On a logic for ‘almost all’ and ‘generic’ reasoning
Paulo A. S. Veloso · LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) · 2002
Some arguments use ‘generic’, or ‘typical’, objects. An explanation for (some aspects of) this idea in terms of ‘almost all’ is suggested. The intuition of ‘almost all’ as ‘but for a few exceptions’ is rendered precise by means of ultrafilters. A logical system, with generalized quantifiers for ‘almost all’, is proposed as a basis for generic reasoning. This logic is monotonic, has a simple sound and complete deductive calculus, and is a conservative extension of classical first-order logic, with which it shares several properties. For generic reasoning, generic individuals are introduced and internalized as generic constants, thereby producing conservative extensions where one can reason about generic objects as intended. A many-sorted version of this logic is introduced to handle distinct notions of ‘large’ subsets. Other possible applications for this logic are indicated.