  Such a demonstration cannot get underway until the concept of validity is defined rigorously. Formal semantics for a logic provides a definition of validity by characterizing the truth behavior of the sentences of the system. In propositional logic, validity can be defined using truth tables. A valid argument is simply one where every truth table row that makes its premises true also makes its conclusion true. However truth tables cannot be used to provide an account of validity in modal logics because there are no truth tables for expressions such as ‘it is necessary that’, ‘it is obligatory that’, and the like. (The problem is that the truth value of \(A\) does not determine the truth value for \(\Box A\). For example, when \(A\) is ‘Dogs are dogs’, \(\Box A\) is true, but when \(A\) is ‘Dogs are pets’, \(\Box A\) is false.) Nevertheless, semantics for modal logics can be defined by introducing possible worlds. We will illustrate possible worlds semantics for a logic of necessity containing the symbols \({\sim}, \rightarrow\), and \(\Box\). Then we will explain how the same strategy may be adapted to other logics in the modal family.