Languages of logic and their applications

Concerning the logical description languages, in the past 40–50 years many authors have introduced a number of structurally very different first-order languages. Some of these languages follow the structure of a given future model, other ones have been prepared for the description of an arbitrary model. Other variations of the first-order languages do not follow the whole structure of any model: they have been prepared only for the relations definable over the universe in order to be able to prove the generalizations of a number of difficult logical results. The semantics of the first-order languages is based on the interpretation of their extralogical symbols by a suitable model. In some cases, in the interpretation all possible models can be in focus, but there are cases when the models over a special universe are regarded. The naming problem of the universe element of the model arises at this stage. The efforts for solving this problem lead to different approaches. Here, we present the most important language definitions and some characteristic semantics. We investigate the different approaches and conclude that they do not indicate essential differences. In fact, they have been only motivated by seeking for an easier way to achieve the just fixed target. Moreover, we try to point out the suitability connections of languages and semantics definitions.