Multivalued, partial evaluation

Question

Everybody says that Valuation is a truth value assignment to all variables in the formula.

1. How do you call the valuation when some (neither single yet nor all) variables are assigned a value?

2. Truth value implies that variables are binary. How do you call the multivalued case?

3. I know that Haskel uses the term "partial application". If "partial application" is supplied with optimization, they call it "partial evaluation". I am not sure whether boolean valuation falls into the application or evaluation or second category?

ps, Dec 2013

1. Is it right that single variable assignment is called Restrict operation? I read Restrict(Function F, variable v, constant k) is defined as "Shannon cofactor of $F$ w.r.t. $v=k$" in Berkly lectures.

Answer 1

Here's what I'd use:

1. partial valuation

2. value

3. "partial evaluation" means something different; for instance, if you have the expression (3+x)*y and you learn that x=5, transforming it to 8*y would be an instance of partial evaluation. Partial evaluation is a technique; it is not a special kind of a valuation.