We begin with some background concepts from mathematics. Semantic analysis deals with the meaning of correctly formed sentences. We start with the problem of syntax analysis. We need some method of specifying, precisely, the collection of syntactically correct sentences of a language. Inductive specification is a tool which may be applied to form strings of symbols chosen from an alphabet.
Inductive specification is a method of precisely specifying a set of values.
As an example, consider the following specification of a certain subset of the natural numbers. We can also reason about the set S in a non-inductive fashion as follows. This leads us to think of the set of non-negative multiples of 2. We can generalize the idea of inductive specification as follows. However, this non-inductive specification is not precise enough for our purposes.