A General GUHA-Method with Associational Quantifers

Abstract

In the present chapter, we use the considerations of Chapter VI for the description and investigation of a particular (rather complex ) GUHA-method. The whole chapter can be viewed as an extensive example capable of concrete machine realization ( c f. the postscript). Remember the notion of a GUHA-method as a parametrical system < ℒ(P) ℘(P), X(P):P parameter> where each ℒ(P) is a semantic system, ℘(P) is an r-problem in ℒ(P), and X (P) is a function associating with each model M of ℒ(P) a solution of ℘(P) in M. The whole of Section 1 is in fact a single (commented) definition: We successively define the set Par of parameters, and the system ( p) and the r-problem ℘(P)defined by the parameter p. In fact, we do not define a single method since some details remain undecided. First, we neglect some formal questions concerning the particular representation (coding) of things, i. e. Par will not be defined uniquely as a set, and, secondly, we do not discuss questions of the particular bounds for various subparameters since this question is relevant only when one is going to write a program f o r a particular machine. Hence, the notion we shall define i s :Y is a GUHA-method with associational quantifiers. We wish to avoid unnecessary formalism: one can read Section 1 as a list (review) of aspects involved in determining an r-problem with an associational quantifier.