Investigations Into The Definability Of Model Classes Of Basic Propositional Logic

Basic propositional logic was given by Albert Visser at the earliest. The snytaxs, semantics and some qualities of basic propositional logic and intuitionistic propositional logic are very similar. However, there are some differences, such as the three following theorems:(1) (p→(q→r))→((p→q)→(p→r)) ; (2) p∧(p→q)→q ; (3) (T→p)→p, which are the theorems of intuitionistic propositional logic, but they are not the theorems of basic propositional logic. The main one of the differences is the frame. The frame of basic propositional logic is reflexive, but the frame of intuitionistic propositional logic is reflexive and transitive. Yde Venema and Rodenburg have studied the definability of modal logic and the definability of intuitionistic propositional logic respectively. Based on the results by Rodenburg and Venema, Robert Goldblatt has improved the definability of intuitionistic propositional logic and has introduced some new concepts such as prime extensions and definable extensions. The definability of the model classes of basic propositional logic has not been discussed by anyone till now. We will generalize Robert Goldblatt’s improved characterization to basic propositional logic by the similar ways of Venema and Robert Goldblatt and prove the theorems of Venema style of basic propositional logic. Then solve the definability of basic propositional logic by new model that is a canonical expansive model.This thesis is composed of the following parts: The first part will primarily introduce the results of the definability of modal logic and the definability of intuitionistic propositional logic. The second part will principally introduce the language, semantics, axiom system and deduction system of basic propositional logic. Then discuss the relation of basic propositional logic and intuitionistic propositional logic. The third part will chiefly checkout the theorems of modal logic and intuitionistic propositional logic whether or not to be the theorems of the model classes of basic propositional logic.The fourth part mainly prove some important theorems and definable theorems of basic propositional logical model classes by canonical extension model.The fifth part will principally discuss the prospects of the definability of basic propositional logic, such as the definability of transitive frame classes of basic propositional logic.