 An example: Suppose that the meaning of walk, or sing is (for each model in the class) defined as the set of individuals who share respectively the property of (being an individual that is) walking or the property of (being an individual that is) singing. By appealing to the principle of compositionality, if there is a rule that combines these two expressions to the verb phrase walk and sing, there must be a corresponding rule that determines the meaning of that verb phrase. In this case, the resulting meaning will be the intersection of the two sets. Consequently, in all models the meaning of walk and sing is a subset of the meaning of walk. Furthermore, we have a rule that combines the noun phrase John with a verb phrase. The resulting sentence John walks and sings means that John is an element of the set denoted by the verb phrase. Note that in any model in which John is element of the intersection of walkers and singers, he is an element of the set of walkers. So John walks and sings entails John walks.