Road rules book contains logical rules regulating behavior of cars and people on roads. Such road rules book is not really thick, may be about one hundred pages or so. Suppose, you come to a cross road. You use those logic from road rules book to generate an exact algorithm how you are going to behave in this specific situation.
Now, can you imagine if all possible situations for all possible cross roads were described in road rules book? How many pages such road rules book should contain?;-) That would be an algorithmic approach.
But we use logic for road regulations, not algorithms. Because logic allows to represent knowledge in a more compact form. Basically, small set of logical rules allows you to describe very large or even infinite set of situations.