A choice of a domain and meanings for the symbols of a formal language, used to evaluate its sentences. The same sentence can have different truth values under different interpretations, unless it is valid under every admitted interpretation.
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In logic, particularly in model theory and formal semantics, an "interpretation" is a mathematical structure that assigns meanings to the symbols and expressions of a formal language. An interpretation provides a way to understand and evaluate the truth of sentences within that language. Here's a breakdown of what an interpretation involves: 1. **Domain of Discourse**: This is a set of objects over which the variables of the language can range.