This chapter introduces modal and continuous time stochastic logics. We discuss these logics here in some detail since we want to define the classical notions of bisimilarity, logical and behavioral equivalence for logics the interpretation of which is well understood. This will enable us later on to draw from this source knowledge as well as experience when defining these terms for coalgebraic logics, and when investigating them. We indicate the results and give sketches for the more interesting proofs, which we will need in later chapters as well. These considerations make substantial use of the techniques that have been developed in the context of stochastic relations, about which we reported in Chapter 1, in particular in Sections 1.6 and 1.7.
KeywordsModal Logic Polish Space Atomic Proposition Kripke Model Projective Limit
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