chapter  4
12 Pages

Soundness and completeness

We have already had some experience, in Chapter 2, of constructing truth trees. In this chapter we shall establish the procedure on a systematic basis and give rigorous proofs of their fundamental properties, namely that if all the members of a finite set of truthfunctional sentences are satisfiable, i.e. true for some distribution of truth-values over their sentence letters, then they generate a finite open tree, while if they are not satisfiable they generate a closed one.