Model theory began with the study of formal languages and their interpretations, and of the kinds of classification that a particular formal language can make.

Epistemic logic is the logic of knowledge and belief. It provides insight into the properties of individual knowers, has provided a means to model complicated scenarios involving groups of knowers and has improved our understanding of the dynamics of inquiry. (See http://plato.stanford.edu )

First-order Model Theory

Tarski's Truth Definitions

In 1933 the Polish logician Alfred Tarski published a paper in which he discussed the criteria that a definition of ‘true sentence’ should meet, and gave examples of several such definitions for particular formal languages.

Sometimes we write or speak a sentence S that expresses nothing either true or false, because some crucial information is missing about what the words mean. If we go on to add this information, so that S comes to express a true or false statement, we are said to interpret S, and the added information is called an interpretation of S.

A sentence S divides all its possible interpretations into two classes, those that are models of it and those that are not. In this way it defines a class, namely the class of all its models, written Mod(S). To take a legal example, the sentence