Undecided variable

Deflnition 9-1 The rule of definite clause inference (denoted DCI) is a natural extension of SLD resolution to implicative goals. Given a goal G, the selected atom is chosen within and the mgu may only bind undecided variables of G. All new variables introduced in the resolvent goal are undecided variables. 

Definition 9-3 Given a goal G, the rule of simplification (denoted Sim) selects two atoms A and B, in and G respectively, that unify with an mgu a that only binds undecided variables of G" the resolvent goal is obtained from Go by deleting A and B. 

Since it is undecidable whether a particular statement can ever be reached in any computation under any interpretation for any input, this condition will be undecidable and thus in our view undesirable. We prefer definitions to be effective, particularly definitions of the basic object under discussion. So this problem is avoided either by using the condition we have given which obviously implies the alternative one, or by always assuming all variables to be input variables, which shortcuts the whole problem. 

We shall show our undecidability results for monadic schemes with one function letter, one predicate letter and two program variables. Let Sn be the family of all schemes with ... 

THEOREM 6.13 The following problems are undecidable for programs (P,I) where P is a monadic flowchart with three program variables and I is any interpretation over the natural numbers allowing x+1, x i 1, x = 0 and the constant 0. 

Prove that the following are undecidable for 2-variable independent variable schemes P- and P2 ... 

Once the set of input variables, associated with the influence of the surrounding world, has been identified, a systematic procedure examines the remaining variables in an effort to determine their unambiguous role as inputs or outputs. It should be clear at the outset of the subsequent discussion that the unique and unambiguous characterization of all the process variables as inputs (causes) or outputs (effects) is in general impossible, and corresponds to an undecideable proposition. 

C. Cleavage Reactions with Variable or Undecided Stereochemistry... 

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