In the revised theory, the Introduction presents the notion of " atomic proposition ", a " datum " that " belongs to the philosophical part of logic ".
12.
Every atomic proposition is constructed from names that correspond to objects , and the interaction of these objects generate states of affairs, which are analogous to what Russell called atomic facts.
13.
The propositions in this language are propositional constants, which are considered atomic propositions, and composite propositions, which are composed by recursively applying operators to propositions . " Application " here is simply a short way of saying that the corresponding concatenation rule has been applied.
14.
Unlike the regular double-negation translation, which maps atomic propositions " p " to ( ( " p " ?! ?" ) ?! ?" ), the continuation passing style replaces ?" by the type of the final expression.
15.
Such a program corresponds to a finite state machine ( FSM ), i . e ., a directed graph consisting of nodes ( or nodes represent states of a system, the edges represent possible transitions which may alter the state, while the atomic propositions represent the basic properties that hold at a point of execution.
16.
A careful reading of the first edition indicates that an n th order predicative function need not be expressed " all the way down " as a huge " matrix " or aggregate of individual atomic propositions . " For in practice only the " relative " types of variables are relevant; thus the lowest type occurring in a given context may be called that of individuals " ( p . 161 ).
