ARBITRARY TRUTH‐VALUE FUNCTIONS AND NATURAL DEDUCTION

ih t h Teaching student.: HENKIN’S completeness proof for first order predicate logic it helpful first, to deal with the simpler case of propositional logic. For most students tis is their first encounter with a non-trivial result in mathematical logic, and to make them appreciate the workings of this beautiful argument it is instructive to let them carry it out in a variety of settings: for different choices of primitive connectives, or for fregnients of the full logic. The reader who hah not thought about this for a ~ v h i l e may try his own hand a t one example: t o axiomatize the fragment of nonequivalence, + (exclusive disjunction). To be sure, this fragment is a logic without theorems, but a characterization in terms of Gentzen sequents or natural deduction i\ still possible.