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 90 a rule table that specifies the new value for each possible combination of neighboring values. In the case of Rule 90, each cell's new value is the exclusive or of the two neighboring values. Equivalently, the next state of this particular automaton is governed by the following rule table: The name of Rule 90 comes from Stephen Wolfram's binary-decimal notation for one-dimensional cellular automaton rules. To calculate the notation for the rule, concatenate the new states in the rule table into a single binary number, and convert the number into decimal: 01011010 = 90. Rule 90 has also been called