Analytic implication
The idea of so-called analytic implication put forward by W. T. Parry may be described informally as follows: a proposition A analytically implies another proposition B iff (1) A necessarily (or strictly) implies B and (2) the ''constitutive content'' of B is contained in the constitutive content of A. In this paper a formalized theory of analytic implication is developed by way of introducing a new relation 'A\(\preccurlyeq B'\) to be read as ''the constitutive content of A is included in that of B''. If this relation is assumed to form a lattice (and moreover to hold necessarily where the underlying logic of necessity is S4), it can be shown that the resulting system for analytic implication to be defined as \((A\to B):=\square (A\supset B)\wedge (B\preccurlyeq A)\) is equivalent to Parry's original system.
scientific article; zbMATH DE number 4006232