This volume examines the notion of an analytic proof as a natural deduction, suggesting that the proof's value may be understood as its normal form--a concept with significant implications to proof-theoretic semantics.

"The Logical Framework (LF) is a system for defining a wide class of logics. It is based on a general treatment of syntax, rules, and proofs in terms of a typed [lambda]-calculus with dependent types. Syntax is treated in a style similar to, but more general than, Martin-Löf's system of arities. The treatment of rules and proofs focuses on his notion of a judgement. Logics are encoded in the LF via a new principle, the judgements as types principle, whereby each (...) judgement is identified with the type of its proofs. This allows for a smooth treatment of discharge and variable occurrence conditions and leads to a uniform treatment of rules and proofs whereby rules are viewed as proofs of higher-order judgements and proof checking is reduced to type checking. The practical benefit of our treatment of formal systems is that logic-independent tools such as proof editors and proof checkers can be constructed.". (shrink)