Anjolina G De Oliveira & Dov M Gabbay 
Functional Interpretation Of Logical Deduction, The [PDF ebook] 

This comprehensive book provides an adequate framework to establish various calculi of logical inference. Being an âenrichedâ 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 âlabelsâ is useful to understand the proof-calculus itself, and also to clarify its connections with model-theoretic interpretations.