Disjunctive Propositional Model Theory

Domain theory is an very important research aspect of lattice topology, the basic aim of its reasearch is to provide semantics model for programme language, so that it can proper for the development of computer science technology. Except for domain's calculus, one also need the logic represent of the domain so that it can server for the highter type deduction more better. In these days, Prof Chen base on the work of Pitts' Horn propositional theroy, Johnstone's disjunctive theroy and Genten's sequent calculus, disjunctive proposition is introduced, he gives the logic represent Of the stable domain and shows L-domain is isomorphic to the set consisting of models of a disjunctive proposition theroy.In this paper, we will further discuss the Disjunctive proposition theory, firstly we discuss the disjunctive proposition theory in the espect of model theory, introduce F-abstract model and set up the related theory T(L) and T~*(L), so we get the logic represent of the dD-semilattice. Secondly we establish the full abstract model, free model and discuss the quality and relationship between them. We get both the general model and natrual model are abstract and free. Except that, With regard to the different object and interpretation, we can build up the category. So in order to consider the category between the theory we discuss the notation of equality and interpretation. In the end, we get two important conclusion, one is every disjunctive theory T to have equality is isomorphic with the induced theory. Another is the category eTHR of dijunctive theories to have equality and interpretations is equivalent to the category dDSL.