In $\Alpha-\Beta Pruning$, an $\ALPHA cut-off occurs$ when the current node value is:
When evaluating a MAX node, if its value v becomes >= $\beta (the MIN ancestor's upper bound)$, the MIN ancestor will never choose this path, triggering a cutoff.
In $\Alpha-\Beta Pruning, a \BETA cut-off occurs$ when evaluating a MIN node whose value v is:
For a MIN node, if v <= $\alpha (the MAX ancestor's best guaranteed lower bound), MAX will never allow reaching$ this state, triggering a cutoff.
What is the optimal effective branching factor of $\Alpha-\Beta Pruning$ when move ordering is perfect?
With perfect move ordering, $\Alpha-\Beta evaluates O(b^{m/2}) nodes, reducing$ the effective branching factor to sqrt(b).
In first-order logic, what is the process of finding a substitution that makes two logical expressions identical?
Unification is an algorithmic process that solves equations between symbolic expressions by finding a common substitution.
In First-Order Logic, what is the process of removing existential quantifiers by replacing them with Skolem functions or constants?
Skolemization eliminates existential quantifiers (∃) by substituting existential variables with Skolem constants or Skolem functions of universally quantified variables.