在学习过程中，尤其是在学习数学逻辑时，可能会看见uninterpreted function这样的词，那这个词到底什么意思呢，这里有一个英文解释，可能会解释得比较清楚一点。
来源自博客园：https://www.cnblogs.com/houguochao/archive/2011/11/07/2240319.html
In mathematical logic, an uninterpreted function or function symbol is one that has no other property than its name and arity. Function symbols are used, together with constants and variables, to form terms.
The theory of uninterpreted functions is also sometimes called the free theory, because it is freely generated, and thus a free object, or theempty theory, being the theory having an empty set of sentences (in analogy to an initial algebra). Theories with a non-empty set of equations are known as equational theories. The decision problem for free theories is a satisfiability problem, and is solved by syntactic unification. It is particularly important, as many other theories can be reduced to it. Interpreters for various computer languages, such as Prolog, require algorithms for solving the free theory.
Example
An array can be specified by the following equational axiom:
select(store(a,i,v),j) = (if i = j then v else select(a,j))
This axiom can be used to deduce
select(store(store(a,1,−1),2,−2),1)
= select(store(a,1,−1),1)
= −1
Note that this reasoning did not use any 'definition' or interpretation for the functions select and store. All that is known is the axiom.
就是说推理过程中没有用到别的什么定义，只用到了前面的一个公理，这样的一个函数。