Using set intersections (Array#:&):
(myarray & ["val1", "val2", "val3", "val4"]).present?
You can also loop (any? will stop at the first occurrence):
myarray.any? { |x| ["val1", "val2", "val3", "val4"].include?(x) }
That’s ok for small arrays, in the general case you better have O(1) predicates:
values = ["val1", "val2", "val3", "val4"].to_set
myarray.any? { |x| values.include?(x) }
With Ruby >= 2.1, use Set#intersect:
myarray.to_set.intersect?(values.to_set)