Fix point interpretation of the minimal model
Christopher John Hogger · 1990
Abstract The process by which the method in Theme 45 generates each interpretation Ik+l from its predecessor lk can be cast as the application of a function Tp: This function, which is a total mapping from the powerset of B(P) to itself, is specific to the given program P (hence the subscript P in its name) and is defined as follows: Clearly this definition just formalizes our earlier informal account of how one interpretation is obtained from another. Given any function f defined on a partially-ordered set [S, ], it is of primary interest to know whether or not that function is monotonic and/or continuous. It is monotonic if and only if for all ueS and veS, f(u) f(v) whenever u v and it is continuous if and only if