these logics to perform necessary retractions in an intuitive and elegant manner.