This comprehensive book provides an adequate framework to establish various calculi of logical inference. Being an `enriched' system of natural deduction, it helps to formulate logical calculi in an operational manner. By uncovering a certain harmony between a functional calculus on the labels and a logical calculus on the formulas, it allows mathematical foundations for systems of logic presentation designed to handle meta-level features at the object-level via a labelling mechanism, such as the D Gabbay's Labelled Deductive Systems. The book truly demonstrates that introducing `labels' is useful to understand the proof-calculus itself, and also to clarify its connections with model-theoretic interpretations.

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