In mathematical logic, the formal languages, formal systems, and theories which are studied have no meaningful content until they are given an interpretation within some other system. An interpretation is a semantic concept which consists in a correlation or assignment of meanings to the symbols of a formal language. The study of interpretations expressed in formal languages is called formal semantics. Giving an interpretation is synonymous with ...
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In mathematical logic, the formal languages, formal systems, and theories which are studied have no meaningful content until they are given an interpretation within some other system. An interpretation is a semantic concept which consists in a correlation or assignment of meanings to the symbols of a formal language. The study of interpretations expressed in formal languages is called formal semantics. Giving an interpretation is synonymous with constructing a model. The term interpretation is also synonymous with the term structure.
In universal algebra and in model theory, a structure is a type of formal interpretation which consists of an underlying set along with a collection of finitary functions and relations which are defined on it. Model theory studies the models of various formal theories. A theory is a set of sentences in a formal language with a particular (signature), while a model is a structure whose interpretation of the symbols of the signature causes the sentences of...
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