Structural rule A famous structural rule is known as cut. Considerable effort is spent by proof theorists in showing that cut rules are superfluous in various logics. More precisely, what is shown is that cut is only (in a sense) a tool for abbreviating proofs, and does not add to the theorems that can be proved. The successful 'removal' of cut rules, known as "cut elimination", is directly related to the philosophy of "computation as normalization" (see Curry–Howard correspondence); it often gives a good indication of the complexity of deciding a given logic. Structural rule In proof theory, a structural rule is
Rule of recognition if the rule of recognition were "what Professor X says is law", then any rule that Professor X spoke would be a valid legal rule. It follows that the rule of recognition is but a factual acknowledgement of what is indeed law; as per the classic illustration of a bill passed by the legislative authority and assented to by a Head-of-State. The fact that the bill has been made law in accordance with proper parliamentary procedure shall, in accordance with the Rule of Recognition, render it valid law. Again, this is primarily based on the fact of its existence in