Limitations
Although first-order logic is sufficient for formalizing much of mathematics, and is commonly used in computer science and other fields, it has certain limitations. These include limitations on its expressiveness and limitations of the fragments of natural languages that it can describe.
For instance, first-order logic is undecidable, meaning a sound, complete and terminating decision algorithm is impossible. This has led to the study of interesting decidable fragments such as C2, first-order logic with two variables and the counting quantifiers and (these quantifiers are, respectively, "there exists at least n" and "there exists at most n") (Horrocks 2010).
Read more about this topic: First-order Logic
Famous quotes containing the word limitations:
“Growing up means letting go of the dearest megalomaniacal dreams of our childhood. Growing up means knowing they can’t be fulfilled. Growing up means gaining the wisdom and skills to get what we want within the limitations imposed by reality—a reality which consists of diminished powers, restricted freedoms and, with the people we love, imperfect connections.”
—Judith Viorst (20th century)
“No man could bring himself to reveal his true character, and, above all, his true limitations as a citizen and a Christian, his true meannesses, his true imbecilities, to his friends, or even to his wife. Honest autobiography is therefore a contradiction in terms: the moment a man considers himself, even in petto, he tries to gild and fresco himself.”
—H.L. (Henry Lewis)
“That all may be so, but when I begin to exercise that power I am not conscious of the power, but only of the limitations imposed on me.”
—William Howard Taft (1857–1930)