Author: a3nm <>
Date: Sun, 17 Jun 2018 02:11:39 +0200
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A **signature** (with relation names and arities) is defined [like in databases](Basic database terminology#signatures). A **structure** for a signature $\sigma$ consists of a **domain** of elements and an **interpretation** for each relation $R$ of $\sigma$, i.e., a set of $n$-tuples of elements of the domain, where $n$ is the arity of $R$. This definition is similar to that of a [database instance](Basic database terminology#instances) except that the domain is explicitly given, and it may be the case that some domain elements do not occur in the interpretation of any relation.
+Unlike in some mathematical fields, none of the logics presented here feature **function symbols**, so we are defining **function-free logics** in the terminology of these fields.
# First-order logic
A **first-order logic** formula is defined over a [signature](Basic database terminology#signatures) $\sigma$, and consists of an expression built from [atoms](Basic database terminology#facts-and-atoms) and using