On The Methods Of Combining Logics

Among the contemporary research on theory and application of logic, the topic of the combining logics or Combination of Logics, is one of the most interesting. The editor of Handbook of Philosophical Logic, Dov.M. Gabby, and other researchers study it and obtain important results. It has important theoretical and applicable value in Philosophy, Logic, artificial intelligence and computer, linguistics etc; and makes logic a powerful tool.At first,the combining of Logics arise the backgroud of Modal logic.Therefore, many ways that was created specially on the one hand modelled the Combination of Kripke structure,on the other hand,modelled the Fibring axiomatic system,although nowadays they are largely applied to Model theory and the concept of proof theory.Dov.M.Gabby and Marcelo Finger in 1992 published "Adding a Temporal Dimension to a Logic System"and put forward Temporalization methods.They published "Combining Temporal Logic Systems" 1996 and discussed the combination between temporal logic system and temporal logic system,that is combining two one-Dimension temporal logic system to obtain a two-Dimension temporal logic system. Marcelo Finger later studied it deeply and published "The Unrestricted Combining of Temporal Logic Systems",generalisationthe combination of the linear time flow to any time flow.The way is not combing arbitraryly two logics,but embeding one logic in temporal logic system and extentlly add the time to it and describe the evolution in time of a theory in L and its models. This mothed can satisfy partly the mutual action between different system operators. And the combined logic system preserves some nature of original temporal logic system, such soundness, completeness and decidability.1996 Dov.M.Gabby established "Fibring". Using the motheds can combin two logic systems and build one new logic. In the new logic not only constructors are mixed, but proof Methods are combined. For it allows the mutual action between different system operators and overcome the defail of fuison and is well understand in the proof and theory, so it is recognized as the most effect method of the combining logics, with great significance in the theory and application of mathematical logic.In order to solve the collapsing problem in fibring proposed by Dov.M.Gabby, Cristina Sernadas, Joao Rasga and Walter A.Carnielli proposed the Modulated Fibring in 2002.After proposed Modulated Fibring, Carlos Caleiro and Jaime Ramos had proposed another method——Cryptofibring to solve collapsing problem.This method is simpler than Modulated Fibring at structure.It uses a generalized fibring semantic of Cryptomorphisms to solve collapsing problem.At present, describe the dynamic features of Epistemic logic is an important issue of the contemporary logic. In the double subject Epistemic logic, the logical system about knowledge or belief is constructed.They provide a basis of analysising and reasoning about knowledge and trust in particular out world.The double subject Epistemic logic can express the static features of knowledge or trust. However, knowledge and trust are the result of observation, which lead to know or trust another act in the absence of explicit guarantees may be believed and trusted and gained target in a particular circumstances. Therefore, knowledgeor trust as a series of specific observations, development and change in time. For some reason a subject, such as recommendations from other subjects may be lost at some point in time, its knowledge, trust, or add new knowledge, trust. If the time is introduced into the logic of the double subject knowledge, we can express the dynamic characteristics of the double subject knowledge and the evolution of the double subject knowledge.This dissertation tries to use Temporalization and Fibring to build two double subjects Epistem Logic systems of Fibring.In summary, this work includes the following three aspects:First, pectination the data on combined logic development of of foreign and detailed the main and the latest approach. Temporalization, Fibring, Modulated fibring and Cryptofibring are discussed in this dissertation. Temporalization and Fibring are created by v.M.Gabby,the contemporary famous international logic scholar. These two ways are used mostly. Fibring is the most important and useful mechanism of the Combining Logic.Most logic scholar researc on it. In order to overcome the problem of Fibring, Modulated fibring and Cryptofibring are created. Secondly,use fibring to build one fibring double subject Epistem Logic system--F(Bm). We combine temporal logic system with double subject Epistem Logic to build one new logics ystem:Logic system of Fibring double subject Epistem Logic--F(Bm).These systems can character dynamic characters of double subject Epistem Logic and the evolution of knowledge.Thirdly, using Temporalization this dissertation combines temporal logic system with Epistem Logic to build one new logics ystem--Temporalization double subject Epistem Logic system T(Bm).If we combine them and build temporal epistem logic system, then we can deal with that formula and character that nutureof the subject cognition depenging on time.