A Logic for Trial and Error Classifiers

Abstract

Trial and error classifiers, corresponding to concepts which change their extensions over time, are introduced and briefly philosophically motivated. A fragment of the language of classical first-order logic is given a new semantics, using $$\omega $$?-sequences of classical models, in order to interpret the basic predicates as classifiers of this kind. It turns out that we can use a natural deduction proof system which differs from classical logic only in the conditions for application of existential elimination. Soundness and completeness theorems are proved for this system.