ABSTRACT
For every class of objects reader may formulate questions of the form: ‘Is so-and-so a member of the class?’ And there is a clear sense in which any given object either is or is not a member of a particular class. The problem of finding a decision procedure for a class is called the decision problem of that class. A particularly important type of decision problem is the decision problem for the class of valid wffs of some logical system. Every logical system has such a decision problem, although not every logical system has a solvable decision problem. It is intuitively clear that the decision problem for propositional calculus (PC) is solvable, for the method of truth-tables enables us to decide the validity of any wff. Every wff of PC has a truth-table, since every wff of PC is built up entirely from truth-functions, and every truth-function has a truth-table.
