Logic without Self-Deductibility
Pierre Ageron · Logica Universalis · 2007
Self-deductibility is the Stoic version of the law of identity : if A, then A. After a discussion on its role, we suggest a natural system of axioms and rules for a logic in which this law is not valid, based on a simple model where proofs are families of strictly injective maps. Finally we develop some general theory of taxonomies (i.e. “categories without identities”) and place this particular example into a more general algebraic picture.