Techniques for Information Logics

This chapter presents the methodological concepts and formal techniques that are employed throughout the book for studying information logics. We present in detail only the core elements and steps of each of these techniques. Any variations or extensions that are needed in connection with a particular logic are usually presented in the chapter where the logic is discussed. In Sect. 6.2 we present model theoretic constructions, including filtration and copying. The method of copying has a special status since it has been introduced in relation to problems specific to information logics. Copying is useful in the situation when some properties of relations from semantic structures of a logic are not expressible in the language of the logic. Sect. 6.3 presents a general framework for deductive systems of information logics. We recall Hilbert-style proof systems for standard modal logics and the notion of canonical structure together with its principal properties. In Sect. 6.4 we present basic definitions and facts related to computational complexity. We recall the major complexity classes relevant to modal logics and we present logical problems that are complete with respect to those classes. The material of this section provides a basis for the developments of Chap. 12.