Semantic Status of Wffs

  Wffs can be categorized by their semantic properties:

• Some wffs are always true. Such wffs are called tautologies.
• Some wffs are always false. Such wffs are called contradictions.
• Some wffs are sometimes true and sometimes false. Such wffs are called  contingencies.

This exhausts the possible semantic properties of individual wffs. A wff is either a tautology, a contradiction or a contingency. In describing these properties, we used the terms "always" and "sometimes". We can be much more precise by describing the semantics of any wff in terms of truth tables as follows:

• A tautology is a wff which comes out true on every row of its truth table.
• A contradiction is a wff which comes out false on every row of its truth table.
• A contingency is a wff which comes out true on at least one row and false on at least one row of its truth table.

 The following sections explain tautologies, contradictions and contingencies in greater detail.