States on Symmetric Logics: Conditional Probability and Independence. II

We study the notions of conditional probabilities, independence and e-independence for states on symmetric logics. We prove that a non-atomic state on the logic with the Lyapunov’s property is determined by its specification of independent events. We present the examples of (1) Δ-subadditive but is not subadditive and (2) two-valued non Δ-subadditive states on symmetric logic. We investigate the independence relation transitivity for a Δ-subadditive state.