Modern Mathematical Logic

We now embark on a careful study of propositional logic. As described in Chapter 1, in this setting, we start with an arbitrary set P, which we think of as our collection of primitive statements. From here, we build up more complicated statements by repeatedly applying connectives. The corresponding process generates a set of syntactic objects that we call formulas. In order to assign meaning to these formulas, we introduce truth assignments, which are functions on P that propagate upward through formulas of higher complexity.