Information Flow Logic Of The Theory

Information flows between situations. Information flow (IF for short) relationships exist among situations and constraints between situation types. IF relationships and constraints represent natural regularities between things. Taking IF relationships and constraints as their study object, an IF theory probes IF's internal mechanism and take up an important position in modern information study. C. E. Shannon's communication theory and F. I. Dretske's information content theory adopt a quantitative method in IF study, while situation theory and information channel theory focus upon the flow of information content. IF inferences can be conducted in accordance with IF relationships and constraints. Daily IF inferences are a kind of sound reasoning on one hand and permit mistakes or exceptions on the other hand. The logical study of the IF theories is a merging study of the IF theories and modern logic, embodying the "informational turn" in the field of modern logic. The study is conducted in two aspects: construction of IF logical systems which can represent IF inferences, and application of techniques of the IF theories to put forward a reasonable explanation for some issues in modern logic. Taking the study of IF logic as focal and the applied study of the IF theories in modern logic as supplemental, the dissertation has conducted work of the following three aspects.First, based on an introduction to the IF theories and the achieved result of the study of IF logic, new IF logic systems are constructed, with construction of IF logic systems able to represent fallible IF inferences as its goal. This is the main originality of the study. In the fourth chapter of the dissertation, idealized IF logic systems are presented which can represent perfect IF inferences. The general semantic framework of idealized IF logic consists of a finite situation set S and the ternary IF relationship R among the situations. Tableau systems of IF logic, which can embody corresponding semantic characteristics, are constructed, the minimal system IS based the connective tableau rules followed by its different extended systems based on the different R rules set up according to the different kinds of IF relationship. Soundness and completeness of the tableau systems are proved. Because perfect IF inferences donot involve modal concepts, idealized IF logic is analogous to classical propositional logic. In the fifth chapter, modal IF systems are constructed, which can represent fallible IF inferences. The modal IF logic which can represent necessary IF inferences comes into shape by re-explaining situations in the semantic framework of idealized IF logic as possible situations and introducing total modal connectives and their tableau rules into the idealized IF logic systems. The constrained modal IF logic systems are constructed then on the basis by further introducing the refinement relationship between situations semantically and constrained modal connectives and their tableau rules syntactically. Constrained IF implication logic is also constructed by directly setting up a constrained IF implication connective and its tableau rule. Constrained modal IF logic and constrained IF implication logic can both represent fallible IF inferences.Secondly, on the basis of an inductive account of the diachronical development of the IF theories from the quantitative study to the qualitative study, some relative concepts and issues in the IF theories are discussed, and the applied study of the IF theories in modern logic is analytically summarized from the following aspects: the information frame derived from the IF theories, viewing conditional logic and relevance logic from a IF perspective.Finally, an explanatory discussion is made about the influences of the IF theories and their logic study in the fields of modern logic, linguistics and information study, and a justification is conducted for what we have done by raising some philosophical consideration about some issues.