Multivalued, partial evaluation

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.
• "Truth value" does not imply that variables are binary. It implies that variables take on truth values. Whether there are ust two truth values is then determined by presence of excluded middle. Commented Jan 16, 2014 at 7:36
• I am asking how do you call f(4).
– Val
Commented Jan 16, 2014 at 8:54
• An application (of $f$ to $4$). The result of $f(4)$ is a value. Commented Jan 16, 2014 at 9:11

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.

• How partial evaluation is different? Is it because not all arguments are assigned or because values are not limited to binary?
– Val
Commented Oct 15, 2013 at 16:43