Formal Systems, Axiomatization, and Model Theory
In this section and the next, we return in greater detail to the study of formal systems from syntactic and semantic perspectives. In this section we focus on the syntactic side, and our aim will be to link together the notion of recursive definition which we introduced in Chapter 1 as a means of specifying sets with the closely related notions of inductive proof, new in this chapter, and of axiomatic system. Some of the close connections between grammars and formal systems will be illustrated, and various string operations will be formalized, although grammars as a topic in their own right will not be taken up until Part E. The discussion in this section will be purely syntactic (in part so as to illustrate what that means); we will return to a semantic investigation of some of the formal systems discussed here in the next section.
KeywordsFormal System Atomic Statement Axiomatic System Predicate Logic Axiom Schema
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